MGMT 101 Final Review
33. Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in a. standard form. b. bounded form. c. feasible form. d. alternative form.
A
The production scheduling problem modeled in the textbook involves capacity constraints on all of the following types of resources except a. material. b. labor. c. machine. d. storage.
A
(T/F) It is improper to combine manufacturing costs and overtime costs in the same objective function.
F
(T/F) Production constraints frequently take the form: beginning inventory + sales − production = ending inventory
F
(T/F) Slack and surplus variables are not useful in integer linear programs.
F
(T/F) The constraint x1 + x2 + x3 + x4 ≤ 2 means that two out of the first four projects must be selected.
F
(T/F) The constraint x1 − x2 = 0 implies that if project 1 is selected, project 2 cannot be.
F
(T/F) The expected value of an alternative can never be negative.
F
(T/F) The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.
F
The dual price associated with a constraint is the change in the value of the solution per unit decrease in the right-hand side of the constraint
False
The dual price for a percentage constraint provides a direct answer to questions about the effect of increases or decreases in that percentage.
False
The earliest start time for an activity is equal to the smallest of the earliest finish times for all its immediate predecessors.
False
The earliest start time for an activity is equal to the smallest of the earliest finish times for all its immediate predecessors.
False
The expected utility is the utility of the expected monetary value.
False
The expected value approach is more appropriate for a one-time decision than a repetitive decision.
False
The expected value of an alternative can never be negative.
False
The expected value of sample information can never be less than the expected value of perfect information.
False
The feasible solution is the best solution possible for a mathematical model
False
The feasible solution is the best solution possible for a mathematical model.
False
The interpretation of the dual price for nonlinear models is different than the interpretation of the dual price for linear models.
False
The latest finish time for an activity is the largest of the latest start times for all activities that immediately follow the activity.
False
The latest finish time for an activity is the largest of the latest start times for all activities that immediately follow the activity.
False
The media selection model presented in the textbook involves maximizing the number of potential customers reached subject to a minimum total exposure quality rating.
False
The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is fully structured
False
The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is fully structured.
False
(T/F) When the number of agents exceeds the number of tasks in an assignment problem, one or more dummy tasks must be introduced in the LP formulation or else the LP will not have a feasible solution.
F
A feasible solution is a global optimum if there are no other feasible solutions with a better objective function value in the immediate neighborhood.
F
A function is quadratic if its nonlinear terms have a power of 4.
F
A path through a project network must reach every node.
F
Any feasible solution to a blending problem without pooled components is feasible to the problem with pooled components.
F
Because most nonlinear optimization codes will terminate with a local optimum, the solution returned by the codes will be the best solution.
F
Crashing refers to an unanticipated delay in a critical path activity that causes the total time to exceed its limit
F
Critical activities are those that can be delayed without delaying the entire project.
F
Decreasing the objective function coefficient of a variable to its lower limit will create a revised problem that is unbounded
F
Each point on the efficient frontier is the maximum possible risk, measured by portfolio variance, for the given return.
F
For a minimization problem, a positive dual price indicates the value of the objective function will increase.
F
For a typical nonlinear problem, duals price are relatively insensitive to small changes in right-hand side values.
F
Functions that are convex have a single local maximum that is also the global maximum.
F
Nonlinear optimization problems can have only one local optimal solution.
F
Output from a computer package is precise and answers should never be rounded.
F
PERT and CPM are applicable only when there is no dependence among activities.
F
The amount of a sunk cost will vary depending on the values of the decision variables.
F
The dual price associated with a constraint is the improvement in the value of the solution per unit decrease in the right-hand side of the constraint.
F
The earliest start time for an activity is equal to the smallest of the earliest finish times for all its immediate predecessors.
F
The expected value approach is more appropriate for a one-time decision than a repetitive decision.
F
The expected value of an alternative can never be negative.
F
The expected value of sample information can never be less than the expected value of perfect information.
F
The interpretation of the dual price for nonlinear models is different than the interpretation of the dual price for linear models.
F
The latest finish time for an activity is the largest of the latest start times for all activities that immediately follow the activity.
F
The problem of maximizing a concave quadratic function over a linear constraint set is relatively difficult to solve.
F
The value of the coefficient of imitation, q, in the Bass model for forecasting adoption of a new product cannot be negative.
F
The variance in the project completion time is the sum of the variances of all activities in the project.
F
There is a dual price for every decision variable in a model.
F
When activity times are uncertain, an activity's most likely time is the same as its expected time.
F
When the right-hand sides of two constraints are each increased by one unit, the objective function value will be adjusted by the sum of the constraints' dual prices.
F
The decision alternative with the best expected monetary value will always be the most desirable decision.
F
The expected utility is the utility of the expected monetary value.
F
Tree Diagram
A graphical representation of the decision problem that shows the sequential nature of the decision-making process
The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means
Agent 3 can be assigned to 2 or less tasks
The assignment problem constraint x31 + x32 + x33 + x34 <= 2 means
Agent 3 can be assigned to 2 tasks
Which of the following is not true regarding an LP model of the assignment problem?
All constraints are of the ≥ form.
Which of the following statements is NOT true?
An infeasible solution violates all constraints
Which of the following statements is NOT true?
An infeasible solution violates all constraints.
When the payoffs become extreme, most decision makers are satisfied with the decision that provides the best expected monetary value. Select one:
F
(T/F) A four-period moving average forecast for period 10 would be found by averaging the values from periods 10, 9, 8, and 7
F(alse)
(T/F) A time series model with a seasonal pattern will always involve quarterly data.
F(alse)
(T/F) All quarterly time series contain seasonality
F(alse)
(T/F) An alpha (α) value of .2 will cause an exponential smoothing forecast to react more quickly to a sudden drop in demand than will an equal to .4.
F(alse)
(T/F) Any recurring sequence of points above and below the trend line lasting less than one year can be attributed to the cyclical component of the time series.
F(alse)
(T/F) Decision alternatives are structured so that several could occur simultaneously.
F(alse)
(T/F) If the random variability in a time series is great and exponential smoothing is being used to forecast, then a high alpha value (α) should be used
F(alse)
(T/F) If the random variability in a time series is great, a high α value should be used to exponentially smooth out the fluctuations.
F(alse)
(T/F) Quantitative forecasting methods can be used when past information about the variable being forecast is unavailable
F(alse)
(T/F) Quantitative forecasting methods do not require that patterns from the past will necessarily continue in the future.
F(alse)
(T/F) Seasonal components with values above 1.00 indicate actual values below the trend line.
F(alse)
(T/F) The expected value approach is more appropriate for a one-time decision than a repetitive decision.
F(alse)
(T/F) The expected value of an alternative can never be negative.
F(alse)
(T/F) The expected value of sample information can never be less than the expected value of perfect information.
F(alse)
(T/F) Trend in a time series must be linear
F(alse)
(T/F) With fewer periods in a moving average, it will take longer to adjust to a new level of data values
F(alse)
A company makes two products, A and B. A sells for $100 and B sells for $90. The variable production costs are $30 per unit for A and $25 for B. The company's objective could be written as: MAX 190x1 - 55x2.
False
A company makes two products, A and B. A sells for $100 and B sells for $90. The variable production costs are $30 per unit for A and $25 for B. The company's objective could be written as: MAX 190x1 − 55x2.
False
A company seeks to maximize profit subject to limited availability of man-hours. Man-hours is a controllable input
False
A company seeks to maximize profit subject to limited availability of man-hours. Man-hours is a controllable input.
False
A decision maker would be wise to not deviate from the optimal solution found by an LP model because it is the best solution.
False
A dummy origin in a transportation problem is used when supply exceeds demand
False
A dummy origin in a transportation problem is used when supply exceeds demand.
False
A feasible solution is a global optimum if there are no other feasible solutions with a better objective fun
False
A feasible solution is one that satisfies at least one of the constraints in the problem.
False
A four-period moving average forecast for period 10 would be found by averaging the values from periods 10, 9, 8, and 7.
False
A function is quadratic if its nonlinear terms have a power of 4.
False
A linear programming problem can be both unbounded and infeasible.
False
A multiple choice constraint involves selecting k out of n alternatives, where k ≥ 2.
False
A path through a project network must reach every node
False
A path through a project network must reach every node.
False
A redundant constraint is a binding constraint.
False
A static simulation model is used in situations where the state of the system affects how the system changes or evolves over time.
False
A time series model with a seasonal pattern will always involve quarterly data.
False
A toy train layout designed to represent an actual railyard is an example of an analog model.
False
A transportation problem with 3 sources and 4 destinations will have 7 decision variables
False
A transportation problem with 3 sources and 4 destinations will have 7 decision variables.
False
A transportation problem with 3 sources and 4 destinations will have 7 variables in the objective function
False
A transportation problem with 3 sources and 4 destinations will have 7 variables in the objective function.
False
All quarterly time series contain seasonality.
False
Alternative optimal solutions occur when there is no feasible solution to the problem
False
Alternative optimal solutions occur when there is no feasible solution to the problem.
False
An alpha (α) value of .2 will cause an exponential smoothing forecast to react more quickly to a sudden drop in demand than will an α equal to .4.
False
An infeasible problem is one in which the objective function can be increased to infinity.
False
Any change to the objective function coefficient of a variable that is positive in the optimal solution will change the optimal solution
False
Any change to the objective function coefficient of a variable that is positive in the optimal solution will change the optimal solution.
False
Any feasible solution to a blending problem without pooled components is feasible to the problem with pooled components.
False
Any recurring sequence of points above and below the trend line lasting less than one year can be attributed to the cyclical component of the time series.
False
Because most nonlinear optimization codes will terminate with a local optimum, the solution returned by the codes will be the best solution.
False
Because surplus variables represent the amount by which the solution exceeds a minimum target, they are given positive coefficients in the objective function.
False
Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side, a dual price cannot be negative.
False
Computer-generated random numbers are normally distributed over the interval from 0 to 1.
False
Computer-generated random numbers are normally distributed.
False
Crashing refers to an unanticipated delay in a critical path activity that causes the total time to exceed its limit.
False
Crashing refers to an unanticipated delay in a critical path activity that causes the total time to exceed its limit.
False
Critical activities are those that can be delayed without delaying the entire project.
False
DEA is used to measure the relative efficiency of two (or more) units in different industries, such as a bank and a school.
False
Decision alternatives are structured so that several could occur simultaneously.
False
Decision alternatives are structures so that several could occur simultaneously.
False
Decision variable limit the degree to which the objective in a linear programming problem is satisfied.
False
Decision variables limit the degree to which the objective in a linear programming problem is satisfied
False
Decision variables limit the degree to which the objective in a linear programming problem is satisfied.
False
Decreasing the objective function coefficient of a variable to its lower limit will create a revised problem that is unbounded.
False
Double-subscript notation for decision variables should be avoided unless the number of decision variables exceeds nine.
False
Each point on the efficient frontier is the maximum possible risk, measured by portfolio variance, for the given return.
False
Expected utility is a particularly useful tool when payoffs stay in a range considered reasonable by the decision maker.
False
Federick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940's
False
For a minimization problem, a positive dual price indicates the value of the objective function will increase.
False
For a scoring model, the decision maker evaluates each decision alternative using equally weighted criteria.
False
For a two-person, zero-sum, mixed-strategy game, it is necessary to solve the LP for each player in order to learn both players' optimal strategies.
False
For a typical nonlinear problem, duals price are relatively insensitive to small changes in right-hand side values.
False
Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940's.
False
Frederick Taylor is credited with forming the first MS/OR interdisplanary team in the 1940's
False
Functions that are convex have a single local maximum that is also the global maximum.
False
Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program.
False
Given two decision makers, one risk neutral and the other a risk avoider, the risk avoider will always give a lower utility value for a given outcome.
False
If Project 5 must be completed before Project 6, the constraint would be x5 − x6 ≤ 0.
False
If a real-world problem is correctly formulated, it is not possible to have alternative optimal solutions.
False
If an LP problem is not correctly formulated, the computer software will indicate it is infeasible when trying to solve it.
False
If the LP relaxation of an integer program has a feasible solution, then the integer program has a feasible solution
False
If the inputs of the composite unit in DEA are greater than the inputs for an individual unit, then the composite is more efficient.
False
If the random variability in a time series is great and exponential smoothing is being used to forecast, then a high alpha (α) value should be used.
False
If the random variability in a time series is great, a high α value should be used to exponentially smooth out the fluctuations.
False
If the range of feasibility for b1 is between 16 and 37, then if b1 = 22 the optimal solution will not change from the original optimal solution.
False
In ACH (alternative competing hypothesis) the goal is to find as much consistent evidence as possible.
False
In ACH, if an item of evidence seems consistent with all the hypothesis, it has great diagnostic value (T/F).
False
In ACH, you prepare a matrix with evidence across the top and hypotheses down the side (T/F).
False
In a Monte Carlo simulation, each simulation trial is dependent upon the result of a previous trial.
False
In a capacitated transshipment problem, some or all of the transfer points are subject to capacity restrictions.
False
In a revenue management model, dual prices tell reservation agents the revenue loss associated with overbooking each ODIF.
False
In a transportation problem with total supply equal to total demand, if there are four origins and seven destinations, and there is a unique optimal solution, the optimal solution will utilize 11 shipping routes.
False
In game theory, the player seeking to maximize the value of the game selects a maximax strategy.
False
In situations where you need to compare forecasting methods for different time periods, relative measures such as mean absolute error (MAE) are preferred.
False
In the LP formulation of a maximal flow problem, a conservation-of-flow constraint ensures that an arc's flow capacity is not exceeded.
False
In the LP formulation of a maximal flow problem, a conservation-of-flow constraint ensures that an arc's flow capacityis not exceeded
False
Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution (T/F)
False
Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.
False
Increasing the right-hand side of a nonbonding constraint will not cause a change in the optimal solution
False
It is improper to combine manufacturing costs and overtime costs in the same objective function.
False
It is possible for DEA to show all operating units to be relatively inefficient.
False
It is possible to have exactly two optimal solutions to a linear programming problem.
False
Model development should be left to quantitative analysts; the model user's involvement should begin at the implementation stage.
False
Nonlinear optimization problems can have only one local optimal solution.
False
Objectives in multicriteria problems seldom conflict.
False
One disadvantage of simulation is that it is limited in the variety of probability distributions that can be used in modeling a system.
False
Only binding constraints form the shape (boundaries) of the feasible region
False
Only binding constraints form the shape (boundaries) of the feasible region.
False
PERT and CPM are applicable only when there is no dependence among activities.
False
Precedence relationships among activities is critical in CPM analysis but not in PERT.
False
Production constraints frequently take the form: beginning inventory + sales − production = ending inventory
False
Quantitative forecasting methods can be used when past information about the variable being forecast is unavailable.
False
Revenue Management methodology was originally develop for the banking industry
False
Revenue management methodology enables an airline to maximize the number of full-fare seats it sells on each flight
False
Revenue management methodology was originally developed for the banking industry.
False
Simulation allows the user to specify certain desired results (for example, profit or service level values), and then the necessary model parameters and operating policies are determined.
False
Simulation is an optimization technique.
False
Slack and surplus variables are not useful in integer linear programs.
False
The 100 percent rule can be applied to changes in both objective function coefficients and right-hand sides at the same time
False
The amount of a sunk cost will vary depending on the values of the decision variables.
False
The constraint 2x1 - x2 = 0 passes through the point (200,100).
False
The constraint 2x1 − x2 = 0 passes through the point (200,100).
False
The constraint x1 − x2 = 0 implies that if project 1 is selected, project 2 cannot be.
False
The decision alternative with the best expected monetary value will always be the most desirable decision.
False
The decision making process includes implementation and evaluation of the decision
False
The decision making process includes implementation and evaluation of the decision.
False
The dual price associated with a constraint is the change in the value of the solution per decrease in the right-hand side of the constraint
False
Decision variables in a linear programming moel are equivalent to what in a transportation problem?
Cells in a transportation table.
How do you interpret a dual price for a constraint?
Say the dual price is 2.33 This would mean the objective function will increase by 2.33 units for every additional unit on the right-hand side of the constraint
(T/F) Media selection problems can maximize exposure quality and use number of customers reached as a constraint, or maximize the number of customers reached and use exposure quality as a constraint.
T
(T/F) Portfolio selection problems should acknowledge both risk and return.
T
(T/F) Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative and the payoff that may actually occur.
T
(T/F) Sample information with an efficiency rating of 100% is perfect information.
T
(T/F) Some linear programming problems have a special structure which guarantees that the variables will have integer values.
T
(T/F) Square nodes in a decision tree indicate that a decision must be made.
T
(T/F) States of nature should be defined so that one and only one will actually occur.
T
(T/F) The LP Relaxation contains the objective function and constraints of the IP problem, but drops all integer restrictions.
T
(T/F) The capacitated transportation problem includes constraints which reflect limited capacity on a route.
T
(T/F) The direction of flow in the shortest-route problem is always out of the origin node and into the destination node.
T
(T/F) The maximal flow problem can be formulated as a capacitated transshipment problem.
T
The Markowitz mean-variance portfolio model presented in the text is a convex optimization problem.
T
The function f (X, Y) = X 2 + Y 2 has a single global minimum and is relatively easy to minimize.
T
The linear programming model for crashing presented in the textbook assumes that any portion of the activity crash time can be achieved for a corresponding portion of the activity crashing cost.
T
The minimum expected opportunity loss provides the best decision, regardless of whether the decision analysis involves minimization or maximization.
T
The primary value of decision trees is as a useful way of organizing how operations managers think about complex multiphase decisions.
T
The project manager should monitor the progress of any activity with a large time variance even if the expected time does not identify the activity as a critical activity.
T
The reduced cost for a positive decision variable is 0
T
There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.
T
When components (or ingredients) in a blending problem must be pooled, the number of feasible solutions is reduced.
T
A high efficiency rating indicates that the sample information is almost as good as perfect information.
T
A risk neutral decision maker will have a linear utility function.
T
Expected utility is a particularly useful tool when payoffs stay in a range considered reasonable by the decision maker.
T
The expected monetary value approach and the expected utility approach to decision making usually result in the same decision choice unless extreme payoffs are involved.
T
The outcome with the highest payoff will also have the highest utility.
T
The risk neutral decision maker will have the same indications from the expected value and expected utility approaches.
T
The risk premium is never negative for a conservative decision maker.
T
The utility function for a risk avoider typically shows a diminishing marginal return for money.
T
To assign utilities, consider the best and worst payoffs in the entire decision situation.
T
When monetary value is not the sole measure of the true worth of the outcome to the decision maker, monetary value should be replaced by utility.
T
When the expected value approach is used to select a decision alternative, the payoff that actually occurs will usually have a value different from the expected value.
T
(T/F) A decision strategy is a sequence of decisions and chance outcomes, where the decisions chosen depend on the yet to be determined outcomes of chance events.
T(rue)
(T/F) After all probabilities and payoffs are placed on a decision tree, the decision maker calculates expected values at state of nature nodes and makes selections at decision nodes.
T(rue)
(T/F) Circular nodes in a decision tree indicate that it would be incorrect to choose a path from the node.
T(rue)
(T/F) EVPI equals the expected regret associated with the minimax decision.
T(rue)
(T/F) EVPI is always greater than or equal to EVSI.
T(rue)
(T/F) Expected value is the sum of the weighted payoff possibilities at a circular node in a decision tree.
T(rue)
(T/F) Exponential smoothing with α=.2 and a moving average with n=5 put the same weight on the actual value for the current period.
T(rue)
(T/F) For a multiplicative time series model, the sum of the seasonal indexes should equal the number of seasons.
T(rue)
(T/F) If a time series has a significant trend pattern, then one should not use a moving average to forecast.
T(rue)
(T/F) Maximizing the expected payoff and minimizing the expected opportunity loss result in the same recommended decision.
T(rue)
(T/F) Qualitative forecasting techniques should be applied in situations where time series data exists, but where conditions are expected to change.
T(rue)
(T/F) Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative and the payoff that may actually occur.
T(rue)
(T/F) Sample information with an efficiency rating of 100% is perfect information.
T(rue)
(T/F) Smoothing methods are more appropriate for a stable time series than when significant trend or seasonal patterns are present.
T(rue)
(T/F) Square nodes in a decision tree indicate that a decision must be made.
T(rue)
(T/F) States of nature should be defined so that one and only one will actually occur.
T(rue)
(T/F) The exponential smoothing forecast for any period is a weighted average of all the previous actual values for the time series
T(rue)
(T/F) The mean squared error is influenced much more by large forecast errors than is the mean absolute error.
T(rue)
(T/F) Time series data can exhibit seasonal patterns of less than one month in duration
T(rue)
(T/F) Time series methods base forecasts only on past values of the variables
T(rue)
(T/F) To make period-to-period comparisons more meaningful and identify trend, the time series should be deseasonalized.
T(rue)
People have a natural tendency to concentrate on confirming hypotheses they already believe to be true, and they commonly give more weight to information that supports a hypothesis than to information that weakens it (T/F).
True
Portfolio selection problems should acknowledge both risk and return
True
Portfolio selection problems should acknowledge both risk and return.
True
Problem solving encompasses both the identification of a problem and the action to resolve it
True
Problem solving encompasses both the identification of a problem and the action to resolve it.
True
Qualitative forecasting techniques should be applied in situations where time series data exists, but where conditions are expected to change.
True
Relevant costs should be reflected in the objective function, but sunk costs should not.
True
Revenue management methodology can be applied in the case of nonperishable assets
True
Revenue management methodology can be applied in the case of nonperishable assets.
True
Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative and the payoff that may actually occur.
True
Sample information with an efficiency rating of 100% is perfect information.
True
Simulation is a trial-and-error approach to problem solving.
True
Simulation is an excellent technique to use when a situation is too complicated to use standard analytical procedures.
True
Simulation models that must take into account how the system changes or evolves over time are referred to as dynamic simulation models.
True
Smoothing methods are more appropriate for a stable time series than when significant trend or seasonal patterns are present.
True
Some linear programming problems have a special structure that guarantees the variables will have integer values.
True
Square Nodes in decision tree indicate a decision must be made.
True
Square nodes in a decision tree indicate that a decision must be made.
True
States of nature should be defined so that one and only one will actually occur.
True
The 100% Rule does not imply that the optimal solution will necessarily change if the percentage exceeds 100%.
True
The LP Relaxation contains the objective function and constraints of the IP problem, but drops all integer restrictions.
True
The Markowitz mean-variance portfolio model presented in the text is a convex optimization problem.
True
The analysis of a two-person, zero-sum game begins with checking to see whether a pure strategy exists.
True
The assignment problem is a special case of the transportation problem in which all supply and demand values equal one
True
The assignment problem is a special case of the transportation problem in which all supply and demand values equal one.
True
The assignment problem is a special case of the transportation problem in which all supply supply and demand values equal one
True
The capacitated transportation problem includes constraints which reflect limited capacity on a route.
True
The classic assignment problem can be modeled as a 0-1 integer program.
True
The constraint 5X1 - 2X2 <= 0 passes through the point (X1 = 20, X2 = 50)
True
The constraint 5x1 - 2x2 £ 0 passes through the point (20, 50).
True
The constraint 5x1 − 2x2 ≤ 0 passes through the point (20, 50).
True
The degree of risk is associated with the probability or magnitude of loss.
True
The difference between an activity's earliest finish time and latest finish time equals the difference between its earliest start time and latest start time.
True
The difference between an activity's earliest finish time and latest finish time equals the difference between its earliest start time and latest start time.
True
The direction of flow in the shortest route problem is always out of the origin node and into the destination node
True
The direction of flow in the shortest-route problem is always out of the origin node and into the destination node
True
The direction of flow in the shortest-route problem is always out of the origin node and into the destination node.
True
The direction of flow in the shortest-route problems always out of the origin node and into the destination node.
True
The earliest finish time for the final activity is the project duration.
True
The expected monetary value approach and the expected utility approach to decision making usually result in the same decision choice unless extreme payoffs are involved.
True
The exponential smoothing forecast for any period is a weighted average of all the previous actual values for the time series.
True
The first step in the decision making process is to identify the problem
True
The first step in the decision making process is to identify the problem.
True
A decision strategy is a sequence of decisions and chance outcomes, where the decisions chosen depend on the yet to be determined outcomes of chance events.
True
A discrete-event simulation reviews the status of the system periodically, whether or not an event occurs.
True
A feasible solution is a global optimum if there are no other feasible points with a better objective function value in the feasible region.
True
A high efficiency rating indicates that the sample information is almost as good as perfect information.
True
A marketing research firm must determine how many daytime interviews (D) and evening interviews (E) to conduct. At least 40% of the interviews must be in the evening. A correct modeling of this constraint is: -0.4D + 0.6E > 0.
True
A negative dual price indicates that increasing the right-hand side of the associated constraint would be detrimental to the objective.
True
A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.
True
A range of optimality is applicable only if the other coefficient remains at its original value.
True
A risk avoider will have a concave utility function.
True
A risk neutral decision maker will have a linear utility function.
True
A simulation model provides a convenient experimental laboratory for the real system.
True
A transshipment constraint must contain a variable for every arc entering or leaving the node
True
A transshipment constraint must contain a variable for every arc entering or leaving the node.
True
A transshipment problem is a generalization of the transportation problem in which certain nodes are neither supply nodes nor destination nodes.
True
ACH involves seeking evidence to refute hypotheses (T/F).
True
AHP allows a decision maker to express personal preferences about the various aspects of a multicriteria problem.
True
Activities require time to complete while events do not.
True
After all probabilities and payoffs are placed on a decision tree, the decision maker calculates expected values at state of nature nodes and makes selections at decision nodes.
True
All activities on a critical path have zero slack time.
True
All uncontrollable inputs or data must be specified before we can analyze the model and recommend a decision or solution for the problem.
True
An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.
True
An unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.
True
Any feasible solution to a blending problem with pooled components is feasible to the problem with no pooling.
True
Bayes Rule can be used to calculate Posterior probabilities
True
Circular nodes in a decision tree indicate that it would be incorrect to choose a path from the node.
True
Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.
True
Compared to the problems in the textbook, real-world problems generally require more variables and constraints.
True
Computer-generated random numbers are not technically random.
True
Constraints in the LP models for crashing decisions are required to compare the activity's earliest finish time with the earliest finish time of each predecessor.
True
Constraints in the LP models for crashing decisions are required to compare the activity's earliest finish time with the earliest finish time of each predecessor.
True
Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints.
True
DEA does not necessarily identify the operating units that are relatively efficient.
True
DEA will show all but one operating unit to be relatively inefficient in the case where an operating unit producing the most of every output and also consumes the least of every input.
True
Data collection for large-scale LP models can be more time-consuming than either the formulation of the model or the development of the computer solution.
True
Decision trees should be organized in a natural or chronological fashion
True
Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs.
True
EVPI equals the expected regret associated with the minimax decision.
True
EVPI is always greater than or equal to EVSI
True
EVPI is always greater than or equal to EVSI.
True
Each simulation run provides only a sample of how the real system will operate.
True
Expected value is the sum of the weighted payoff possibilities at a circular node in a decision tree.
True
Exponential smoothing with α = .2 and a moving average with n = 5 put the same weight on the actual value for the current period.
True
Flow in a transportation network is limited to one direction
True
Flow in a transportation network is limited to one direction.
True
For a minimization problem, a point is a global minimum if there are no other feasible points with a smaller objective function value.
True
For any constraint, either its slack/surplus value must be zero or its dual price must be zero
True
For any constraint, either its slack/surplus value must be zero or its dual price must be zero.
True
For any constraint, either its slack/surplus value must be zero or its dual value must be zero
True
For any waiting line system, (Average number of units in waiting line) = (Total waiting time) divided by (Total time of simulation).
True
For the multiperiod production scheduling problem in the textbook, period n − 1's ending inventory variable was also used as period n's beginning inventory variable.
True
If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables, rounding down will always provide a feasible integer solution.
True
If a pure strategy solution exists for a two-person, zero-sum game, it is the optimal solution to the game.
True
If a time series has a significant trend pattern, then one should not use a moving average to forecast.
True
If a transportation problem has four origins and five destinations, the LP formulation of the problem will have nine constraints.
True
If the dual price for the right-hand side of a ≤ constraint is zero, there is no upper limit on its range of feasibility.
True
If the optimal solution to the LP relaxation problem is integer, it is the optimal solution to the integer linear program.
True
If the optimal value of a decision variable is zero and its reduced cost is zero, this indicates that alternative optimal solutions exist.
True
If the range of feasibility indicates that the original amount of a resource which was 20, can increase by 5, then the amount of the resources can increase to 25.
True
If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25.
True
If x1 + x2 ≤ 500y1 and y1 is 0 - 1, then if y1 is 0, x1 and x2 will be 0.
True
If you are deciding to buy either machine A, B, or C with the objective of minimizing the sum of labor, material and utility costs, you are dealing with a single-criterion decision.
True
In ACH, you work across the rows of the matrix, examining one item of evidence at a time to see how consistent that item of evidence is with each of the hypotheses (T/F).
True
In a feasible problem, an equal-to constraint cannot be nonbinding.
True
In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables (T/F)
True
In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.
True
In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.
True
In a two-person, zero-sum, pure-strategy game, there is no advantage to either player to switch from its strategy even if one of the players discovers the other player's strategy in advance.
True
In comparing different policies using simulation, one should use the same set of random numbers whenever possible.
True
In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values.
True
In order to tell the impact of a change in a constraint coefficient, the change must be made and then the model resolved.
True
In portfolio models, risk is minimized by diversification
True
In portfolio models, risk is minimized by diversification.
True
In quantitative analysis, the optimal solution is the mathematically-best solution.
True
In the case of functions with multiple local optima, most nonlinear optimization software methods can get stuck and terminate at a local optimum.
True
In the general assignment problem, one agent can be assigned to several tasks.
True
Integer linear programs are harder to solve than linear programs.
True
It is possible for the optimal solution to a nonlinear optimization problem to lie in the interior of the feasible region.
True
It is possible to have more than one critical path at a time.
True
Many linear programming algorithms such as the simplex method optimize by examining only the extreme points
True
Maximizing the expected payoff and minimizing the expected opportunity loss result in the same recommended decision.
True
Media selection problems can maximize exposure quality and use number of customers reached as a constraint, or maximize the number of customers reached and use exposure quality as a constraint (T/F)
True
Media selection problems can maximize exposure quality and use number of customers reached as a constraint, or maximize the number of customers reached and use exposure quality as a constraint.
True
Most practical applications of integer linear programming involve only 0 -1 integer variables.
True
Multiple choice constraints involve binary variables.
True
No matter what value it has, each objective function line is parallel to every other objective function line in a problem.
True
Nonlinear programming algorithms are more complex than linear programming algorithms.
True
The function f (X, Y) = X 2 + Y 2 has a single global minimum and is relatively easy to minimize.
True
The goal of portfolio models is to create a portfolio that provides the best balance between risk and return.
True
The length of time an activity can be delayed without affecting the project completion time is the slack.
True
The length of time an activity can be delayed without affecting the project completion time is the slack.
True
The linear programming model for crashing presented in the textbook assumes that any portion of the activity crash time can be achieved for a corresponding portion of the activity crashing cost.
True
The linear programming model for crashing presented in the textbook assumes that any portion of the activity crash time can be achieved for a corresponding portion of the activity crashing cost.
True
The marketing research model presented in the textbook involves minimizing total interview cost subject to interview quota guidelines.
True
The maximal flow problem can be formulated as a capacitated transshipment problem.
True
The mean squared error is influenced much more by large forecast errors than is the mean absolute error.
True
The minimum expected opportunity loss provides the best decision, regardless of whether the decision analysis involves minimization or maximization.
True
The most critical component in determining the success or failure of any quantitative approach to decision making is problem definition.
True
The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.
True
The outcome with the highest payoff will also have the highest utility.
True
The point (3, 2) is feasible for the constraint 2x1 + 6x2 <= 30.
True
The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30.
True
The primary value of decision trees is as a useful way of organizing how operations managers think about complex multiphase decisions.
True
The process of decision making is more limited than that of problem solving
True
The process of decision making is more limited than that of problem solving.
True
The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.
True
The project manager should monitor the progress of any activity with a large time variance even if the expected time does not identify the activity as a critical activity.
True
The project manager should monitor the progress of any activity with a large time variance even if the expected time does not identify the activity as a critical activity.
True
The reduced cost for a positive decision variable is 0 (T/F)
True
The reduced cost for a positive decision variable is 0.
True
The risk neutral decision maker will have the same indications from the expected value and expected utility approaches.
True
The risk premium is never negative for a conservative decision maker.
True
The shortest- route problem is a special case of the transshipment problem.
True
The shortest-route problem is a special case of the transshipment problem
True
The shortest-route problem is a special case of the transshipment problem.
True
The standard form of a linear programming problem will have the same solution as the original problem.
True
The utility function for a risk avoider typically shows a diminishing marginal return for money.
True
The value of any model is that it enables the user to make inferences about the real situation
True
The value of any model is that it enables the user to make inferences about the real situation (T/F)
True
The value of any model is that it enables the user to make inferences about the real situation.
True
The way most people solve problems is to pick out what they suspect intuitively is the most likely answer, then look at the available information from the point of view of whether or not it supports this answer (T/F).
True
There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.
True
Time series data can exhibit seasonal patterns of less than one month in duration.
True
Time series methods base forecasts only on past values of the variables.
True
To assign utilities, consider the best and worst payoffs in the entire decision situation.
True
To properly interpret dual prices, one must know how costs were allocated in the objective function.
True
To use Excel to generate a normally distributed random variable, you must know the mean and standard deviation of the distribution and have a random number between 0 and 1.
True
Transshipment problem allows shipments both in and out of some nodes while transportation problems do not
True
Transshipment problem allows shipments both in and out of some nodes while transportation problems do not.
True
Trials of a simulation show what would happen when values of the probabilistic input change.
True
Trials of a simulation show what would happen when values of the probablistic input change.
True
Using simulation to perform risk analysis is like playing out many what-if scenarios by randomly generating values for the probabilistic inputs.
True
When a route in a transportation is unacceptable, the corresponding variable can be removed from the LP formulation
True
When a route in a transportation problem is unacceptable, the corresponding variable can be removed from the LP formulation.
True
When a route in a transportation problem is unacceptable, the corresponding variable can be removed from the LP foundation
True
When activity times are uncertain, total project time is normally distributed with mean equal to the sum of the means of all of the critical activities.
True
When activity times are uncertain, total project time is normally distributed with mean equal to the sum of the means of all of the critical activities.
True
When components (or ingredients) in a blending problem must be pooled, the number of feasible solutions is reduced.
True
When monetary value is not the sole measure of the true worth of the outcome to the decision maker, monetary value should be replaced by utility.
True
When monetary value is not the sole measure of the true worth of the outcome to the decision maker, monetary value should be replaces by utility.
True
When the expected value approach is used to select a decision alternative, the payoff that actually occurs will usually have a value different from the expected value.
True
When using a moving average of order k to forecast, a small value for k is preferred if only the most recent values of the time series are considered relevant.
True
Whenever total supply is less than total demand in a transportation problem, the LP model does not determine how the unsatisfied demand is handled.
True
The constraint 5x1 - 2x2 <= 0 passes through the point (x1= 20, x2 = 50)
True, just separate unknown variables and plug in the point
The shortest-route problem is a special case of the transshipment problem
True: 1 supply 1 demand
Which of the following is the common approach to time series analysis?
Try several techniques and use the best results
39. A redundant constraint results in a. no change in the optimal solution(s) b. an unbounded solution c. no feasible solution d. alternative optimal solutions
a. no change in the optimal solution(s)
The efficiency of sample information is a. EVSI*(100%) b. EVSI/EVPI*(100%) c. EVwoSI/EVwoPI*(100%) d. EVwSI/EVwoSI*(100%)
b. EVSI/EVPI*(100%)
When events occur at discrete points in time
a simulation clock is required, the simulation advances to the next event and the model is a discrete-event simulation (all of the above).
A transportation problem is
a special case of linear programming that deals with the distribution of goods and services from multiple services to multiple destinations in order to minimize distribution costs.
A cost that is incurred no matter what values the decision variable assume is
a sunk cost
A cost that is incurred no matter what values the decision variables assume is
a sunk cost
In a transportation problem represented as a network, an arc between a source and destination represents
a valid shipping route in the real world.
The normal distribution tends to be a better approximation of the distribution of total time for shorter projects where the critical path has relatively few activities.
False
The normal distribution tends to be a better approximation of the distribution of total time for shorter projects where the critical path has relatively few activities.
False
The parameters of a simulation model are the controllable inputs.
False
The primary limitation of linear programming's applicability is the requirement that all decision variables be nonnegative.
False
The problem of maximizing a concave quadratic function over a linear constraint set is relatively difficult to solve.
False
The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.
False
The terms 'stochastic' and 'deterministic' have the same meaning in quantitative analysis
False
The terms 'stochastic' and 'deterministic' have the same meaning in quantitative analysis.
False
The terns 'stochastic' and 'deterministic' have the same meaning in quantitative analysis (T/F)
False
The value of the coefficient of imitation, q, in the Bass model for forecasting adoption of a new product cannot be negative.
False
The variance in the project completion time is the sum of the variances of all activities in the project.
False
The variance in the project completion time is the sum of the variances of all activities in the project.
False
The volume that results in marginal revenue equaling marginal cost is called the break-even point
False
The volume that results in marginal revenue equaling marginal cost is called the break-even point.
False
There is a dual price for every decision variable in a model
False
There is a dual price for every decision variable in a model.
False
To find the choice that provides the highest profit and the fewest employees, apply a single-criterion decision process (T/F)
False
To find the choice that provides the highest profit and the fewest employees, apply a single-criterion decision process.
False
Trend in a time series must be linear.
False
Uncontrollable inputs are decision variables for a model (T/F)
False
Uncontrollable inputs are the decision variable for a model.
False
Uncontrollable inputs are the decision variables for a model
False
Uncontrollable inputs are the decision variables for a model.
False
Using minutes as the unit of measurement on the left hand side of a consent and using hours on the right-hand side is acceptable since both are a measure of time
False
Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time
False
Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time.
False
Validation determines that the computer procedure is operating as it is intended to operate.
False
Verification is the process of ensuring that the simulation model provides an accurate representation of the real system.
False
When activity times are uncertain, an activity's most likely time is the same as its expected time.
False
When activity times are uncertain, an activity's most likely time is the same as its expected time.
False
When the number of agents exceeds the number of tasks in an assignment problem, one or more dummy tasks must be introduced in the LP formulation or else the LP will not have a feasible solution.
False
When the payoffs become extreme, most decision makers are satisfied with the decision that provides the best expected monetary value.
False
When the right-hand sides of two constraints are each increased by one unit, the objective function value will be adjusted by the sum of the constraints' dual prices.
False
With fewer periods in a moving average, it will take longer to adjust to a new level of data values.
False
he constraint x1 + x2 + x3 + x4 ≤ 2 means that two out of the first four projects must be selected.
False
Revenue management methodology was originally developed for the banking industry
False - for an Airline
Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution
False - it could affect the optimal solution
Uncontrollable inputs are decision variables for a model
False - the decision variables are controllable
A rounded down integer solution can never result in a less than optimal solution. True/False?
False!
Transportation problems do or do not ALWAYS involve shipping goods from one location to another?
False.
The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is fully structured.
False. It is an interative process.
The three methods for obtaining an initial solution arw
Northwest corner method, Short cut method, and the Approximation Method (VAM Method)
Let Pij = the production of product i in period j. To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units,
P13 − P14 ≤ 100; P14 − P13 ≤ 100
To study consumer characteristics, attitudes, and preferences, a company would engage in
marketing research.
A model that uses a system of symbols to represent a problem is called
mathematical
The quantitative analysis approach requires
mathematical expressions for the relationships
For a maximization problem, the optimistic approach is often referred to as the
maximax approach
For a minimization problem, the optimistic approach is often referred to as the
maximax approach
For a maximization problem, the conservative approach is often referred to as the
maximin approach
When the cost of a resource is sunk, then the dual price can be interpreted as the
maximum amount the firm should be willing to pay for one additional unit of the resource
In PERT, the activity duration time is equal to the
mean duration
For a minimization problem, the conservative approach is often referred to as the
minimax approach
The objective function for portfolio selection problems usually is maximization of expected return or
minimization of risk
The objective of the transportation problem is to
minimize the cost of shipping products from several origins to several destinations.
Blending Problems arise whenever a managers must decide how to
mix two or more resource to produce one or more products
Blending problem arise whenever a manager must decide how to
mix two or more resources to produce one or more products
The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal pattern is
moving average.
To visualize a transportation problem, a
network representation can be used.
A time-series which has a significant upward or downward trend is referred to as
non-stationary
In a balanced transportation model, supply does
not equal demand at all constraints, and they are inequalities.
An index is just a
number. Any number that can be zero.
In a transportation problem, nodes represent:
plants that produce products, warehouses that hold goods, and customers that require goods.
Arcs in a project network indicate
precedence relationships.
The amount by which an objective function coefficient would have to improve before it would be possible for the corresponding variable to assume a positive value in the optimal solution is called the
reduced cost.
A constraint that does not affect the feasible region is a
redundant constraint
The trend pattern is easy to identify by using
regression analysis.
Making a good decision
requires a clear understanding of decision alternatives, states of nature, and payoffs.
A decision with more than one objective
requires the decision maker to place the objectives in some order of importance.
The amount that the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the
reduced cost
The amount the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the
reduced cost
For an activity with more than one immediate successor activity, its latest-finish time is equal to the
smallest latest-start time among its immediate successors.
Integer programming models are linear programming models with the added complication that
some or all of the decision variables are restricted to integer values.
In using rounding of a linear programming model to obtain an integer solution, the solution that is produced is
sometimes optimal and feasible.
If a decision variable is not positive in the optimal solution, its reduced cost is
the amount its objective function value would need to improve before it could become positive.
If a decision variable is not positive in the optimal solution, its reduced cost is
the amount its objective function value would need to improve before it could become positive
Consider a maximal flow problem in which vehicle traffic entering a city is routed among several routes before eventually leaving the city. When represented with a network,
the arcs represent one way streets.
Computer solutions are based off of the
the branch and bound method.
Consider a shortest route problem in which a bank courier must travel between branches and the main operations center. When represented with a network,
the branches and the operations center are all nodes and the streets are the arcs.
The dual price measures, per unit increase in the right hand side of the constraint
the change in the value of the optimal solution
Which of the methods for decision making best protects the decision maker from undesirable results?
the conservative approach
Which of the methods for decision making without probabilities best protects the decision maker from undesirable results?
the conservative approach
A required step in the analytic hierarchy process is the determine
the relative importance of a set of features based on a criterion.
The range of feasibility measures
the right-hand side values for which the dual prices will not change.
The range of feasibility measures
the right-hand-side values for which the dual prices will not change
The range of feasiblity measures
the right-hang-side values for which the dual prices will not change.
In a transportation problem, the arcs represent
the routes the goods follow.
Sometimes one or more of the routes of the
transportation model are prohibited.
The problem which deals with the distribution of goods from several sources to several destinations is the
transportation problem
The assignment problem is NOT a special form of the __
transportation problem where all supply and demand values equal zero.
The assignment problem is a special case of the
transportation problem.
Let x1 , x2 , and x3 be 0-1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?
x1 + x2 + x3 ≥ 2
In a model, x1 ≥ 0 and integer, x2 ≥ 0, and x3 = 0, 1. Which solution would not be feasible?
x1 = 2, x2 = 3, x3 = .578
Let x1 and x2 be 0-1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer below indicates that project 2 can be done only if project 1 is done?
x1 − x2 ≥ 0
The number of units shipped from origin i to destination j is represented by
xij
In a capital budgeting example, a firm wants to select no more than three projects from a set of five projects. Which of the following constraints will ensure this?
y1+y2+y3+y4+y5<3
23. Which of the following is a valid objective function for a linear programming problem? a. Max 5xy b. Min 4x + 3y + (2/3)z c. Max 5x2 + 6y2 d. Min (x1 + x2)/x3
b. Min 4x + 3y + (2/3)z
32. A constraint that does not affect the feasible region is a a. non-negativity constraint. b. redundant constraint. c. standard constraint. d. slack constraint.
b. redundant constraint.
A decision maker whose utility function graphs as a straight line is a. conservative. b. a risk taker. c. risk neutral. d. a risk avoider.
c. risk neutral.
Components are referred to as pooled if they a. are shared by two or more customers b. have common ingredients c. share a storage facility d. are interchangeable
c. share a storage facility
29. When the value of the output cannot be determined even if the value of the controllable input is known, the model is a. deterministic. b. analog. c. stochastic. d. digital.
c. stochastic.
Simulation
does not guarantee optimality , is flexible and does not require the assumptions of theoretical models, allows testing of the system without affecting the real system (all of the alternatives are correct).
Sensitivity analysis for integer linear programming
does not have the same interpretation and should be disregarded.
The amount the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the
dual price
The improvement in the value of the objective function per unit increase in a right-hand side is the
dual price
The word "uniform" in the term "uniform random numbers" means
each number has an equal probability of being drawn.
Problem definition
each of the above is true
The field of management science
each of the above is true
The field of management science
each of the choices are true
In an assignment problem,
each person is assigned to his/her own best job.
The difference between the transportation and assignment problem is that
each supply and demand value is 1 in the assignment problem
The difference between the transportation and assignment problems is that
each supply and demand value is 1 in the assignment problem
The dual price for a constraint that compares funds used with funds available is .058. This means that
if more funds can be obtained at a rate of 5.5%, some should be.
With the rounding method you will never know
if your answer is the optimal solution.
A value for probablistic input from a discrete probability distribution
is given by matching the probablistic input with an interval of random numbers.
States of nature should be defined so that one and only one will actually occur.
T
A critical activity can be part of a noncritical path.
True
What is a requirement of the transportation model?
Shipping unit costs per unit are constant, goods to be shipped are the same, and there is one route between each source and destination.
A transportation problem with n origins and m destinations will have how many origins?
(n)(m)
The number of units expected to be sold is uniformly distributed between 300 and 500. If r is a random number between 0 and 1, then the proper expression for sales is
300 + r(200)
The field of management science:
- Approaches decision making rationally, with techniques based on the scientific method - Concentrates on the use of quantitative method to assist in decision making - Is another name for decision science and operations research
Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then
-.5A + .5B - .5C <= 0
let A, B and C be the amounts invested in companies A, B and C. If no more than 50% of the tax investment can be in company B, then
-0.5A + 0.5B - 0.5C <= 0
Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B then:
-0.5A + 0.5B -0.5C <= 0
If P(high) = .3, P(low) = .7, P(favorable | high) = .9, and P(unfavorable | low) = .6, then P(favorable) =
.55
If P(high) = .3, P(low) = .7, P(favorable/high) = .9, and P(unfavorable/low) = .6, then P(favorable) =
.55
Infeasibility means that the number of solutions to the linear programming model that satisfies all constraints is
0
Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is
0
Infeasibility means the the number of solution to the linear programming model that satisfies all constraints is
0
In 0-1 Integer programming, what does 0 and 1 stand for?
1 if assigned= success. 0 if assigned= otherwise.
When integers are used to represent yes or no decisions, typically the following values are
1, 0.
In a linear programming formulation of an assignment problem with 3 jobs to be done by 3 person available to these jobs, how many constraints will it have?
6
Develop an objective function that would minimize the total cost
6(X1) + 5.50(X2)
If a basic transportation problem (with no capacity constraints for arcs) has four origins and five destinations, the LP formulation will have
9 Constraints Supply: 4 constraints saying only ____ can be assigned to _____ Demand: 5 constraints saying ____ can be accepted to _____
If basic transportation problem (with no capacity constraints for arcs) has four origins and five destinations, the LP formulation of the problem will have
9 constraints
22. Decision variables a. tell how much or how many of something to produce, invest, purchase, hire, etc. b. represent the values of the constraints. c. measure the objective function. d. must exist for each constraint.
A
23. Decision alternatives a. should be identified before decision criteria are established. b. are limited to quantitative solutions c. are evaluated as a part of the problem definition stage. d. are best generated by brain-storming.
A
24. Decision criteria a. are the ways to evaluate the choices faced by the decision maker. b. are the choices faced by the decision maker. c. must be unique for a problem. d. are the problems faced by the decision maker.
A
26. The quantitative analysis approach requires a. mathematical expressions for the relationships. b. the manager's prior experience with a similar problem. c. a relatively uncomplicated problem.
A
28. Which of the following special cases does not require reformulation of the problem in order to obtain a solution? a. alternate optimality b. infeasibility c. unboundedness d. each case requires a reformulation.
A
37. In what part(s) of a linear programming formulation would the decision variables be stated? a. objective function and the left-hand side of each constraint b. objective function and the right-hand side of each constraint c. the left-hand side of each constraint only d. the objective function only
A
39. A redundant constraint results in a. no change in the optimal solution(s) b. an unbounded solution c. no feasible solution d. alternative optimal solutions
A
An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost. The correct interpretation of the dual price associated with the labor hours constraint is a. the maximum premium (say for overtime) over the normal price that the company would be willing to pay. b. the upper limit on the total hourly wage the company would pay. c. the reduction in hours that could be sustained before the solution would change. d. the number of hours by which the right-hand side can change before there is a change in the solution point.
A
Decision tree probabilities refer to the probability of a. an uncertain event occurring. b. the decision being made. c. finding an optimal value. d. overlooked choices.
A
For a minimization problem, the conservative approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
A
For a two-person, zero-sum, mixed-strategy game, it is necessary to solve the LP for only one of the players to learn the optimal strategies for both players. a. 1. b. the number of operating units. c. 100. d. any arbitrary value.
A
In data envelopment analysis, the percentage of an individual operating unit's resources that are available to the composite operating unit is the a. efficiency index. b. saddle point. c. maximin. d. minimax.
A
In general, every DEA linear programming model will include a constraint that requires the weights for the operating units to sum to a. 1. b. the number of operating units. c. 100. d. any arbitrary value.
A
Let Pij = the production of product i in period j. To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units, a. P13 − P14 ≤ 100; P14 − P13 ≤ 100 b. P13 − P14 ≤ 100; P13 − P14 ≥ 100 c. P13 − P14 ≤ 100; P14 − P13 ≥ 100 d. P13 − P14 ≥ 100; P14 − P13 ≥ 100
A
Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done? a. x1 + x2 + x3 ≥ 2 b. x1 + x2 + x3 ≤ 2 c. x1 + x2 + x3 = 2 d. x1 − x2 = 0
A
Media selection problems usually determine a. how many times to use each media source. b. the coverage provided by each media source. c. the cost of each advertising exposure. d. the relative value of each medium.
A
Most practical applications of integer linear programming involve a. only 0-1 integer variables and not ordinary integer variables. b. mostly ordinary integer variables and a small number of 0-1 integer variables. c. only ordinary integer variables. d. a near equal number of ordinary integer variables and 0-1 integer variables.
A
Rounded solutions to linear programs must be evaluated for a. feasibility and optimality. b. sensitivity and duality. c. relaxation and boundedness. d. each of these choices are true.
A
States of nature a. can describe uncontrollable natural events such as floods or freezing temperatures. b. can be selected by the decision maker. c. cannot be enumerated by the decision maker. d. All of the alternatives are true.
A
The 0-1 variables in the fixed cost models correspond to a. a process for which a fixed cost occurs. b. the number of products produced. c. the number of units produced. d. the actual value of the fixed cost.
A
The 100% Rule compares a. proposed changes to allowed changes. b. new values to original values. c. objective function changes to right-hand side changes. d. dual prices to reduced costs.
A
The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means a. agent 3 can be assigned to 2 tasks. b. agent 2 can be assigned to 3 tasks. c. a mixture of agents 1, 2, 3, and 4 will be assigned to tasks. d. there is no feasible solution.
A
The assignment problem is a special case of the a. transportation problem. b. transshipment problem. c. maximal flow problem. d. shortest-route problem.
A
The focus of smoothing methods is to smooth out a. the random fluctuations. b. wide seasonal variations. c. significant trend effects. d. long range forecasts.
A
The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal pattern is a. moving average b. mean squared error c. mean average error d. qualitative forecasting
A
The number of units shipped from origin i to destination j is represented by a. xij. b. xji. c. cij. d. cji.
A
The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is a. the indifference probability. b. the lottery probability. c. the uncertain probability. d. the utility probability.
A
The solution to the LP Relaxation of a maximization integer linear program provides a. an upper bound for the value of the objective function. b. a lower bound for the value of the objective function. c. an upper bound for the value of the decision variables d. a lower bound for the value of the decision variables
A
To solve a linear programming problem with thousands of variables and constraints a. a personal computer can be used. b. a mainframe computer is required. c. the problem must be partitioned into subparts. d. unique software would need to be developed.
A
Using a naive forecasting method, the forecast for next week's sales volume equals a. the most recent week's sales volume b. the most recent week's forecast c. the average of the last four weeks' sales volumes d. next week's production volume
A
We assume in the maximal flow problem that a. the flow out of a node is equal to the flow into the node. b. the source and sink nodes are at opposite ends of the network. c. the number of arcs entering a node is equal to the number of arcs exiting the node. d. None of the alternatives is correct.
A
When consequences are measured on a scale that reflects a decision maker's attitude toward profit, loss, and risk, payoffs are replaced by a. utility values. b. multicriteria measures. c. sample information. d. opportunity loss.
A
When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery, the decision maker is a. a risk avoider. b. a risk taker. c. an optimist. d. an optimizer.
A
Whenever a categorical variable such as season has k levels, the number of dummy variables required a. k - 1 b. k c. k + 1 d. 2k
A
Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables? a. supply chain design b. bank location c. capital budgeting d. product design and market share optimization
A
Which of the following exponential smoothing constant values puts the same weight on the most recent time series value as does a 5-period moving average? a. α = .2 b. α = .25 c. α = .75 d. α = .8
A
Which of the operations management applications modeled in the text has an objective function that minimizes the sum of manufacturing costs, purchasing costs, and overtime costs? a. make-or-buy decision b. blending c. production scheduling d. workforce assignment
A
Risk Neutral
A decision maker whose utility function graphs as a straight line...
When a transportation model is formulated into a spreadsheet, which of the following is required?
A parameter table and a solution table.
The 0-1 variable is in the fixed cost models correspond to
A process for which a fixed cost occurs.
There are three basic types of integer linear programming models:
A total integer model, a 0-1 integer model, and a mixed integer model.
Department 3 has 2500 hours. Transfers are allowed to departments 2 and 4, and from departments 1 and 2. If Ai measures the labor hours allocated to department i and Tij the hours transferred from department i to department j, then
A3 − T13 − T23 + T32 + T34 = 2500
The options from which a decision maker chooses a course of action are
All of the alternatives are true. a. called the decision alternatives. b. under the control of the decision maker. c. not the same as the states of nature.
Why might we not be able to build a regression model to predict a dependent variable?
All of these are true
Which of the following special cases does not require reformulation of the problem in order to obtain a solution?
Alternate optimality
(T/F) A multiple choice constraint involves selecting k out of n alternatives, where k ≥ 2.
F
(T/F) A transportation problem with 3 sources and 4 destinations will have 7 decision variables.
F
(T/F) Decision alternatives are structured so that several could occur simultaneously.
F
(T/F) If a real-world problem is correctly formulated, it is not possible to have alternative optimal solutions.
F
Which of the methods for decision making best protects the decision maker from undesirable results? a. the optimistic approach b. the conservative approach c. minimum regret d. minimax regret
B
23. Which of the following is a valid objective function for a linear programming problem? a. Max 5xy b. Min 4x + 3y + (2/3)z c. Max 5x2 + 6y2 d. Min (x1 + x2)/x3
B
26. Slack a. is the difference between the left and right sides of a constraint. b. is the amount by which the left side of a ≤ constraint is smaller than the right side. c. is the amount by which the left side of a ≥ constraint is larger than the right side. d. exists for each variable in a linear programming problem.
B
28. Inputs to a quantitative model a. must all be deterministic if the problem is to have a solution. b. are uncertain for a stochastic model. c. are a trivial part of the problem solving process. d. are uncontrollable for the decision variables.
B
29. The improvement in the value of the objective function per unit increase in a right-hand side is the a. sensitivity value. b. dual price. c. constraint coefficient. d. slack value.
B
31. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is a. at least 1. b. 0. c. an infinite number. d. at least 2.
B
31. Management science and operations research both involve a. operational management skills. b. quantitative approaches to decision making. c. scientific research as opposed to applications. d. qualitative managerial skills.
B
32. A constraint that does not affect the feasible region is a a. non-negativity constraint. b. redundant constraint. c. standard constraint. d. slack constraint.
B
33. The first step in problem solving is a. definition of decision variables. b. the identification of a difference between the actual and desired state of affairs. c. determination of the correct analytical solution procedure. d. implementation.
B
36. If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation? a. 300x1 + 125x2 > 4,000 b. 300x1 + 125x2 < 4,000 c. 425(x1 + x2) < 4,000 d. 300x1 + 125x2 = 4,000
B
40. A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is a. a standard variable b. a slack variable c. a surplus variable d. a non-negative variable
B
A DEA linear programming model involving 4 input measures and 3 output measures will have a. 7 constraints. b. 8 constraints. c. 12 constraints. d. 13 constraints.
B
A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(25000) + (1 p)(5000). If the utility of 25,000 is 0 and of 5000 is 1, then the utility of 10,000 is a. .5 b. .6 c. .4 d. 4
B
The dual price for a < constraint a. will always be < 0. b. will always be > 0. c. will be < 0 in a minimization problem and > 0 in a maximization problem. d. will always equal 0.
B
The dual price for a constraint that compares funds used with funds available is .058. This means that a. the cost of additional funds is 5.8%. b. if more funds can be obtained at a rate of 5.5%, some should be. c. no more funds are needed. d. the objective was to minimize.
B
The efficiency of sample information is a. EVSI*(100%) b. EVSI/EVPI*(100%) c. EVwoSI/EVwoPI*(100%) d. EVwSI/EVwoSI*(100%)
B
The graph of a problem that requires x1 and x2 to be integer has a feasible region a. the same as its LP relaxation. b. of dots. c. of horizontal stripes. d. of vertical stripes.
B
The problem which deals with the distribution of goods from several sources to several destinations is the a. maximal flow problem b. transportation problem c. assignment problem d. shortest-route problem
B
The shortest-route problem finds the shortest-route a. from the source to the sink. b. from the source to any other node. c. from any node to any other node. d. from any node to the sink.
B
To perform sensitivity analysis involving an integer linear program, it is recommended to a. use the dual prices very cautiously. b. make multiple computer runs. c. use the same approach as you would for a linear program. d. use LP relaxation.
B
To study consumer characteristics, attitudes, and preferences, a company would engage in a. client satisfaction processing. b. marketing research. c. capital budgeting. d. production planning.
B
Using exponential smoothing, the demand forecast for time period 10 equals the demand forecast for time period 9 plus a. α times (the demand forecast for time period 8) b. α times (the error in the demand forecast for time period 9) c. α times (the observed demand in time period 9) d. α times (the demand forecast for time period 9)
B
Utility reflects the decision maker's attitude toward a. probability and profit. b. profit, loss, and risk. c. risk and regret. d. probability and regret.
B
Which of the following is the most useful contribution of integer programming? a. finding whole number solutions where fractional solutions would not be appropriate b. using 0-1 variables for modeling flexibility c. increased ease of solution d. provision for solution procedures for transportation and assignment problems
B
When the cost of a resource is sunk, then the dual price can be interpreted as the a. minimum amount the firm should be willing to pay for one additional unit of the resource. b. maximum amount the firm should be willing to pay for one additional unit of the resource. c. minimum amount the firm should be willing to pay for multiple additional units of the resource. d. maximum amount the firm should be willing to pay for multiple additional units of the resource.
B
Which of the following forecasting methods puts the least weight on the most recent time series value? a. exponential smoothing with α = .3 b. exponential smoothing with α = .2 c. moving average using the most recent 4 periods d. moving average using the most recent 3 periods
B
Which of the following is not true regarding an LP model of the assignment problem? a. Costs appear in the objective function only. b. All constraints are of the ≥ form. c. All constraint left-hand side coefficient values are 1. d. All decision variable values are either 0 or 1.
B
Decision criteria
Are the ways to evaluate the choices faced by the decision maker
All of the following statements about a redundant constraint are correct EXCEPT
At the optimal solution, a redundant constraint will have zero slack
A section of output from The Management Scientist is shown here. Variable Lower Limit Current Value Upper Limit 1 60 100 120 What will happen to the solution if the objective function coefficient for variable 1 decreases by 20? a. Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same. b. The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same. c. The same decision variables will be positive, but their values, the objective function value, and the dual prices will change. d. The problem will need to be resolved to find the new optimal solution and dual price.
B
All of the following are true about qualitative forecasting methods except a. They generally involve the use of expert judgment to develop forecasts. b. They assume the pattern of the past will continue into the future. c. They are appropriate when past data on the variable being forecast are not applicable. d. They are appropriate when past data on the variable being forecast are not available.
B
All of the following are true about time series methods except a. They discover a pattern in historical data and project it into the future. b. They involve the use of expert judgment to develop forecasts. c. They assume that the pattern of the past will continue into the future. d. Their forecasts are based solely on past values of the variable or past forecast errors.
B
Assuming W1, W2 and W3 are 0 -1 integer variables, the constraint W1 + W2 + W3 < 1 is often called a a. multiple-choice constraint. b. mutually exclusive constraint. c. k out of n alternatives constraint. d. corequisite constraint.
B
Blending problems arise whenever a manager must decide how to a. mix several different asset types in one investment strategy. b. mix two or more resources to produce one or more products. c. combine the results of two or more research studies into one. d. allocate workers with different skill levels to various work shifts.
B
Consider a maximal flow problem in which vehicle traffic entering a city is routed among several routes before eventually leaving the city. When represented with a network, a. the nodes represent stoplights. b. the arcs represent one way streets. c. the nodes represent locations where speed limits change. d. None of the alternatives is correct.
B
Constraints in a transshipment problem a. correspond to arcs. b. include a variable for every arc. c. require the sum of the shipments out of an origin node to equal supply. d. All of the alternatives are correct.
B
For a maximization problem, the conservative approach is often referred to as the a. minimax approach. b. maximin approach. c. maximax approach. d. minimin approach.
B
Forecast errors a. are the difference in successive values of a time series b. are the differences between actual and forecast values c. should all be nonnegative d. should be summed to judge the goodness of a forecasting model
B
If Pij = the production of product i in period j, then to indicate that the limit on production of the company's three products in period 2 is 400, a. P21 + P22 + P23 ≤ 400 b. P12 + P22 + P32 ≤ 400 c. P32 ≤ 400 d. P23 ≤ 400
B
If a decision variable is not positive in the optimal solution, its reduced cost is a. what its objective function value would need to be before it could become positive. b. the amount its objective function value would need to improve before it could become positive. c. zero. d. its dual price.
B
If a transportation problem has four origins and five destinations, the LP formulation of the problem will have a. 5 constraints b. 9 constraints c. 18 constraints d. 20 constraints
B
If data for a time series analysis is collected on an annual basis only, which pattern does not need to be considered? a. trend b. seasonal c. cyclical d. horizontal
B
In an influence diagram, decision nodes are represented by a. circles or ovals b. squares or rectangles c. diamonds d. triangles
B
In situations where you need to compare forecasting methods for different time periods, the most appropriate accuracy measure is a. MSE b. MAPE c. MAE d. ME
B
Making a good decision a. requires probabilities for all states of nature. b. requires a clear understanding of decision alternatives, states of nature, and payoffs. c. implies that a desirable outcome will occur. d. All of the alternatives are true.
B
Modeling a fixed cost problem as an integer linear program requires a. adding the fixed costs to the corresponding variable costs in the objective function. b. using 0-1 variables. c. using multiple-choice constraints. d. using LP relaxation.
B
Revenue management methodology was originally developed for a. a cruise line. b. an airline. c. a car rental company. d. a hotel chain.
B
Seasonal patterns a. cannot be predicted. b. are regular repeated patterns. c. are multiyear runs of observations above or below the trend line. d. reflect a shift in the time series over time.
B
Sensitivity analysis information in computer output is based on the assumption of a. no coefficient changes. b. one coefficient changes. c. two coefficients change. d. all coefficients change.
B
The approach to determining the optimal decision strategy involves a. a forward (left to right) pass through the decision tree. b. a backward (right to left) pass through the decision tree. c. choosing the outcome of a chance event with the greatest probability. d. choosing the outcome of a chance event with the greatest payoff.
B
The cost that varies depending on the values of the decision variables is a a. reduced cost. b. relevant cost. c. sunk cost. d. dual cost.
B
The difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information is called the a. information sensitivity. b. expected value of sample information. c. expected value of perfect information. d. efficiency of sample information.
B
24. Which of the following statements is NOT true? a. A feasible solution satisfies all constraints. b. An optimal solution satisfies all constraints. c. An infeasible solution violates all constraints. d. A feasible solution point does not have to lie on the boundary of the feasible region.
C
25. A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called a. optimal. b. feasible. c. infeasible. d. semi-feasible.
C
25. In a multicriteria decision problem a. successive decisions must be made over time. b. it is impossible to select a single decision alternative. c. the decision maker must evaluate each alternative with respect to each criterion. d. each of these choices are true.
C
27. A physical model that does not have the same physical appearance as the object being modeled is a. a qualitative model. b. a mathematical model. c. an analog model. d. an iconic model.
C
29. When the value of the output cannot be determined even if the value of the controllable input is known, the model is a. deterministic. b. analog. c. stochastic. d. digital.
C
Which of the following is not a question answered by sensitivity analysis?
By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility?
Which of the following is not a question answered by sensitivity analysis?
By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility?
30. As long as the slope of the objective function stays between the slopes of the binding constraints a. the value of the objective function won't change. b. there will be alternative optimal solutions. c. the values of the dual variables won't change. d. there will be no slack in the solution.
C
35. A model that uses a system of symbols to represent a problem is called a. iconic. b. constrained. c. mathematical. d. analog.
C
35. All linear programming problems have all of the following properties EXCEPT a. a linear objective function that is to be maximized or minimized. b. a set of linear constraints. c. alternative optimal solutions. d. variables that are all restricted to
C
36. Which of the following is not one of the commonly used names for the body of knowledge involving quantitative approaches to decision-making? a. efficiency studies b. management science c. business analytics d. operations research
C
A constraint with a positive slack value a. will have a positive dual price. b. will have a negative dual price. c. will have a dual price of zero. d. has no restrictions for its dual price.
C
A cost that is incurred no matter what values the decision variables assume is a. a reduced cost. b. an optimal cost. c. a sunk cost. d. a dual cost.
C
A decision maker whose utility function graphs as a straight line is a. conservative. b. a risk taker. c. risk neutral. d. a risk avoider.
C
A linear programming application used to measure the relative efficiency of operating units with the same goals and objectives is a. game theory. b. asset allocation. c. data envelopment analysis. d. revenue management.
C
A negative dual price for a constraint in a minimization problem means a. as the right-hand side increases, the objective function value will increase. b. as the right-hand side decreases, the objective function value will increase. c. as the right-hand side increases, the objective function value will decrease. d. as the right-hand side decreases, the objective function value will decrease.
C
A payoff a. is always measured in profit. b. is always measured in cost. c. exists for each pair of decision alternative and state of nature. d. exists for each state of nature.
C
All of the following are true about a cyclical pattern except a. It is often due to multiyear business cycles. b. It is often combined with long-term trend patterns and called trend-cycle patterns. c. It usually is easier to forecast than a seasonal pattern due to less variability. d. It is an alternating sequence of data points above and below the trend line.
C
Arcs in a transshipment problem a. must connect every node to a transshipment node. b. represent the cost of shipments. c. indicate the direction of the flow. d. All of the alternatives are correct.
C
Consider a shortest route problem in which a bank courier must travel between branches and the main operations center. When represented with a network, a. the branches are the arcs and the operations center is the node. b. the branches are the nodes and the operations center is the source. c. the branches and the operations center are all nodes and the streets are the arcs. d. the branches are the network and the operations center is the node.
C
For a maximization problem, the optimistic approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
C
For a two-person, zero-sum, mixed-strategy game, each player selects its strategy according to a. what strategy the other player used last. b. a fixed rotation of strategies. c. a probability distribution. d. the outcome of the previous game.
C
In a model, x1 ≥ 0 and integer, x2 ≥ 0, and x3 = 0, 1. Which solution would not be feasible? a. x1 = 5, x2 = 3, x3 = 0 b. x1 = 4, x2 = .389, x3 = 1 c. x1 = 2, x2 = 3, x3 = .578 d. x1 = 0, x2 = 8, x3 = 0
C
In a production scheduling LP, the demand requirement constraint for a time period takes the form a. beginning inventory + production + ending inventory > demand. b. beginning inventory production ending inventory = demand. c. beginning inventory + production ending inventory = demand. d. beginning inventory production ending inventory > demand.
C
In an all-integer linear program, a. all objective function coefficients must be integer. b. all right-hand side values must be integer. c. all variables must be integer. d. all objective function coefficients and right-hand side values must be integer.
C
Linear trend is calculated as . The trend projection for period 15 is a. 11.25 b. 28.50 c. 39.75 d. 44.25
C
One measure of the accuracy of a forecasting model is the a. smoothing constant b. linear trend c. mean absolute error d. seasonal index
C
Revenue management methodology enables an airline to a. maximize the number of full-fare seats it sells on each flight. b. minimize the number of discount-fare seats it sells on each flight. c. increase the average number of passengers per flight. d. decrease the number of overbooked flights.
C
Rounding the solution of an LP Relaxation to the nearest integer values provides a. a feasible but not necessarily optimal integer solution. b. an integer solution that is optimal. c. an integer solution that might be neither feasible nor optimal. d. an infeasible solution.
C
Sensitivity analysis considers a. how sensitive the decision maker is to risk. b. changes in the number of states of nature. c. changes in the values of the payoffs. d. changes in the available alternatives.
C
Sensitivity analysis for integer linear programming a. can be provided only by computer. b. has precisely the same interpretation as that from linear programming. c. does not have the same interpretation and should be disregarded. d. is most useful for 0 - 1 models.
C
Sensitivity analysis is concerned with how certain changes affect a. the feasible solution. b. the unconstrained solution. c. the optimal solution. d. the degenerative solution.
C
The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the a. optimal solution. b. dual solution. c. range of optimality. d. range of feasibility.
C
The amount the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the a. dual price. b. surplus variable. c. reduced cost. d. upper limit.
C
The difference between the transportation and assignment problems is that a. total supply must equal total demand in the transportation problem b. the number of origins must equal the number of destinations in the transportation problem c. each supply and demand value is 1 in the assignment problem d. there are many differences between the transportation and assignment problems
C
The expected utility approach a. does not require probabilities. b. leads to the same decision as the expected value approach. c. is most useful when excessively large or small payoffs are possible. d. requires a decision tree.
C
The overall goal of portfolio models is to create a portfolio that provides the best balance between a. short-term and long-term investments. b. gains and losses. c. risk and return. d. liquidity and stability.
C
The parts of a network that represent the origins are a. the capacities b. the flows c. the nodes d. the arcs
C
The purchase of insurance and lottery tickets shows that people make decisions based on a. expected value. b. sample information. c. utility. d. maximum likelihood.
C
The range of feasibility measures a. the right-hand-side values for which the objective function value will not change. b. the right-hand-side values for which the values of the decision variables will not change. c. the right-hand-side values for which the dual prices will not change. d. each of these choices are true.
C
The trend pattern is easy to identify by using a. a moving average b. exponential smoothing c. regression analysis d. a weighted moving average
C
To find the EVSI, a. use the EVPI to calculate sample information probabilities. b. use indicator probabilities to calculate prior probabilities. c. use prior and sample information probabilities to calculate revised probabilities. d. use sample information to revise the sample information probabilities.
C
Which of the following approaches to decision making requires knowledge of the probabilities of the states of nature? a. minimax regret b. maximin c. expected value d. conservative
C
Which of the following is not a question answered by standard sensitivity analysis information? a. If the right-hand side value of a constraint changes, will the objective function value change? b. Over what range can a constraint's right-hand side value without the constraint's dual price possibly changing? c. By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility? d. By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality?
C
Which of the following is not true regarding the linear programming formulation of a transportation problem? a. Costs appear only in the objective function. b. The number of variables is (number of origins) x (number of destinations). c. The number of constraints is (number of origins) x (number of destinations). d. The constraints' left-hand side coefficients are either 0 or 1.
C
States of Nature
Can describe uncontrollable natural events such as floods or freezing temperatures.
In a transshipment problem, shipments
Can occur between any to nodes
Zero integer programming can be used for
Capital budgeting, facility location, and fixed charge/
Which of the following is not a quantitative technique for evaluating the accuracy of a time series modeling technique?
Constructing line graphs of the data
What is not a type a type of a integer programming model?
Continuous
Which of the following is a general rule for crashing activities?
Crash activities with zero slack.
. The field of management science a. approaches decision making rationally, with techniques based on the scientific method. b. concentrates on the use of quantitative methods to assist in decision making. c. is another name for decision science and for operations research. d. each of these choices are true.
D
27. To find the optimal solution to a linear programming problem using the graphical method a. find the feasible point that is the farthest away from the origin. b. find the feasible point that is at the highest location. c. find the feasible point that is closest to the origin. d. None of the alternatives is correct.
D
30. The volume that results in total revenue being equal to total cost is the a. profit mix. b. marginal volume. c. marginal cost. d. break-even point.
D
32. George Dantzig is important in the history of management science because he developed a. the scientific management revolution. b. powerful digital computers. c. World War II operations research teams. d. the simplex method for linear programming.
D
34. All of the following statements about a redundant constraint are correct EXCEPT a. A redundant constraint does not affect the optimal solution. b. A redundant constraint does not affect the feasible region. c. Recognizing a redundant constraint is easy with the graphical solution method. d. At the optimal solution, a redundant constraint will have zero slack.
D
34. Problem definition a. must involve the analyst and the user of the results. b. includes specific objectives and operating constraints. c. must occur prior to the quantitative analysis process. d. each of these choices are true.
D
38. The three assumptions necessary for a linear programming model to be appropriate include all of the following except a. proportionality b. additivity c. divisibility d. normality
D
A decision tree a. presents all decision alternatives first and follows them with all states of nature. b. presents all states of nature first and follows them with all decision alternatives. c. alternates the decision alternatives and states of nature. d. arranges decision alternatives and states of nature in their natural chronological order.
D
A decision tree provides a. a heuristic method for analyzing decisions. b. a deterministic approach to decision analysis. c. the absolute value of the decision. d. an objective way of determining the relative value of each decision alternative.
D
A marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories and there is a constraint that HD ≥ 100. The solution indicates that interviewing another homeowner during the day will increase costs by 10.00. What do you know? a. the objective function coefficient of HD is 10. b. the dual price for the HD constraint is 10. c. the objective function coefficient of HD is −10. d. the dual price for the HD constraint is −10.
D
A mutual fund manager must decide how much money to invest in Atlantic Oil (A) and how much to invest in Pacific Oil (P). At least 60% of the money invested in the two oil companies must be in Pacific Oil. A correct modeling of this constraint is a. 0.4A + 0.6P > 0. b. -0.4A + 0.6P > 0. c. 0.6A + 0.4P > 0. d. -0.6A + 0.4P > 0.
D
A section of output from The Management Scientist is shown here. Constraint Lower Limit Current Value Upper Limit 2 240 300 420 What will happen if the right-hand-side for constraint 2 increases by 200? a. Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same. b. The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same. c. The same decision variables will be positive, but their values, the objective function value, and the dual prices will change. d. The problem will need to be resolved to find the new optimal solution and dual price.
D
All of the following are true about a stationary time series except a. Its statistical properties are independent of time. b. A plot of the series will always exhibit a horizontal pattern. c. The process generating the data has a constant mean d. There is no variability in the time series over time.
D
Decision tree probabilities refer to a. the probability of finding the optimal strategy b. the probability of the decision being made c. the probability of overlooked choices d. the probability of an uncertain event occurring
D
Department 3 has 2500 hours. Transfers are allowed to departments 2 and 4, and from departments 1 and 2. If Ai measures the labor hours allocated to department i and Tij the hours transferred from department i to department j, then a. T13 + T23 − T32 − T34 − A3 = 2500 b. T31 + T32 − T23 − T43 + A3 = 2500 c. A3 + T13 + T23 − T32 − T34 = 2500 d. A3 − T13 − T23 + T32 + T34 = 2500
D
For a minimization problem, the optimistic approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
D
Gradual shifting of a time series to relatively higher or lower values over a long period of time is called a. periodicity. b. cycles. c. seasonality. d. trend.
D
Identification and definition of a problem a. is the final step of problem solving. b. cannot be done until alternatives are proposed. c. requires consideration of multiple criteria. d. is the first step of decision making.
D
If P(high) = .3, P(low) = .7, P(favorable | high) = .9, and P(unfavorable | low) = .6, then P(favorable) = a. .10 b. .27 c. .30 d. .55
D
If it is optimal for both players in a two-person, zero-sum game to select one strategy and stay with that strategy regardless of what the other player does, the game a. has more than one equilibrium point. b. will have alternating winners. c. will have no winner. d. has a pure strategy solution.
D
If the acceptance of project A is conditional on the acceptance of project B, and vice versa, the appropriate constraint to use is a a. multiple-choice constraint. b. k out of n alternatives constraint. c. mutually exclusive constraint. d. corequisite constraint.
D
If the payoff from outcome A is twice the payoff from outcome B, then the ratio of these utilities will be a. 2 to 1. b. less than 2 to 1. c. more than 2 to 1. d. unknown without further information.
D
In a transshipment problem, shipments a. cannot occur between two origin nodes. b. cannot occur between an origin node and a destination node. c. cannot occur between a transshipment node and a destination node. d. can occur between any two nodes.
D
In the general linear programming model of the assignment problem, a. one agent can do parts of several tasks. b. one task can be done by several agents. c. each agent is assigned to its own best task. d. one agent is assigned to one and only one task.
D
Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then a. B ≤ 5 b. A − .5B + C ≤ 0 c. .5A − B − .5C ≤ 0 d. −.5A + .5B − .5C ≤ 0
D
Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is a. Max 2M + 3B b. Min 4000 (M + B) c. Max 8000M + 12000B d. Min 2M + 3B
D
Let x1 and x2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer below indicates that project 2 can be done only if project 1 is done? a. x1 + x2 = 1 b. x1 + x2 = 2 c. x1 − x2 ≤ 0 d. x1 − x2 ≥ 0
D
Modern revenue management systems maximize revenue potential for an organization by helping to manage a. pricing strategies. b. reservation policies. c. short-term supply decisions. d. All of the alternatives are correct.
D
Sensitivity analysis is often referred to as a. feasibility testing. b. duality analysis. c. alternative analysis. d. postoptimality analysis.
D
The composite unit in DEA a. has as output a weighted average of the outputs of the individual units. b. has as input a weighted average of the inputs of the individual units. c. has outputs greater than or equal to the outputs of any individual unit. d. All of the alternatives are correct.
D
The dual price measures, per unit increase in the right hand side of the constraint, a. the increase in the value of the optimal solution. b. the decrease in the value of the optimal solution. c. the improvement in the value of the optimal solution. d. the change in the value of the optimal solution.
D
The maximization or minimization of a quantity is the a. goal of management science. b. decision for decision analysis. c. constraint of operations research. d. objective of linear programming.
D
The network flows into and out of demand nodes are what makes the production and inventory application modeled in the textbook a a. shortest-route model. b. maximal flow model. c. transportation model d. transshipment model
D
The objective of the transportation problem is to a. identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost. b. minimize the number of origins used to satisfy total demand at the destinations. c. minimize the number of shipments necessary to satisfy total demand at the destinations. d. minimize the cost of shipping products from several origins to several destinations.
D
The options from which a decision maker chooses a course of action are a. called the decision alternatives. b. under the control of the decision maker. c. not the same as the states of nature. d. All of the alternatives are true.
D
To develop a portfolio that provides the best return possible with a minimum risk, the linear programming model will have an objective function which a. minimizes the maximum risk. b. minimizes total risk. c. maximizes return and minimizes risk. d. maximizes the minimum return.
D
To select a value for α for exponential smoothing a. use a small α when the series varies substantially. b. use a large α when the series has little random variability. c. use a value between 0 and 1 d. All of the alternatives are true.
D
Values of utility a. must be between 0 and 1. b. must be between 0 and 10. c. must be nonnegative. d. must increase as the payoff improves.
D
When the utility function for a risk-neutral decision maker is graphed (with monetary value on the horizontal axis and utility on the vertical axis), the function appears as a. a convex curve. b. a concave curve. c. an 'S' curve. d. a straight line.
D
Which of the following is not a characteristic of assignment problems? a. costs appear in the objective function only b. the RHS of all constraints is 1 c. the value of all decision variables is either 0 or 1 d. the signs of constraints are always <
D
Which of the following is not an advantage of using decision tree analysis? a. the ability to see clearly what decisions must be made b. the ability to see clearly in what sequence the decisions must occur c. the ability to see clearly the interdependence of decisions d. the ability to see clearly the future outcome of a decision
D
(T/F) If an LP problem is not correctly formulated, the computer software will indicate it is infeasible when trying to solve it.
F
(T/F) In the LP formulation of a maximal flow problem, a conservation-of-flow constraint ensures that an arc's flow capacity is not exceeded.
F
C1j is
Distribution cost/Unit between source I and destination J.
Which of the following is always true about a critical activity?
ES = LS.
The efficiency of sample information is
EVSI/EVPI*(100%)
The difference between the transportation and assignment problem is that
Each supply and demand value is 1 in the assignment problem
An 0-1 variable can be used to determine:
Either/or constraints, mutually exclusive items, and set up costs.
(T/F) A constraint with non-zero slack will have a positive dual price, and a constraint with non-zero surplus will have a negative dual price.
F
(T/F) A dummy origin in a transportation problem is used when supply exceeds demand.
F
Mutually exclusive constraint:
In order for the sum of x1 and x2 to be less than or equal to one, either of the variables can have a value of one, or both variable can equal zero.
Rounding up method leads to a what solution?
Infeasible.
Deterministic
Known for sure like tax rate
The determination of the MSE-minimizing value of the wi is a non-linear optimization problem because
MSE is a non-linear objective function
Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is
Min 2M + 3B
Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is
Min 2M + 3B
Which of the following is a valid objective function for a linear programming problem?
Min 4x + 3y + (2/3)z
A decision maker who looks at the worst result for every decision, and chooses the decision with the least disappointing possibility is operating according to the
Minimax regret approach
A linear programming model in which some of the decision variables are restricted to integer variables is called
Mixed integer programming model.
To find the optimal solution to a linear programming problem using the graphical method
None of the alternatives is correct
Sensitivity analysis information in computer output is based in the assumption of
One coefficient changes
Binary values can be what?
Only 0 or 1
If Pij = the production of product i in period j, then to indicate that the limit on production of the company's three products in period 2 is 400,
P12 + P22 + P32 ≤ 400
Making a good decision
Required a clear understanding of decision alternatives, states of nature, payoffs
Model the expression for total revenue
Revenue = Profit - Cost
There are 5 different types of solution methods:
Rounding off, graphical solution, branch and bound method (2 variable), Gowary method, and Excel.
Constraints in a linear programming model would be equivalent to what in the transportation model?
Rows and columns of the transportation model.
The 100% Rule does not imply that the optimal solution will necessarily change if the percentage exceeds 100%.
T
(T/F) If the optimal solution to the LP relaxation problem is integer, it is the optimal solution to the integer linear program.
T
Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in
Standard form
(T/F) If x1 + x2 ≤ 500y1 and y1 is 0-1, then if y1 is 0, x1 and x2 will be 0.
T
(T/F) In a model involving fixed costs, the 0-1 variable guarantees that the capacity is not available unless the cost has been incurred.
T
Which is not a requirement of the transportation model?
Supply and demand must be equal./
The key characteristics of the balanced transportation problem are:
Supply equals demand.
(T/F) A decision strategy is a sequence of decisions and chance outcomes, where the decisions chosen depend on the yet to be determined outcomes of chance events.
T
(T/F) A transshipment constraint must contain a variable for every arc entering or leaving the node.
T
(T/F) After all probabilities and payoffs are placed on a decision tree, the decision maker calculates expected values at state of nature nodes and makes selections at decision nodes.
T
(T/F) An LP model for a large-scale production scheduling problem involving numerous products, machines, and time periods can require thousands of decision variables and constraints.
T
(T/F) Circular nodes in a decision tree indicate that it would be incorrect to choose a path from the node.
T
(T/F) Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints.
T
(T/F) Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs.
T
(T/F) EVPI equals the expected regret associated with the minimax decision.
T
(T/F) EVPI ≥ EVSI
T
(T/F) Expected value is the sum of the weighted payoff possibilities at a circular node in a decision tree.
T
(T/F) For the marketing research problem presented in the textbook, the research firm's objective is to conduct the market survey so as to meet the client's needs at a minimum cost.
T
(T/F) If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables, rounding down will always provide a feasible integer solution.
T
(T/F) If a transportation problem has four origins and five destinations, the LP formulation of the problem will have nine constraints.
T
(T/F) In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values.
T
(T/F) The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.
T
(T/F) The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.
T
(T/F) The shortest-route problem is a special case of the transshipment problem
T
(T/F) To properly interpret dual prices, one must know how costs were allocated in the objective function.
T
(T/F) Transshipment problem allows shipments both in and out of some nodes while transportation problems do not.
T
(T/F) When a route in a transportation problem is unacceptable, the corresponding variable can be removed from the LP formulation.
T
(T/F) Whenever total supply is less than total demand in a transportation problem, the LP model does not determine how the unsatisfied demand is handled.
T
A critical activity can be part of a noncritical path
T
A decision strategy is a sequence of decisions and chance outcomes, where the decisions chosen depend on the yet to be determined outcomes of chance events.
T
A feasible solution is a global optimum if there are no other feasible points with a better objective function value in the feasible region
T
A negative dual price indicates that increasing the right-hand side of the associated constraint would be detrimental to the objective
T
A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear
T
A risk avoider will have a concave utility function.
T
After all probabilities and payoffs are placed on a decision tree, the decision maker calculates expected values at state of nature nodes and makes selections at decision nodes.
T
Any feasible solution to a blending problem with pooled components is feasible to the problem with no pooling.
T
Circular nodes in a decision tree indicate that it would be incorrect to choose a path from the node.
T
Constraints in the LP models for crashing decisions are required to compare the activity's earliest finish time with the earliest finish time of each predecessor.
T
Decision alternatives are structured so that several could occur simultaneously.
T
Decision variables must be clearly defined before constraints can be written.
T
EVPI equals the expected regret associated with the minimax decision.
T
EVPI is always greater than or equal to EVSI.
T
Expected value is the sum of the weighted payoff possibilities at a circular node in a decision tree.
T
For a minimization problem, a point is a global minimum if there are no other feasible points with a smaller objective function value.
T
For any constraint, either its slack/surplus value must be zero or its dual price must be zero
T
Given two decision makers, one risk neutral and the other a risk avoider, the risk avoider will always give a lower utility value for a given outcome.
T
If the optimal value of a decision variable is zero and its reduced cost is zero, this indicates that alternative optimal solutions exist.
T
If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25.
T
In the case of functions with multiple local optima, most nonlinear optimization software methods can get stuck and terminate at a local optimum.
T
In the integer programming model it is desired to have the Variable x1 be exactly twice the value of the variable x2, the constraint would be written as x1-2x2=0.
T
Many linear programming algorithms such as the simplex method optimize by examining only the extreme points of the feasible region.
T
Maximizing the expected payoff and minimizing the expected opportunity loss result in the same recommended decision.
T
Nonlinear programming algorithms are more complex than linear programming algorithms
T
Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative and the payoff that may actually occur.
T
Sample information with an efficiency rating of 100% is perfect information.
T
Square nodes in a decision tree indicate that a decision must be made.
T
Expect value of sample information
The difference between the expected value of an optimal strategy based on sample information and the best expected value without any sample information is called...
EVSI/EVPI
The efficiency of sample information is...
Which of the following statements is INCORRECT regarding the disadvantages of simulation?
The larger the number of probablistic inputs a system has, the less likely a simulation will provide the best approach for studying the system.
Which of the following is not true regarding the linear programming formulation of a transportation problem?
The number of constraints is (number of origins) × (number of destinations).
Constraint:2 Lower Limit: 240 Current Value:300 Upper Limit:420 What will happen if the right-hand side for constraint 2 increases by 200?
The problem will need to be resolved to find the new optimal solution and dual price.
Utility
The purchase of insurance and lottery tickets shows the people make decision based on...
Range of feasibility
The range in which a resource can increase/decrease before the dual price changes.
Range of optimality
The range that the objective coefficient of X can vary before a new solution becomes optimal. i.e. You subtract the allowable increase and allowable decrease from the current value. And thus, the optimal solution will not change as long as the profit contribution of each Fliptop model is between ___ and ___.
Unit shipping distance is not used needed with what model?
The transportation mode.
A section of output from The Management Scientist is shown here. Variable: 1 Lower Limit: 60 Current Value: 100 Upper Limit: 120
The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.
A section of output from The Management Scientist is shown here: Variable: 1 Lower Limit: 60 Current Value: 100 Upper Limit: 120 What will happen to the solution if the objective function coefficient for variable 1 decrease by 20?
The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.
If a transportation problem has a dummy customer, then:
There are dummy arcs from the dummy supply node, no goods are supplied from the dummy supply node, and demand exceeds supply.
If customer 2 has a service time of 1.6, and if customer 3 has an interval time of 1.1 and a service time of 2.3, when will customer 3's service be completed?
There is not enough information to answer.
The problem which deals with the distribution of goods from several sources to several destinations is the
Transportation problem
A company makes two products from steel; one requires 2 tons of steel and the other requires 3 tons. There are 100 tons of steel available daily. A constraint on daily production could be written as: 2x1 + 3x2 <= 100 (T/F)
True
A company makes two products from steel; one requires 2 tons of steel and the other requires 3 tons. There are 100 tons of steel available daily. A constraint on daily production could be written as: 2x1 + 3x2 <= 100.
True
A company makes two products from steel; one requires 2 tons of steel and the other requires 3 tons. There are 100 tons of steel available daily. A constraint on daily production could be written as: 2x1 + 3x2 ≤ 100.
True
A consistency ratio greater than 0.10 indicates inconsistency in the pair-wise comparisons.
True
Stochastic
Unknown like demand
Profit, Loss, Risk
Utility reflects the decision makers attitude toward...
Must increase as payoff improves
Values of utility
A multiple choice constraint
When a model forces a choice between two things with a solution that would include x1=1 or x2=1 but both would not equal one (nor would both equal zero).
Risk Avoider
When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery, the decision maker is...
Co-requisite constraint:
Wherein if one facility is "constructed", the other one will also be constructed and vice versa. Written as x2=x1
Conservative Approach
Which methods for decision making without probabilities best protects the decision maker from undesirable results.
A snack food manufacturers buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is $6.00 and the price per unit of the Illinois corn is $5.50 Define variable that would tell how many units to purchase from each source.
X1 = # units from Iowa X2 = # units from Illinois
If a dual price/shadow price is zero, does this make sense?
Yes it does make sense, as it means that the overall profit will not change if more molding time etc. is made available. This is due to the fact that it is a non-binding constraint. If there is slack, that means there is a value of 0 for the dual price.
A simulation model uses the mathematical expressions and logical relationships of the a. real system. b. computer model. c. performance measures. d. estimated inferences.
a
Activities K, M and S immediately follow activity H, and their latest start times are 14, 18, and 11. The latest finish time for activity H a. is 11. b. is 14. c. is 18. d. cannot be determined.
a
For an activity with more than one immediate predecessor activity, which of the following is used to compute its earliest finish (EF) time? a. the largest EF among the immediate predecessors. b. the average EF among the immediate predecessors. c. the largest LF among the immediate predecessors. d. the difference in EF among the immediate predecessors.
a
Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done? a. x1 + x2 + x3 ≥ 2 b. x1 + x2 + x3 ≤ 2 c. x1 + x2 + x3 = 2 d. x1 − x2 = 0
a
Most practical applications of integer linear programming involve a. only 0-1 integer variables and not ordinary integer variables. b. mostly ordinary integer variables and a small number of 0-1 integer variables. c. only ordinary integer variables. d. a near equal number of ordinary integer variables and 0-1 integer variables.
a
Numerical values that appear in the mathematical relationships of a model and are considered known and remain constant over all trials of a simulation are a. parameters. b. probabilistic input. c. controllable input. d. events.
a
Rounded solutions to linear programs must be evaluated for a. feasibility and optimality. b. sensitivity and duality. c. relaxation and boundedness. d. each of these choices are true.
a
The 0-1 variables in the fixed cost models correspond to a. a process for which a fixed cost occurs. b. the number of products produced. c. the number of units produced. d. the actual value of the fixed cost.
a
The focus of smoothing methods is to smooth out a. the random fluctuations. b. wide seasonal variations. c. significant trend effects. d. long range forecasts.
a
The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal pattern is a. moving average b. mean squared error c. mean average error d. qualitative forecasting
a
The main difference between CPM and PERT is a. the use of different activity time estimates. b. PERT analysis is less expensive to conduct. c. PERT lends itself to computerization while CPM networks must be constructed manually. d. CPM integrates time and cost performance while PERT is based solely on time performance.
a
The process of generating probabilistic inputs and computing the value of the output is called a. simulation. b. verification. c. validation. d. implementation.
a
The solution to the LP Relaxation of a maximization integer linear program provides a. an upper bound for the value of the objective function. b. a lower bound for the value of the objective function. c. an upper bound for the value of the decision variables d. a lower bound for the value of the decision variables
a
Using a naive forecasting method, the forecast for next week's sales volume equals a. the most recent week's sales volume b. the most recent week's forecast c. the average of the last four weeks' sales volumes d. next week's production volume
a
Whenever a categorical variable such as season has k levels, the number of dummy variables required a. k - 1 b. k c. k + 1 d. 2k
a
Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables? a. supply chain design b. bank location c. capital budgeting d. product design and market share optimization
a
Which of the following exponential smoothing constant values puts the same weight on the most recent time series value as does a 5-period moving average? a. α = .2 b. α = .25 c. α = .75 d. α = .8
a
States of nature a. can describe uncontrollable natural events such as floods or freezing temperatures. b. can be selected by the decision maker. c. cannot be enumerated by the decision maker. d. All of the alternatives are true.
a (can describe uncontrollable natural events such as floods or freezing temperatures.)
1. Time series methods a. discover a pattern in historical data and project it into the future. b. include cause-effect relationships. c. are useful when historical information is not available. d. All of the alternatives are true.
a (discover a pattern in historical data and project it into the future.)
15. For a minimization problem, the conservative approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
a (minimax approach)
13. The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal effect is a. moving averages b. mean squared error c. mean average deviation d. qualitative forecasting methods
a (moving averages)
5. The focus of smoothing methods is to smooth a. the irregular component. b. wide seasonal variations. c. significant trend effects. d. long range forecasts.
a (the irregular component.)
19. Which of the following exponential smoothing constant values puts the same weight on the most recent time series value as does a 5-period moving average? a. α = .2 b. α = .25 c. α = .75 d. α = .8
a (α = .2)
To solve a linear programming problem with thousands of variables and constraints
a personal computer can be used
To solve a linear programming problem with thousands of variables and constraints
a personal computer can be used.
The 0-1 variables in the fixed cost models correspond to
a process for which a fixed cost occurs.
Assignment problems are cost minimization problems that CAN BE solved as
a profit maximization problem.
When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery, the decision maker is a. a risk avoider. b. a risk taker. c. an optimist. d. an optimizer.
a. a risk avoider.
28. Which of the following special cases does not require reformulation of the problem in order to obtain a solution? a. alternate optimality b. infeasibility c. unboundedness d. each case requires a reformulation.
a. alternate optimality
Decision tree probabilities refer to the probability of a. an uncertain event occurring. b. the decision being made. c. finding an optimal value. d. overlooked choices.
a. an uncertain event occurring.
24. Decision criteria a. are the ways to evaluate the choices faced by the decision maker. b. are the choices faced by the decision maker. c. must be unique for a problem. d. are the problems faced by the decision maker.
a. are the ways to evaluate the choices faced by the decision maker.
A convex function is a. bowl-shaped up. b. bowl-shaped down. c. elliptical in shape. d. sinusoidal in shape.
a. bowl-shaped up.
A convex function is a. bowl-shaped up. b. bowl-shaped down. c. elliptical in shape. d. sinusoidal in shape.
a. bowl-shaped up.
States of nature a. can describe uncontrollable natural events such as floods or freezing temperatures. b. can be selected by the decision maker. c. cannot be enumerated by the decision maker. d. All of the alternatives are true.
a. can describe uncontrollable natural
Activities K, M and S immediately follow activity H, and their latest start times are 14, 18, and 11. The latest finish time for activity H
a. is 11.
Activities K, M and S immediately follow activity H, and their latest start times are 14, 18, and 11. The latest finish time for activity H a. is 11. b. is 14. c. is 18. d. cannot be determined.
a. is 11.
When the number of blending components exceeds the number of storage facilities, the number of feasible solutions to the blending problem a. is reduced. b. is increased. c. is unchanged. d. is zero.
a. is reduced.
When the number of blending components exceeds the number of storage facilities, the number of feasible solutions to the blending problem a. is reduced. b. is increased. c. is unchanged. d. is zero.
a. is reduced.
26. The quantitative analysis approach requires a. mathematical expressions for the relationships. b. the manager's prior experience with a similar problem. c. a relatively uncomplicated problem.
a. mathematical expressions for the relationships.
For a minimization problem, the conservative approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
a. minimax approach
To determine how to crash activity times
a. normal activity costs and costs under maximum crashing must be known. b. shortest times with crashing must be known. c. realize that new paths may become critical. D. ALL THE ALTERNATIVES ARE TRUE
37. In what part(s) of a linear programming formulation would the decision variables be stated? a. objective function and the left-hand side of each constraint b. objective function and the right-hand side of each constraint c. the left-hand side of each constraint only d. the objective function only
a. objective function and the left-hand side of each constraint
23. Decision alternatives a. should be identified before decision criteria are established. b. are limited to quantitative solutions c. are evaluated as a part of the problem definition stage. d. are best generated by brain-storming.
a. should be identified before decision criteria are established.
33. Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in a. standard form. b. bounded form. c. feasible form. d. alternative form.
a. standard form.
22. Decision variables a. tell how much or how many of something to produce, invest, purchase, hire, etc. b. represent the values of the constraints. c. measure the objective function. d. must exist for each constraint.
a. tell how much or how many of something to produce, invest, purchase, hire, etc.
The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is a. the indifference probability. b. the lottery probability. c. the uncertain probability. d. the utility probability.
a. the indifference probability.
For an activity with more than one immediate predecessor activity, which of the following is used to compute its earliest finish (EF) time? a. the largest EF among the immediate predecessors. b. the average EF among the immediate predecessors. c. the largest LF among the immediate predecessors. d. the difference in EF among the immediate predecessors.
a. the largest EF among the immediate predecessors
For an activity with more than one immediate predecessor activity, which of the following is used to compute its earliest finish (EF) time?
a. the largest EF among the immediate predecessors.
When consequences are measured on a scale that reflects a decision maker's attitude toward profit, loss, and risk, payoffs are replaced by a. utility values. b. multicriteria measures. c. sample information. d. opportunity loss.
a. utility values.
The number of units shipped from origin i to destination j is represented by
a. xij
In CPM, for activities with more than one immediate predecessor activity, which of the following is used to compute its earliest finish (EF) time
a. largest EF among the immediate predecessors
The main difference between CPM and PERT is
a. the use of different activity time estimates.
Revenue management methodology was originally developed for
an airline
Which is not a significant challenge of project scheduling?
activities are independent.
The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means
agent 3 can be assigned to 2 tasks.
In a mixed integer linear programming model, some but not
all of decision variables are restricted to integer values.
The assignment problem is a transportation problem where
all supply and demand values are equal to one.
0-1 Integer Programming is when
all variables have variables of 0 or 1.
In an all-integer linear program,
all variables must be integer.
Pure-Integer Programming is when
all variables must have integer programming, some but not a programming.
All linear programming problems have all of the following properties EXCEPT
alternative optimal solution
A physical model that does not have the same physical appearance as the object being modeled is
an analog model
Rounding the solution of an LP Relaxation to the nearest integer values provides
an integer solution that might be neither feasible nor optimal.
The solution to the LP Relaxation of a maximization integer linear program provides
an upper bound for the value of the objective function.
A negative dual price for a constraint in a minimization problem means
as the right-hand side increases, the objective function value will decrease
Values for the probablistic inputs to a simulation
are randomly generated based on historical information.
Seasonal paterns
are regular repeated patterns.
In a mixed integer model, some of the decision variables (not all)
are required to have integer solutions.
Decision criteria
are the choices faced by the decision maker
Forecast errors
are the differences between actual and forecast values.
The overall priorities for decision alternatives
are the sum of the products of the criterion priority times the priority of the decision alternative with respect to that criterion, sum to 1, and indicate what choice is preferred but do not force that choice to be made (each of the above is true).
Decision Criteria
are the ways to evaluate the choices faced by the decision maker
Inputs to a quantitative model
are uncertain for a stochastic (unknown) model stochastic/probabilistic: unknown deterministic: known for sure
Inputs to a quantitative model
are uncertain for a stochastic model
Inputs to a quantitative model
are uncertain for a stochastic model.
A decision tree
arranges decision alternatives and states of nature in their natural chronological order.
A simulation model used in situations where the state of the system at one point in time does not affect the state of the system at future points in time is called a a. dynamic simulation model. b. static simulation model. c. steady-state simulation model. d. discrete-event simulation model.
b
A value for probabilistic input from a discrete probability distribution a. is the value given by the RAND() function. b. is given by matching the probabilistic input with an interval of random numbers. c. is between 0 and 1. d. must be non-negative.
b
Activities following a node a. can begin as soon as any activity preceding the node has been completed. b. have an earliest start time equal to the largest of the earliest finish times for all activities entering the node. c. have a latest start time equal to the largest of the earliest finish times for all activities entering the node. d. None of the alternatives is correct.
b
All of the following are true about qualitative forecasting methods except a. They generally involve the use of expert judgment to develop forecasts. b. They assume the pattern of the past will continue into the future. c. They are appropriate when past data on the variable being forecast are not applicable. d. They are appropriate when past data on the variable being forecast are not available.
b
All of the following are true about time series methods except a. They discover a pattern in historical data and project it into the future. b. They involve the use of expert judgment to develop forecasts. c. They assume that the pattern of the past will continue into the future. d. Their forecasts are based solely on past values of the variable or past forecast errors.
b
Arcs in a project network indicate a. completion times. b. precedence relationships. c. activities. d. the critical path.
b
Assuming W1, W2 and W3 are 0 -1 integer variables, the constraint W1 + W2 + W3 < 1 is often called a a. multiple-choice constraint. b. mutually exclusive constraint. c. k out of n alternatives constraint. d. corequisite constraint.
b
Forecast errors a. are the difference in successive values of a time series b. are the differences between actual and forecast values c. should all be nonnegative d. should be summed to judge the goodness of a forecasting model
b
If data for a time series analysis is collected on an annual basis only, which pattern does not need to be considered? a. trend b. seasonal c. cyclical d. horizontal
b
In order to verify a simulation model a. compare results from several simulation languages. b. be sure that the procedures for calculations are logically correct. c. confirm that the model accurately represents the real system. d. run the model long enough to overcome initial start-up results.
b
In situations where you need to compare forecasting methods for different time periods, the most appropriate accuracy measure is a. MSE b. MAPE c. MAE d. ME
b
Modeling a fixed cost problem as an integer linear program requires a. adding the fixed costs to the corresponding variable costs in the objective function. b. using 0-1 variables. c. using multiple-choice constraints. d. using LP relaxation.
b
Seasonal patterns a. cannot be predicted. b. are regular repeated patterns. c. are multiyear runs of observations above or below the trend line. d. reflect a shift in the time series over time.
b
Slack equals a. LF − EF. b. EF − LF. c. EF − LS. d. LF − ES.
b
The earliest start time rule a. compares the starting times of all activities for successors of an activity. b. compares the finish times for all immediate predecessors of an activity. c. determines when the project can begin. d. determines when the project must begin.
b
The graph of a problem that requires x1 and x2 to be integer has a feasible region a. the same as its LP relaxation. b. of dots. c. of horizontal stripes. d. of vertical stripes.
b
To perform sensitivity analysis involving an integer linear program, it is recommended to a. use the dual prices very cautiously. b. make multiple computer runs. c. use the same approach as you would for a linear program. d. use LP relaxation.
b
Using exponential smoothing, the demand forecast for time period 10 equals the demand forecast for time period 9 plus a. α times (the demand forecast for time period 8) b. α times (the error in the demand forecast for time period 9) c. α times (the observed demand in time period 9) d. α times (the demand forecast for time period 9)
b
When activity times are uncertain, a. assume they are normally distributed. b. calculate the expected time, using (a + 4m + b)/6. c. use the most likely time. d. calculate the expected time, using (a + m + b)/3.
b
Which is not a significant challenge of project scheduling? a. deadlines exist. b. activities are independent. c. many employees could be required. d. delays are costly.
b
Which of the following forecasting methods puts the least weight on the most recent time series value? a. exponential smoothing with α = .3 b. exponential smoothing with α = .2 c. moving average using the most recent 4 periods d. moving average using the most recent 3 periods
b
Which of the following is a general rule for crashing activities? a. Crash only non-critical activities. b. Crash activities with zero slack. c. Crash activities with the greatest number of predecessors. d. Crash the path with the fewest activities.
b
Which of the following is the most useful contribution of integer programming? a. finding whole number solutions where fractional solutions would not be appropriate b. using 0-1 variables for modeling flexibility c. increased ease of solution d. provision for solution procedures for transportation and assignment problems
b
Which of the following statements is INCORRECT regarding the advantages of simulation? a. Simulation is relatively easy to explain and understand. b. Simulation guarantees an optimal solution. c. Simulation models are flexible. d. A simulation model provides a convenient experimental laboratory for the real system.
b
11. A qualitative forecasting method that obtains forecasts through "group consensus" is known as the a. Autoregressive model b. Delphi approach c. mean absolute deviation d. None of these alternatives is correct.
b (Delphi approach)
10. The efficiency of sample information is a. EVSI*(100%) b. EVSI/EVPI*(100%) c. EVwoSI/EVwoPI*(100%) d. EVwSI/EVwoSI*(100%)
b (EVSI/EVPI*(100%))
3. Seasonal components a. cannot be predicted. b. are regular repeated patterns. c. are long runs of observations above or below the trend line. d. reflect a shift in the series over time.
b (are regular repeated patterns.)
6. Forecast errors a. are the difference in successive values of a time series b. are the differences between actual and forecast values c. should all be nonnegative d. should be summed to judge the goodness of a forecasting model
b (are the differences between actual and forecast values)
10. Causal models a. should avoid the use of regression analysis. b. attempt to explain a time series' behavior. c. do not use time series data. d. All of the alternatives are true.
b (attempt to explain a time series' behavior.)
17. Which of the following forecasting methods puts the least weight on the most recent time series value? a. exponential smoothing with α = .3 b. exponential smoothing with α = .2 c. moving average using the most recent 4 periods d. moving average using the most recent 3 periods
b (exponential smoothing with α = .2)
12. For a maximization problem, the conservative approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
b (maximin approach)
4. Making a good decision a. requires probabilities for all states of nature. b. requires a clear understanding of decision alternatives, states of nature, and payoffs. c. implies that a desirable outcome will occur. d. All of the alternatives are true.
b (requires a clear understanding of decision alternatives, states of nature, and payoffs.)
14. If data for a time series analysis is collected on an annual basis only, which component may be ignored? a. trend b. seasonal c. cyclical d. irregular
b (seasonal)
6. Which of the methods for decision making without probabilities best protects the decision maker from undesirable results? a. the optimistic approach b. the conservative approach c. minimum regret d. minimax regret
b (the conservative approach)
18. Using exponential smoothing, the demand forecast for time period 10 equals the demand forecast for time period 9 plus a. α times (the demand forecast for time period 8) b. α times (the error in the demand forecast for time period 9) c. α times (the observed demand in time period 9) d. α times (the demand forecast for time period 9)
b (α times (the error in the demand forecast for time period 9))
Which of the following is a general rule for crashing activities? a. Crash only non-critical activities. b. Crash activities with zero slack. c. Crash activities with the greatest number of predecessors. d. Crash the path with the fewest activities.
b. Crash activities with zero slack.
A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(25000) + (1 p)(5000). If the utility of 25,000 is 0 and of 5000 is 1, then the utility of 10,000 is a. .5 b. .6 c. .4 d. 4
b. .6
31. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is a. at least 1. b. 0. c. an infinite number. d. at least 2.
b. 0.
36. If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation? a. 300x1 + 125x2 > 4,000 b. 300x1 + 125x2 < 4,000 c. 425(x1 + x2) < 4,000 d. 300x1 + 125x2 = 4,000
b. 300x1 + 125x2 < 4,000
Which of the following is a general rule for crashing activities?
b. Crash activities with zero slack.
Slack equals a. LF − EF. b. EF − LF. c. EF − LS. d. LF − ES.
b. EF − LF
Slack equals
b. EF − LF.
The approach to determining the optimal decision strategy involves a. a forward (left to right) pass through the decision tree. b. a backward (right to left) pass through the decision tree. c. choosing the outcome of a chance event with the greatest probability. d. choosing the outcome of a chance event with the greatest payoff.
b. a backward (right to left) pass through the decision tree.
40. A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is a. a standard variable b. a slack variable c. a surplus variable d. a non-negative variable
b. a slack variable
Which is not a significant challenge of project scheduling?
b. activities are independent.
28. Inputs to a quantitative model a. must all be deterministic if the problem is to have a solution. b. are uncertain for a stochastic model. c. are a trivial part of the problem solving process. d. are uncontrollable for the decision variables.
b. are uncertain for a stochastic model.
When activity times are uncertain,
b. calculate the expected time, using (a + 4m + b)/6.
When activity times are uncertain, a. assume they are normally distributed. b. calculate the expected time, using (a + 4m + b)/6. c. use the most likely time. d. calculate the expected time, using (a + m + b)/3.
b. calculate the expected time, using (a + 4m + b)/6.
The earliest start time rule
b. compares the finish times for all immediate predecessors of an activity.
The earliest start time rule a. compares the starting times of all activities for successors of an activity. b. compares the finish times for all immediate predecessors of an activity. c. determines when the project can begin. d. determines when the project must begin.
b. compares the finish times for all immediate predecessors of an activity.
If the coefficient of each squared term in a quadratic function is positive, the function is a. concave. b. convex. c. elliptical. d. sinusoidal.
b. convex
If the coefficient of each squared term in a quadratic function is positive, the function is a. concave. b. convex. c. elliptical. d. sinusoidal.
b. convex.
29. The improvement in the value of the objective function per unit increase in a right-hand side is the a. sensitivity value. b. dual price. c. constraint coefficient. d. slack value.
b. dual price.
The difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information is called the a. information sensitivity. b. expected value of sample information. c. expected value of perfect information. d. efficiency of sample information.
b. expected value of sample information.
Activities following a node
b. have an earliest start time equal to the largest of the earliest finish times for all activities entering the node.
Activities following a node a. can begin as soon as any activity preceding the node has been completed. b. have an earliest start time equal to the largest of the earliest finish times for all activities entering the node. c. have a latest start time equal to the largest of the earliest finish times for all activities entering the node. d. None of the alternatives is correct.
b. have an earliest start time equal to the largest of the earliest finish times for all activities entering the node.
26. Slack a. is the difference between the left and right sides of a constraint. b. is the amount by which the left side of a ≤ constraint is smaller than the right side. c. is the amount by which the left side of a ≥ constraint is larger than the right side. d. exists for each variable in a linear programming problem.
b. is the amount by which the left side of a ≤ constraint is smaller than the right side.
For a maximization problem, the conservative approach is often referred to as the a. minimax approach. b. maximin approach. c. maximax approach. d. minimin approach.
b. maximin approach.
In the Bass model for forecasting the adoption of a new product, the objective function a. minimizes the sum of forecast errors. b. minimizes the sum of squared forecast errors. c. maximizes the number of adoptions. d. maximizes the number of adoptions and imitations.
b. minimizes the sum of squared forecast errors.
In the Bass model for forecasting the adoption of a new product, the objective function a. minimizes the sum of forecast errors. b. minimizes the sum of squared forecast errors. c. maximizes the number of adoptions. d. maximizes the number of adoptions and imitations.
b. minimizes the sum of squared forecast errors.
Arcs in a project network indicate
b. precedence relationships.
Arcs in a project network indicate a. completion times. b. precedence relationships. c. activities. d. the critical path.
b. precedence relationships.
Utility reflects the decision maker's attitude toward a. probability and profit. b. profit, loss, and risk. c. risk and regret. d. probability and regret.
b. profit, loss, and risk.
31. Management science and operations research both involve a. operational management skills. b. quantitative approaches to decision making. c. scientific research as opposed to applications. d. qualitative managerial skills.
b. quantitative approaches to decision making.
Making a good decision a. requires probabilities for all states of nature. b. requires a clear understanding of decision alternatives, states of nature, and payoffs. c. implies that a desirable outcome will occur. d. All of the alternatives are true.
b. requires a clear understanding of decision alternatives, states of nature, and payoffs.
In an influence diagram, decision nodes are represented by a. circles or ovals b. squares or rectangles c. diamonds d. triangles
b. squares or rectangles
Which of the following is not a parameter of the Bass model for forecasting adoption of a new product? a. the coefficient of innovation b. the coefficient of interaction c. the coefficient of imitation d. the estimated number of people to eventually adopt the new product
b. the coefficient of interaction
Which of the following is not a parameter of the Bass model for forecasting adoption of a new product? a. the coefficient of innovation b. the coefficient of interaction c. the coefficient of imitation d. the estimated number of people to eventually adopt the new product
b. the coefficient of interaction
Which of the methods for decision making best protects the decision maker from undesirable results? a. the optimistic approach b. the conservative approach c. minimum regret d. minimax regret
b. the conservative approach
33. The first step in problem solving is a. definition of decision variables. b. the identification of a difference between the actual and desired state of affairs. c. determination of the correct analytical solution procedure. d. implementation.
b. the identification of a difference between the actual and desired state of affairs.
The problem which deals with the distribution of goods from several sources to several destinations is the
b. transportation problem
A critical activity is one that
b. has no room for schedule slippage
In order to verify a simulation model
be sure that the procedures for calculations are logically correct.
The volume that results in total revenue being equal to total cost is the
break-even point
A critical activity is a. an activity that consumes no time but shows precedence between events. b. a milestone accomplishment within the project. c. an activity with zero slack. d. the beginning of an event.
c
A graphical tool that helps describe the logic of the simulation model is a a. Gantt chart. b. histogram. c. flowchart. d. stem-and-leaf display.
c
A quantity that is difficult to measure with certainty is called a a. risk analysis. b. project determinant. c. probabilistic input. d. profit/loss process.
c
Activities G, P, and R are the immediate predecessors for activity W. If the earliest finish times for the three are 12, 15, and 10, then the earliest start time for W a. is 10. b. is 12. c. is 15. d. cannot be determined.
c
Activities with zero slack a. can be delayed. b. must be completed first. c. lie on a critical path. d. have no predecessors.
c
All of the following are true about a cyclical pattern except a. It is often due to multiyear business cycles. b. It is often combined with long-term trend patterns and called trend-cycle patterns. c. It usually is easier to forecast than a seasonal pattern due to less variability. d. It is an alternating sequence of data points above and below the trend line.
c
Common features of simulations--generating values from probability distributions, maintaining records, recording data and summarizing results--led to the development of a. Excel and Lotus. b. BASIC, FORTRAN, PASCAL, and C. c. GPSS, SIMSCRIPT, SLAM, and Arena d. LINDO and The Management Scientist
c
In a model, x1 ≥ 0 and integer, x2 ≥ 0, and x3 = 0, 1. Which solution would not be feasible? a. x1 = 5, x2 = 3, x3 = 0 b. x1 = 4, x2 = .389, x3 = 1 c. x1 = 2, x2 = 3, x3 = .578 d. x1 = 0, x2 = 8, x3 = 0
c
In an all-integer linear program, a. all objective function coefficients must be integer. b. all right-hand side values must be integer. c. all variables must be integer. d. all objective function coefficients and right-hand side values must be integer.
c
Linear trend is calculated as . The trend projection for period 15 is a. 11.25 b. 28.50 c. 39.75 d. 44.25
c
One measure of the accuracy of a forecasting model is the a. smoothing constant b. linear trend c. mean absolute error d. seasonal index
c
Rounding the solution of an LP Relaxation to the nearest integer values provides a. a feasible but not necessarily optimal integer solution. b. an integer solution that is optimal. c. an integer solution that might be neither feasible nor optimal. d. an infeasible solution.
c
Sensitivity analysis for integer linear programming a. can be provided only by computer. b. has precisely the same interpretation as that from linear programming. c. does not have the same interpretation and should be disregarded. d. is most useful for 0 - 1 models.
c
The process of determining that the computer procedure that performs the simulation calculations is logically correct is called a. implementation. b. validation. c. verification. d. repetition.
c
The trend pattern is easy to identify by using a. a moving average b. exponential smoothing c. regression analysis d. a weighted moving average
c
Values for the probabilistic inputs to a simulation a. are selected by the decision maker. b. are controlled by the decision maker. c. are randomly generated based on historical information. d. are calculated by fixed mathematical formulas.
c
Which of the following is always true about a critical activity? a. LS = EF. b. LF = LS. c. ES = LS. d. EF = ES.
c
8. Linear trend is calculated as T_t = 28.5 + .75t. The trend projection for period 15 is a. 11.25 b. 28.50 c. 39.75 d. 44.25
c (39.75)
7. Sensitivity analysis considers a. how sensitive the decision maker is to risk. b. changes in the number of states of nature. c. changes in the values of the payoffs. d. changes in the available alternatives.
c (changes in the values of the payoffs.)
9. The multiplicative model a. uses centered moving averages to smooth the trend fluctuations. b. removes trend before isolating the seasonal components. c. deseasonalizes a time series by dividing the values by the appropriate seasonal index. d. provides a unique seasonal index for each observation of the time series.
c (deseasonalizes a time series by dividing the values by the appropriate seasonal index.)
3. A payoff a. is always measured in profit. b. is always measured in cost. c. exists for each pair of decision alternative and state of nature. d. exists for each state of nature.
c (exists for each pair of decision alternative and state of nature.)
14. For a maximization problem, the optimistic approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
c (maximax approach)
15. One measure of the accuracy of a forecasting model is the a. smoothing constant b. trend component c. mean absolute deviation d. seasonal index
c (mean absolute deviation)
12. The trend component is easy to identify by using a. moving averages b. exponential smoothing c. regression analysis d. the Delphi
c (regression analysis)
The measure of risk most often associated with the Markowitz portfolio model is the a. portfolio average return. b. portfolio minimum return. c. portfolio variance. d. portfolio standard deviation.
c. portfolio variance.
8. To find the EVSI, a. use the EVPI to calculate sample information probabilities. b. use indicator probabilities to calculate prior probabilities. c. use prior and sample information probabilities to calculate revised probabilities. d. use sample information to revise the sample information probabilities.
c (use prior and sample information probabilities to calculate revised probabilities.)
24. Which of the following statements is NOT true? a. A feasible solution satisfies all constraints. b. An optimal solution satisfies all constraints. c. An infeasible solution violates all constraints. d. A feasible solution point does not have to lie on the boundary of the feasible region.
c. An infeasible solution violates all constraints
Which of the following is always true about a critical activity?
c. ES = LS.
Which of the following is always true about a critical activity? a. LS = EF. b. LF = LS. c. ES = LS. d. EF = ES.
c. ES = LS.
Which of the following is not true regarding a concave function? a. It is bowl-shaped down. b. It is relatively easy to maximize. c. It has multiple local maxima. d. It has a single global maximum.
c. It has multiple local maxima.
Which of the following is not true regarding a concave function? a. It is bowl-shaped down. b. It is relatively easy to maximize. c. It has multiple local maxima. d. It has a single global maximum.
c. It has multiple local maxima.
Which of the following is not true regarding the linear programming formulation of a transportation problem?
c. The number of constraints is (number of origins) x (number of destinations).
35. All linear programming problems have all of the following properties EXCEPT a. a linear objective function that is to be maximized or minimized. b. a set of linear constraints. c. alternative optimal solutions. d. variables that are all restricted to
c. alternative optimal solutions.
27. A physical model that does not have the same physical appearance as the object being modeled is a. a qualitative model. b. a mathematical model. c. an analog model. d. an iconic model.
c. an analog model.
36. Which of the following is not one of the commonly used names for the body of knowledge involving quantitative approaches to decision-making? a. efficiency studies b. management science c. business analytics d. operations research
c. business analytics
Sensitivity analysis considers a. how sensitive the decision maker is to risk. b. changes in the number of states of nature. c. changes in the values of the payoffs. d. changes in the available alternatives.
c. changes in the values of the payoffs.
The difference between the transportation and assignment problems is that
c. each supply and demand value is 1 in the assignment problem
A payoff a. is always measured in profit. b. is always measured in cost. c. exists for each pair of decision alternative and state of nature. d. exists for each state of nature.
c. exists for each pair of decision alternative and state of nature.
Which of the following approaches to decision making requires knowledge of the probabilities of the states of nature? a. minimax regret b. maximin c. expected value d. conservative
c. expected value
25. A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called a. optimal. b. feasible. c. infeasible. d. semi-feasible.
c. infeasible.
28. Activities G, P, and R are the immediate predecessors for activity W. If the earliest finish times for the three are 12, 15, and 10, then the earliest start time for W
c. is 15.
Activities G, P, and R are the immediate predecessors for activity W. If the earliest finish times for the three are 12, 15, and 10, then the earliest start time for W a. is 10. b. is 12. c. is 15. d. cannot be determined.
c. is 15.
The expected utility approach a. does not require probabilities. b. leads to the same decision as the expected value approach. c. is most useful when excessively large or small payoffs are possible. d. requires a decision tree.
c. is most useful when excessively large or small payoffs are possible.
Activities with zero slack
c. lie on a critical path.
Activities with zero slack a. can be delayed. b. must be completed first. c. lie on a critical path. d. have no predecessors.
c. lie on a critical path.
35. A model that uses a system of symbols to represent a problem is called a. iconic. b. constrained. c. mathematical. d. analog.
c. mathematical.
For a maximization problem, the optimistic approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
c. maximax approach
The key idea behind constructing an index fund is to choose a portfolio of securities that a. is a mix of growth-oriented and income-oriented stocks. b. minimizes risk without sacrificing liquidity. c. mimics the performance of a broad market index. d. balances short-term and long-term investments.
c. mimics the performance of a broad market index.
The key idea behind constructing an index fund is to choose a portfolio of securities that a. is a mix of growth-oriented and income-oriented stocks. b. minimizes risk without sacrificing liquidity. c. mimics the performance of a broad market index. d. balances short-term and long-term investments.
c. mimics the performance of a broad market index.
The measure of risk most often associated with the Markowitz portfolio model is the a. portfolio average return. b. portfolio minimum return. c. portfolio variance. d. portfolio standard deviation.
c. portfolio variance.
25. In a multicriteria decision problem a. successive decisions must be made over time. b. it is impossible to select a single decision alternative. c. the decision maker must evaluate each alternative with respect to each criterion. d. each of these choices are true.
c. the decision maker must evaluate each alternative with respect to each criterion.
The parts of a network that represent the origins are
c. the nodes
30. As long as the slope of the objective function stays between the slopes of the binding constraints a. the value of the objective function won't change. b. there will be alternative optimal solutions. c. the values of the dual variables won't change. d. there will be no slack in the solution.
c. the values of the dual variables won't change.
To find the EVSI, a. use the EVPI to calculate sample information probabilities. b. use indicator probabilities to calculate prior probabilities. c. use prior and sample information probabilities to calculate revised probabilities. d. use sample information to revise the sample information probabilities.
c. use prior and sample information probabilities to calculate revised probabilities.
The purchase of insurance and lottery tickets shows that people make decisions based on a. expected value. b. sample information. c. utility. d. maximum likelihood.
c. utility.
A critical activity is
c. an activity with zero slack.
When activity times are uncertain,
calculate the expected time, using (a + 4m + b)/6.
The options from which a decision maker chooses a course of action are
called the decision alternatives, under the control of the decision maker, not the same as the states of nature (all of the above).
States of nature
can describe uncontrollable natural events such as floods or freezing temperatures.
In a transshipment problem, shipments
can occur between any two nodes
In a transshipment problem, shipments
can occur between any two nodes.
Sensitivity analysis considers
changes in the values of the payoffs.
Pair-wise comparisons are used to
compare criteria in terms of the overall goal and compare choices on each criterion (both a and b are true).
The earliest start time rule
compares the finish times for all immediate predecessors of an activity.
If the acceptance of project A is conditional on the acceptance of project B, and vice versa, the appropriate constraint to use is a
corequisite constraint.
A table of uniformly distributed random numbers should be read a. from left to right. b. from top to bottom. c. diagonally, starting from the top left corner and moving to the bottom right. d. in any consistent sequence.
d
All of the following are true about a stationary time series except a. Its statistical properties are independent of time. b. A plot of the series will always exhibit a horizontal pattern. c. The process generating the data has a constant mean d. There is no variability in the time series over time.
d
For an activity with more than one immediate successor activity, its latest-finish time is equal to the a. largest latest-finish time among its immediate successors. b. smallest latest-finish time among its immediate successors. c. largest latest-start time among its immediate successors. d. smallest latest-start time among its immediate successors.
d
Gradual shifting of a time series to relatively higher or lower values over a long period of time is called a. periodicity. b. cycles. c. seasonality. d. trend.
d
If customer 2 has a service time of 1.6, and if customer 3 has an interarrival time of 1.1 and a service time of 2.3, when will customer 3's service be completed? a. 5.0 b. 3.9 c. 3.4 d. There is not enough information to answer.
d
If the acceptance of project A is conditional on the acceptance of project B, and vice versa, the appropriate constraint to use is a a. multiple-choice constraint. b. k out of n alternatives constraint. c. mutually exclusive constraint. d. corequisite constraint.
d
In PERT, the activity duration time is equal to the a. pessimistic time. b. optimistic time. c. most likely time. d. mean duration.
d
In deciding which activities to crash, one must a. crash all critical activities. b. crash largest-duration activities. c. crash lowest-cost activities. d. crash activities on the critical path(s) only.
d
Let x1 and x2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer below indicates that project 2 can be done only if project 1 is done? a. x1 + x2 = 1 b. x1 + x2 = 2 c. x1 − x2 ≤ 0 d. x1 − x2 ≥ 0
d
PERT and CPM a. are most valuable when a small number of activities must be scheduled. b. have different features and are not applied to the same situation. c. do not require a chronological relationship among activities. d. have been combined to develop a procedure that uses the best of each.
d
Simulation a. does not guarantee optimality. b. is flexible and does not require the assumptions of theoretical models. c. allows testing of the system without affecting the real system. d. All of the alternatives are correct.
d
The critical path a. is any path that goes from the starting node to the completion node. b. is a combination of all paths. c. is the shortest path. d. is the longest path.
d
The number of units expected to be sold is uniformly distributed between 300 and 500. If r is a random number between 0 and 1, then the proper expression for sales is a. 200(r) b. r + 300 c. 300 + 500(r) d. 300 + r(200)
d
The word "uniform" in the term "uniform random numbers" means a. all the numbers have the same number of digits. b. if one number is, say, 10 units above the mean, the next number will be 10 units below the mean. c. all the numbers are odd or all are even. d. each number has an equal probability of being drawn.
d
To calculate an activity's latest finish time, you should consider its a. predecessors' latest finish times b. predecessors' latest start times c. successors' earliest start times d. successors' latest start times
d
To determine how to crash activity times a. normal activity costs and costs under maximum crashing must be known. b. shortest times with crashing must be known. c. realize that new paths may become critical. d. All of the alternatives are true.
d
To select a value for α for exponential smoothing a. use a small α when the series varies substantially. b. use a large α when the series has little random variability. c. use a value between 0 and 1 d. All of the alternatives are true.
d
When events occur at discrete points in time a. a simulation clock is required. b. the simulation advances to the next event. c. the model is a discrete-event simulation. d. All of the alternatives are correct.
d
Which of the following statements is INCORRECT regarding the disadvantages of simulation? a. Each simulation run only provides a sample of how the real system will operate. b. The summary of the simulation data only provides estimates about the real system. c. The process of developing a simulation model of a complex system can be time-consuming. d. The larger the number of probabilistic inputs a system has, the less likely a simulation will provide the best approach for studying the system.
d
9. If P(high) = .3, P(low) = .7, P(favorable|high) = .9, and P(unfavorable|low) = .6, then P(favorable) = a. .10 b. .27 c. .30 d. .55
d (.55)
1. The options from which a decision maker chooses a course of action are a. called the decision alternatives. b. under the control of the decision maker. c. not the same as the states of nature. d. All of the alternatives are true.
d (All of the alternatives are true.)
7. To select a value for α for exponential smoothing a. use a small α when the series varies substantially. b. use a large α when the series has little random variability. c. use any value between 0 and 1 d. All of the alternatives are true.
d (All of the alternatives are true.)
16. Which of the following is a qualitative forecasting method? a. trend projection b. time series method c. smoothing method d. Delphi method
d (Delphi method)
5. A decision tree a. presents all decision alternatives first and follows them with all states of nature. b. presents all states of nature first and follows them with all decision alternatives. c. alternates the decision alternatives and states of nature. d. arranges decision alternatives and states of nature in their natural chronological order.
d (arranges decision alternatives and states of nature in their natural chronological order.)
20. The time series component that is analogous to the seasonal component but over a longer period of time is the a. irregular component b. trend component c. causal component d. cyclical component
d (cyclical component)
13. For a minimization problem, the optimistic approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
d (minimin approach)
4. Short-term, unanticipated, and nonrecurring factors in a time series provide the random variability known as a. uncertainty. b. the forecast error. c. the residuals. d. the irregular component.
d (the irregular component.)
11. Decision tree probabilities refer to a. the probability of finding the optimal strategy b. the probability of the decision being made c. the probability of overlooked choices d. the probability of an uncertain event occurring
d (the probability of an uncertain event occurring)
2. Gradual shifting of a time series over a long period of time is called a. periodicity. b. cycle. c. regression. d. trend.
d (trend.)
If P(high) = .3, P(low) = .7, P(favorable | high) = .9, and P(unfavorable | low) = .6, then P(favorable) = a. .10 b. .27 c. .30 d. .55
d. .55
Which of the following is incorrect? a. A global optimum is a local optimum in a nonlinear optimization problem. b. A local maximum is a global maximum in a concave nonlinear optimization problem. c. A global minimum is a local minimum in a convex nonlinear optimization problem. d. A local optimum is a global optimum in a nonlinear optimization problem.
d. A local optimum is a global optimum in a nonlinear optimization problem.
Which of the following is incorrect? a. A global optimum is a local optimum in a nonlinear optimization problem. b. A local maximum is a global maximum in a concave nonlinear optimization problem. c. A global minimum is a local minimum in a convex nonlinear optimization problem. d. A local optimum is a global optimum in a nonlinear optimization problem.
d. A local optimum is a global optimum in a nonlinear optimization problem.
The options from which a decision maker chooses a course of action are a. called the decision alternatives. b. under the control of the decision maker. c. not the same as the states of nature. d. All of the alternatives are true.
d. All of the alternatives are true.
To determine how to crash activity times a. normal activity costs and costs under maximum crashing must be known. b. shortest times with crashing must be known. c. realize that new paths may become critical. d. All of the alternatives are true.
d. All of the alternatives are true.
34. All of the following statements about a redundant constraint are correct EXCEPT a. A redundant constraint does not affect the optimal solution. b. A redundant constraint does not affect the feasible region. c. Recognizing a redundant constraint is easy with the graphical solution method. d. At the optimal solution, a redundant constraint will have zero slack.
d. At the optimal solution, a redundant constraint will have zero slack.
27. To find the optimal solution to a linear programming problem using the graphical method a. find the feasible point that is the farthest away from the origin. b. find the feasible point that is at the highest location. c. find the feasible point that is closest to the origin. d. None of the alternatives is correct.
d. None of the alternatives is correct.
When the utility function for a risk-neutral decision maker is graphed (with monetary value on the horizontal axis and utility on the vertical axis), the function appears as a. a convex curve. b. a concave curve. c. an 'S' curve. d. a straight line.
d. a straight line.
A decision tree provides a. a heuristic method for analyzing decisions. b. a deterministic approach to decision analysis. c. the absolute value of the decision. d. an objective way of determining the relative value of each decision alternative.
d. an objective way of determining the relative value of each decision alternative.
A decision tree a. presents all decision alternatives first and follows them with all states of nature. b. presents all states of nature first and follows them with all decision alternatives. c. alternates the decision alternatives and states of nature. d. arranges decision alternatives and states of nature in their natural chronological order.
d. arranges decision alternatives and states of nature in their natural chronological order.
30. The volume that results in total revenue being equal to total cost is the a. profit mix. b. marginal volume. c. marginal cost. d. break-even point.
d. break-even point.
In deciding which activities to crash, one must
d. crash activities on the critical path(s) only.
In deciding which activities to crash, one must a. crash all critical activities. b. crash largest-duration activities. c. crash lowest-cost activities. d. crash activities on the critical path(s) only.
d. crash activities on the critical path(s) only.
. The field of management science a. approaches decision making rationally, with techniques based on the scientific method. b. concentrates on the use of quantitative methods to assist in decision making. c. is another name for decision science and for operations research. d. each of these choices are true.
d. each of these choices are true
34. Problem definition a. must involve the analyst and the user of the results. b. includes specific objectives and operating constraints. c. must occur prior to the quantitative analysis process. d. each of these choices are true.
d. each of these choices are true.
An investor can pick the mean-variance tradeoff that he or she is most comfortable with by looking at a graph of the a. feasible region. b. pooled components. c. rolling horizon. d. efficient frontier.
d. efficient frontier.
An investor can pick the mean-variance tradeoff that he or she is most comfortable with by looking at a graph of the a. feasible region. b. pooled components. c. rolling horizon. d. efficient frontier.
d. efficient frontier.
PERT and CPM
d. have been combined to develop a procedure that uses the best of each.
PERT and CPM a. are most valuable when a small number of activities must be scheduled. b. have different features and are not applied to the same situation. c. do not require a chronological relationship among activities. d. have been combined to develop a procedure that uses the best of each.
d. have been combined to develop a procedure that uses the best of each.
Identification and definition of a problem a. is the final step of problem solving. b. cannot be done until alternatives are proposed. c. requires consideration of multiple criteria. d. is the first step of decision making.
d. is the first step of decision making.
The critical path
d. is the longest path.
The critical path a. is any path that goes from the starting node to the completion node. b. is a combination of all paths. c. is the shortest path. d. is the longest path.
d. is the longest path.
For a minimization problem, the optimistic approach is often referred to as the a. minimax approach b. maximin approach c. maximax approach d. minimin approach
d. minimin approach
The objective of the transportation problem is to
d. minimize the cost of shipping products from several origins to several destinations.
Values of utility a. must be between 0 and 1. b. must be between 0 and 10. c. must be nonnegative. d. must increase as the payoff improves.
d. must increase as the payoff improves.
38. The three assumptions necessary for a linear programming model to be appropriate include all of the following except a. proportionality b. additivity c. divisibility d. normality
d. normality
The maximization or minimization of a quantity is the a. goal of management science. b. decision for decision analysis. c. constraint of operations research. d. objective of linear programming.
d. objective of linear programming.
Components that share a storage facility are called a. constrained components. b. indexed components. c. blended components. d. pooled components.
d. pooled components.
Components that share a storage facility are called a. constrained components. b. indexed components. c. blended components. d. pooled components.
d. pooled components.
For an activity with more than one immediate successor activity, its latest-finish time is equal to the
d. smallest latest-start time among its immediate successors.
For an activity with more than one immediate successor activity, its latest-finish time is equal to the a. largest latest-finish time among its immediate successors. b. smallest latest-finish time among its immediate successors. c. largest latest-start time among its immediate successors. d. smallest latest-start time among its immediate successors.
d. smallest latest-start time among its immediate successors.
To calculate an activity's latest finish time, you should consider its
d. successors' latest start times
Which of the following is not an advantage of using decision tree analysis? a. the ability to see clearly what decisions must be made b. the ability to see clearly in what sequence the decisions must occur c. the ability to see clearly the interdependence of decisions d. the ability to see clearly the future outcome of a decision
d. the ability to see clearly the future outcome of a decision
Decision tree probabilities refer to a. the probability of finding the optimal strategy b. the probability of the decision being made c. the probability of overlooked choices d. the probability of an uncertain event occurring
d. the probability of an uncertain event occurring
32. George Dantzig is important in the history of management science because he developed a. the scientific management revolution. b. powerful digital computers. c. World War II operations research teams. d. the simplex method for linear programming.
d. the simplex method for linear programming.
If the payoff from outcome A is twice the payoff from outcome B, then the ratio of these utilities will be a. 2 to 1. b. less than 2 to 1. c. more than 2 to 1. d. unknown without further information.
d. unknown without further information.
In PERT, the activity duration time is equal to the
d. mean duration.
An integer condition that some or all of the
decision variables be integer.
The steps of the scoring model include all of the following EXCEPT
develop a pair-wise comparison matrix for each criterion.
Problems involving integer variables are much more
difficult to solve than linear programming problems.
All the constraint coefficients in a transportation model are
equal to one.
A payoff
exists for each pair of decision alternative and state of nature.
Which of the following approaches to decision making requires knowledge of the probabilities of the states of nature?
expected value
Rounded solutions to linear programs must be evaluated for
feasibility and optimality.
The initial solution is the
feasible ble solution.
PERT and CPM
have been combined to develop a procedure that uses the best of each.
In a transportation problem, items are allocated
from sources to destinations at minimum costs.
The shortest-route problem finds the shortest-route
from the source to any other node.
The linear programming model for a transportation problem
has constraints for supply at each source and demand at each destination.
Media selection problems usually determine
how many times to use each media source
Media selection problems usually determine
how many times to use each media source.
Constraints in a transshipment problem
include a variable for every arc.
When testing for optimality using the stepping stone method, it helps calculate an
index.
Arcs in a transshipment problem
indicate the direction of the flow.
A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called
infeasible
In a total integer model, all the decision variables are required to have
integer solution values.
In a total integer model, all the decision variables are required to have
integer values of zero or one.
Activities G, P, and R are the immediate predecessors for activity W. If the earliest finish times for the three are 12, 15, and 10, then the earliest start time for W
is 15.
Expect Value
is equal to the expected opportunity loss
Slack
is the amount by which the left side of a <= constraint is small than the right side
Slack
is the amount by which the left side of a <= constraint is smaller than the right side
Slack
is the amount by which the left side of a =< constraint is smaller than the right side.
Slack
is the amount by which the left side of a £ constraint is smaller than the right side
Identification and definition of a problem
is the first step of decision making
The critical path
is the longest path.
Transportation, transshipment and assignment problems are part of linear programming models
known as network flow problems.
Activities with zero slack
lie on a critical path.
To perform sensitivity analysis involving an integer linear program, it is recommended to
make multiple computer runs.
Added integer requirements to a linear programming problem
makes the feasible solution smaller.
A transportation problem with n origins and m destinations will have how many constraints
n+m
The maximization or minimization of a quantity is the
objective of linear programming
The maximization or minimization of a quantity is the
objective of linear programming.
The steps in obtaining a solution of a transportation problem is
obtaining an initial solution, test solution for optimality, and improve sub optimal solution.
The graph of a problem that requires x1 and x2 to be integer has a feasible region
of dots.
In the general linear programming model of the assignment problem,
one agent is assigned to one and only one task.
Sensitivity analysis information in computer output is based on the assumption of
one coefficient change
Sensitivity analysis information in computer output is based on the assumption of
one coefficient change.
Sensitivity analysis information in computer output is based on the assumption of
one coefficient changes
Most practical applications of integer linear programming involve
only 0-1 integer variables and not ordinary integer variables.
The 100% Rule compares
proposed changes to allowed changes
A quantity that is difficult to measure with certainty is called a
probablistic input.
The sources in a transportation problem are
production facilities.
Management science and operations research both involve
quantitative approaches to decision making
The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the
range of optimality
The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the
range of optimality
The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the
range of optimality.
A simulation model uses the mathematical expressions and logical relationships of the
real system.
For a portfolio selection problem with the objective of maximizing expected return, the dual price for the available funds constraint provides information about the
return from additional investment funds
The overall goal of portfolio models is to create a portfolio that provides the best balance between
risk and return
The overall goal of portfolio models is to create a portfolio that provides the best brace between s
risk and return
A feasible solution is not ensure by
rounding down integer solution values
After solving a linear programming problem, one has fractional values for the decision variable. The problem demands that the solution be integer. The process of moving each fractional value to the nearest value to the nearest integer is
rounding.
If data for a time series analysis is collected on an annual basis only, which pattern does not need to be considered?
seasonal
The objective of the transportation problem is to
ship goods from supply to demand at the least cost.
Decision Alternatives
should be identified before decision criteria are established
States if Nature
should include all possible happenings
The transportation problem can be solved by the
simplex method.
When the value of the output cannot be determined even if the value of the controllable input is known, the model is
stochastic
In an influence diagram, decision nodes are represented by
squares or rectangles
Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in
standard form
A time-series which has no significant upward or downward trend is referred to as
stationary
If the transportation problem has a dummy customer, then:
supply equals demand, there is a dummy arc connecting the dummy customer, and no goods are sent to the dummy customer.
Decision Variable
tell how much or how many of something to produce, invest, purchase, hire etc.
Decision variables
tell how much or how many of something to produce, invest, purchase, hire etc.
Decision variables
tell how much or how many of something to produce, invest, purchase, hire, etc.
Conditional constraints:
the "Construction" of one facility is conditional upon the construction of another. X2<x1
In a multicriteria decision problem
the decision maker must evaluate each alternative with respect to each criterion
In a multicriteria decision problem
the decision maker must evaluate each alternative with respect to each criterion.
C1 in a transportation problem is
the destination.
The transportation problem assumes that the shipping costs are NOT directly dependent on
the distance that the goals are shipped.
A marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories and there is a constraint that HD ³ 100. The solution indicates that interviewing another homeowner during the day will increase costs by 10.00. What do you know?
the dual price for the HD constraint is -10
A marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories and there is a constraint that HD ≥ 100. The solution indicates that interviewing another homeowner during the day will increase costs by 10.00. What do you know?
the dual price for the HD constraint is −10.
We assume in the maximal flow problem that
the flow out of a node is equal to the flow into the node.
The first step in problem solving is
the identification of a difference between the actual and desired state of affairs
The first step in problem solving is
the identification of a difference between the actual and desired state of affairs.
The dual price measures, per unit increase in the right hand side,
the improvement in the value of the optimal solution.
All of the following are true about time series methods except
the involve the use of expert judgment to develop forecasts.
An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost. The correct interpretation of the dual price associated with the labor hours constraint is
the maximum premium (say for overtime) over the normal price that the company would be willing to pay.
An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost. The correct interpretation of the dual price associated with the labor hours constraint is
the maximum premium (say for overtime) over the normal price that the company would be willing to pay
The parts of a network that represent the origins are
the nodes
In an assignment problem, dummy people or jobs are created when
the number of people and jobs is equal.
When evaluating a decision tree
the probabilities following each state-of-nature branch must sum to one.
Decision tree probabilities refer to
the probability of an uncertain event occurring
A transportation problem where demand and supply are not equal,
the problem can be solved.
In an assignment problem where the number of jobs does not equal the number of people-
the problem can be solved. FO SHO!
The distributions place are
to somewhere else.
George Dantzig is important in the history of management science because he developed
the simplex method for linear programming
The primary determinants of computational difficulty for an 0-1 programming model is
the special structure of the model.
The two methods for testing optimality arw
the stepping stone method, modified Distribution Method (MODI).
The main difference between CPM and PERT is
the use of different activity time estimates
As long as the slope of the objective function stays between the slopes of the binding constraints
the values of the dual variables won't change
In an unbalanced transportation problem, a suppy node actually represents:
there is a shortage of goods.
A method of prohibiting a shipping route in a transportation problem is
to assign a shipping cost M to this route.
In a transportation problem , shipments from a dummy origin are used
to signify demand.
Gradual shifting of a time series to relatively higher or lower values over a long period of time is called
trend.
Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints
true
Whenever total supply is less than total demand in a transportation problem, the LP model does not determine how the unsatisfied demand is handled
true
The branch and bound method has
two variables.
In an assignment problem, if the number of persons is not the same as the number of jobs, then the problem is
unbalanced.
The transportation problem requires a
unit cost for every source and destination point.
In a transportation problem with a maximization objective on which there is a prohibited route, the method often used to prohibit such a route is
use a negative m cost to the route.
To find the EVSI,
use prior and sample information probabilities to calculate revised probabilities.
Which of the following is the most useful contribution of integer programming?
using 0-1 variables for modeling flexibility
Modeling a fixed cost problem as an integer linear program requires
using 0-1 variables.
A constraint with a positive slack value
will have a dual price of zero
A constraint with positive slack value
will have a dual price of zero
A constraint with a positive slack value
will have a dual price of zero Slack only occurs in non-binding constraints Dual values are zero for non-binding constraints because you don't use all the available resource in the first place anyway.
A constraint with a positive slack value
will have a dual price of zero.
Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then
−.5A + .5B − .5C ≤ 0