ARE 155 FINAL
Demand Node
(destination, sinks) denotes a location such as a retail outlet that consumes goods. Goods leave the nework at that node.
Origin
(source). A supply location or source in a transportation model.
Global Optimal Solution Input-Output Models Forward Pass Flow Out Flow IN Flow Balance and net-flow-balance equation Expected value and simulated value Coefficients - constraints and decision variables Columns in a database - an attribute of the row Dual Duality Local optimal solution Nonbinding Nonnegativity Parameters Primal Reduced cost Rows in a database - a record or member of the database Satisficing Service value chain
...
The underlying assumptions are: (queing)
1. Arrivals are FIFO. 2. There is no balking or reneging. 3. Arrivals are independent. 4. Arrivals are Poisson. 5. Service times are independent. 6. Average service rate exceeds average arrival rate.
The enumeration method is not a practical means of solving
5 x 5 or 7 x 7 problems because of the number of possible assignments to be considered. In the 5 x 5 case, there are 5! = (5 x 4 x 3 x 2 x 1) = 120 alternatives that need to be evaluated. In the 7 x 7 case, there are 7! = 5,040 alter
Redundant Constraint
A constraint that doesn't affect the feasible solution region.
Destination
A demand location in a tranportation model.
CPM
A deterministic network technique that is similar to PERT but uses only one time estimate. USe for monitoring budgets and project crashing.
Dummy Arc
A fictitious activity that consumes no time and is inserted into an AOA project network to display the proper precedence relationships between activities.
Consider the following constraint and its associated binary decision variables: XA + XB + XC ≥ 2. This constraint is an example of a(n):
A"k out of n choices constraint" - page 221-222
Gantt Chart
An alternative to project networks for showing a project schedule.
Supply Node
An origin or a source, denotes a lcation such as a factory that creates goods. Goods enter the nework at a node.
Deterministic Model
Assumes that all the relevant input data values are known with certainty; they assume that all the information needed for modeling a decision making problme environment is available, with fixed and known values. An example is deciding how many sections of a course to offer during a semester can be modeled as a deterministic
Uncapaciated ARC
Can support an unlimited flow, Not a constraint.
The objective of queuing theory is to minimize the ______ plus the ______ .
Cost of providing service Cost of waiting time
Impact of changes in RHS values of constraints is typically measured by the: A) reduced cost B) RHS allowable increase value C) RHS allowable decrease value D) shadow price E) objective function coefficients
D
Which of the following statements concerning the transshipment model are FALSE? A) A supply node is one where the total flow into the node is less than the total flow out of the node. B) A transshipment node is one where the total flow into the node equals the total flow of the node. C) The flow balance for a demand node should show a positive RHS value. D) The flow balance for a transshipment node should show a negative RHS value. E) The flow balance for a supply node should show a negative RHS value.
D
A constraint has a slack of 5 units. This implies that: A) this constraint has exceeded its minimal requirement by 5 units B) this constraint has consumed 5 units of its resource C) this constraint has a surplus of 5 units D) this constraint is binding E) this constraint has 5 units of its resource unconsumed
E
Bidirectional ARC
Flow can occur in either direction.
ARC
Line that connects 2 nodes together. Can be one way or two ways.
Node
Location of a specific point on the network. Can be origins, destinations, or transshipment.
Allowable increase OFC
Max amount by which the OFC a a decision variable can increase for the current optimal solution to remain optimal
Allowable decrease OFC
Max amount by which the OFC of a decision variable can decrease for the current optimal solution to remain optimal
Allowable increase RHS value
Max amount by which the RHS value of a constraint can increase for the shadow price to be valid
Variables
Measurable quantity that usually has a known value. May vary and subject to change. Can be controlled or uncontrolled.
#4. The staffing problems from Chapter 3 can have two differing types of objective functions. What the two types of objective functions>
Minimize cost or minimize the number of staff.
Can you have a surplus with a <= constraint?
NO
. The student should provide five realistic examples of IP..
One good exercise would be to require students to find five articles and use those as examples
In goal programming we use a ______ model as we cannot always achieve the contending goals.
Satisficing
Earliest starting time
Th earliest time that an activity can start without violation of precedence requirements.
Earliest finish time
The earliest time that an activity can be finished without violation of precedence requirements
There are several major differences between PERT and CPM.
With PERT, three estimates of activity time and completion are made. These are the optimistic, most likely, and pessimistic time estimates. From these estimates, the expected completion time and completion variance can be determined. CPM allows the use of crashing. This technique allows a manager to reduce the total project completion time by expending additional resources on activities within the network. CPM is used in determining the least-cost method of crashing a project or network.
7) In a maximal flow problem, all the net flows are typically: A) zero, +1, and -1 B) both +1 and -1 C) zero D) there are no rule to follow for the net flows for the maximal flow problems.
Zero
1. In the LP models the objective function component of the model is a: a. point estimate b. range of estimates c. can be either a point estimated or a range of estimates depending on the model used.
a
5. Slack is zero in a ______ constraint
a. Binding
18. A linear programming model generates an optimal solution with fractional values. This solution satisfies which basic linear programming assumption? a. certainty b. divisibility c. proportionality d. linearity e. non-negativity
b
20 PERT is a ____________ technique, whereas CPM is a _____________technique. a. probabilistic and deterministic b. deterministic and probabilistic c. both are probabilistic d. both are deterministic
b
Surplus is typically associated with which type of constraints? Also, where is the constraint in the LP model in Solve? _____________ A) ≤ B) ≥ C) = D) ≠ E) ±
b
Which of the following is note an assumption of the LP model: a. Certainty b. Proportionality c. Rationality d. Divisiblity
c
The minimal-spanning model is one that will find the best way to
connect all the nodes in a network together while minimizing the total distance between nodes or the total cost of connecting the nodes together. A number of decision modeling problems can be solved using this model: an example was given connecting water and power to a real estate development project. This model can also be used to determine the best way to deliver cable TV to households, connect computers on a computer network, install an oil pipeline, develop a natural gas network, and more.
What is the symbol used for underachieved goals?
di-
Surplus
differance between LHS and RHS of a >= constraint. Oversatisfaction of a requirement (LHS-RHS)
A change in a resource's availability (right-hand-side) changes the size of a
feasible region. An increase means more units of that resource are available, causing the feasible region to increase in size. A decrease means fewer units are available. Obviously, if more units of a binding resource are available, it may be possible for the optimal objective value to improve. In contrast, if more units of a non-binding resource are available, the additional units would just contribute to more slack and there would be no improvement in the optimal objective value.
The shortest-path model can be used to
install a phone cable between two major cities. Any time items must be moved from one place to another or something, like a cable, must be used to connect two points, the shortest-path model can be used.
. Simultaneous changes in input data values are extremely logical in many contexts. For example,
it may be possible to trade one type of resource for another, causing a decrease in the availability of one resource and an increase in the other's availability. Likewise, market conditions may cause us to simultaneously reduce the price of all our products, not just in a single product.
Crashing (crash time)
reducing a projects duration the shortest duration of an activity.
A constraint that does not affect the feasible region is a
redundant constraint
Deviation variables, similar to slack variables in LP, are the difference between
set goals and the current solution. In LP models, only "real" variables are used, representing physical quanitites
Critical activities have no
slack time
Decision variable
tell how much or how many of something to produce, invest, purchase, hire, etc.
When a system contains elements that exhibit chance in their behavior, the-- method of simulation may be applied.
the Monte Carlo method of simulation may be applied. The basis of Monte Carlo simulation is experimentation on the chance (or probabilistic) elements through random sampling. Monte Carlo steps: (1) set up probability distribution(s), (2) set up cumulative probabilities, (3) establish random number intervals, (4) generate random numbers, and (5) simulate trials.
. A problem can be unbounded if one or more constraints are missing, such that
the objective value can be made infinitely larger or smaller without violating any constraints (refer to Section 2.6 in the chapter).
The objective function of goal programming problem, in general form, is to:
to minimize the deviations
. A balanced transportation problem is one in which
total demand (from all destinations) is exactly equal to total supply (from all sources). If a problem is unbalanced, either the demand or the supply constraints must be inequalities.
To specify the entire table as the Changing Cells in Solver for a maximal-flow network model, we assign a capacity of
zero for all arcs that do not actually exist. This will prevent any flow on those arcs.
100% rule can be using to measure simultaneous changes in which of the following?
Either lhs or rhs but not both A rule used to verify the validity of the information in a Sensitivity Report when dealing with simultaneous changes to more than one RHS value or more than one OFC value
Unidirectional ARC
Flow can occur only in one direction as ina one way road.
Capacitated ARC
Has a limited capacity.
Binding Constraint
Intersect at the optimal corner point and are, hence exactly satisfied at the optimal solution.
. The requirements for an LP problem are listed in Section 2.2.
It is also assumed that conditions of certainty exist; that is, coefficients in the objective function and constraints are known with certainty and do not change during the period being studied. Another basic assumption that mathematically sophisticated students should be made aware of is proportionality in the objective function and constraints. For example, if one product uses 5 hours of a machine resource, then making 10 of that product uses 50 hours of machine time. LP also assumes additivity. This means that the total of all activities equals the sum of each individual activity. For example, if the objective function is to maximize Profit = 6X1 + 4X2, and if X1 = X2 = 1, the profit contributions of 6 and 4 must add up to produce a sum of 10.
Satisficing is a term used in GP because it is often not possible to
"optimize" a multi-goal problem. We come as close as possible to reaching goals.
Major steps are:
(1) define problem, (2) introduce important variables, (3) construct model, specify values to test, (4) conduct simulation, (5) examine results, (6) select best plan.
. Advantages of simulation:
1) relatively straightforward; (2) can solve large, complex problems; (3) allows "what if" questions; (4) does not interfere with real-world systems; (5) allows study of interactive variables; (6) allows time compression; (7) allows inclusion of real-world complications. Disadvantages; (1) cost; (2) no optimal solutions; (3) managers must generate conditions to test; (4) each model is unique.
The seven operating characteristics are:
1. Average number of customers in the system (L) 2. Average time spent in the system (W) 3. Average number in the queue (Lq) 4. Average time in the queue (Wq) 5. Utilization factor (ρ) 6. Percent idle time (Po) 7. Probability there are exactly n customers in the system (Pn)
1. Know term from chapters 3, 4, 5, 6, 7 2. Recognize constraints and objective functions And five short answer questions: 1. Know the models from chapters 4, 5, 6 2. Be able to write out objective functions for those chapters.
1. Know term from chapters 3, 4, 5, 6, 7 2. Recognize constraints and objective functions And five short answer questions: 1. Know the models from chapters 4, 5, 6 2. Be able to write out objective functions for those chapters.
A constraint has a surplus of 10 units. This implies that: A) this constraint has exceeded its minimal requirement by 10 units B) this constraint has consumed 10 units of its resource C) this constraint has a slack of 10 units D) this constraint has 10 units of its resource unconsumed E) this constraint is binding
A
In an unbalanced transportation problem where total demand exceeds total supply, the demand constraints will typically have: A) "≤" inequalities. B) "≥" inequalities C) both types of inequalities D) either but not both inequalities
A
Objective function
A mathematical statement of the goal of an organization, stated as an intent to maximize or minimize some important quantity, such as profit or cost.
PERT
A probabilistic modeling procedure that allows 3x estimates for each activity in a project. Optimismistic time, most likely time, pessimistic time.
Forward Pass
A procedure that moves from the beginning of a network to the end of the network. Used in determining an activity's est start and finish time.
backward Pass
A procedure that moves from the end of the network to the beginning of the network and is used in determining an activity's LFT and LST. It finds all the latest times
Sensitivity Analysis
A process that involves determining how sensitive a solution is to changes in the formulation of a problem. How sensitive an optimal solution is to model assumptions and to data change.
Constraints
A restriction that inhibits the value that can be achieved by the objective function.
Infeasible
A solution that satisfies the constraints of a linear programming problem except the nonnegativity constraints is called
Isoprofit Line
A straight line that represents all nonnegative combinations of the decision variables for a particular level.
max amount by which the rhs value of a constraint can decrease for the shadow price to be valid
Allowable decrease for RHS value
Transshipment Model
An extension of the transportation model in which some points have both flows in and out
Transshipment
An extension of the transportation model n which some points have both flows in and out
An activity is a task that requires a fixed amount of time and resources to complete.
An immediate predecessor is an activity that must be completely finished before another activity can be started.
What are the four classifications of arcs?
Answer: Unidirectional, bidirectional, capacitated, uncapacitated - Page 163
Probabilistic Models (stochastic)
Assume that some input data values are not known with certainty. They assume that the values of some important values of some important variables will not be known before decision are made. For example, their own career based on their choice of a major for their undergraduate study can be modeled as a probabilistic model.
Reduced Cost
Reduced Cost: This is the difference between the marginal contribution of a decision variable - usually its price, AND, the marginal worth of the resources the decision variable uses - usually measured no by the cost of the resources but by the shadow prices of the resources used.
Assume that the shadow price of a non-binding "≤" constraint is 5. This implies that: A) if the right-hand side value of the constraint increases by 1 unit, the objective function value will increase by 5 units B) if the right-hand side value of the constraint increases by 1 unit, the objective function value will decrease by 5 units C) if the right-hand side value of the constraint increases by 1 unit, the objective function value will remain unchanged D) if the right-hand side value of the constraint decreases by 1 unit, the objective function value will increase by 5 units E) if t
Shadow Price: The change in the objective function value for a one-unit change constraint's RHS value. Also, what is the shadow price of a non-binding constraint relative to a binding constraint? Answers: C and zero since a nonbinding constraint usually has slack - unused resources so adding one unit to unused resources does not have any effect as we see in this question.
RHS
The amount of resources available <= or the minimum requirement of some criterion (>= constraint) Constant in sensitivity report.
Slack Time CPN
The amount of time that an activity can be delayed with out delaying the entire project. Slack: LST-Est or LFT-EFT
Slack time in CPM
The amount of time that an activity can be delayed without delaying the entire project. Slack= LST-Est or LFT-EFT Free time for an activity
Cost of providing service - in queuing theory
The cost of providing a particular level of service
Cost of waiting time - in queuing theory
The cost to a firm of having customers or units waiting in line to be served
Slack
The difference between the RHS and LHS of a <=constraint unused resouces. (RHS-LHS)
Reduced Cost
The difference between the marginal contribution to the objective function value from the inclusion of a decision variable and the marginal worth of the resources it consumes. IF optimal value=0, its the min amount by which OFC can change.
Latest finish Time
The latest time than an activity can be finished without delaying the entire project
Latest Start time
The latest time that an activity can be started with out delaying the entire project.
A problem can have alternative optimal solutions if
The level profit or level cost line runs parallel to one of the problem's binding constraints (refer to Section 2.6 in the chapter).
Shadow Price
The magnitude of the change in the objective function value for a one unit increase in the RHS of a constraint
Decision variables
The unknown quantities in a problem for which optimal solution values are to be found. Examples include how many inventory items to order, how many courses to take this semester, how much money to invest in retirement plans this year, etc.
23. A constraint has a surplus of 10 units. This implies that a. this constraint has exceeded its minimal requirement by 10 units b. this constraint has consumed 10 units of its resource c. this constraint has a slack of 10 units d. this constraint has 10 units of its resource unconsumed e. this constraint is binding
a
A company wants to select one product from a set of 3 possible products. Which of the following ensures that only one product will be selected? a. XA + XB + XC = 1 b. XA + XB + XC ≤ 1 c. XA + XB + XC ≥ 1 d. XA + XB + XC ≥ 0 e. XA - XB - XC = 1
a
The component of the Monte Carlo simulation that is deterministic is the: a. expected value b. simulated value c. the final random distribution d. the initial probability distribution e. none of the answers are correct. The Monte Carlo model has no deterministic components
a
The presence of zeros in the Allowable Increase or Allowable decrease columns for objective function values indicates a.alternate optimal solution b. unbounded solution c. redundant constraint d. infeasible solution e. unique solution
a
Problem parameter
a measurable (usually known) quantity that is inherent in the problem. Examples include the cost of placing an order for more inventory items, the tuition payable for taking a course, the annual fees payable for establishing a retirement plan, etc.
In the ______ the objective is find the longest time path thru the network. It helps determine the_
a. CPM or critical path method Project schedule
In goal programming we want to minimize the ______ variables
a. Deviation
The ______ arc is used to balance the flow from the origin the to destination at the flow's highest level.
a. Dummy
In a balanced model for a transportation problem the ______ equals the ______ .
a. Flow in b. Flow out
In project management two tools used for high level reporting are the ______ and the ______ .
a. Gantt charts b. PERT charts
The last step in the graphical solution to a LP problem is to draw the ______ .
a. Isoprofit line or corner point
In the nonlinear models the reason we rerun the models is the presence of ______ .
a. Local optimal solution
There is more variability in the ______ chain compared to the ______ chain as we have more control over the processes in the latter than the former.
a. Service value b. value
. Of the components to a LP model, the ones that is not normally changed during sensitivity analysis or program modification are the ______.
a. constraint coefficients
The earliest activity start times are determined using a ______ through the project network
a. forward pass
In the diagrams of a network model we use ______ and ______ to represent the network.
a. nodes b. arcs
At the start of the class we discussed some of the terms used in LP. For the values or data that we would use we separated them into two classifications depending on how the vales varied in the models we used. The terms we used were ______ and ______.
a. variables b. parameters
The earliest activity start time is the earliest time that an
activity can be started after all predecessor activities are completely finished. The earliest activity start times are determined using a forward pass through the project network. The latest activity start time represents the latest time that an activity can be started without delaying the entire project. Latest activity start times are determined by making a backward pass through the network.
2. The economic interpretation of the constraint coefficients in a profit maximizing LP would best be described as: a. variables b. a horizontal supply function c. the upward sloping traditional supply function d. two of the answers are correct e. none of the answers provided are correct
b
21. In LP problem where integer constraints are used, all the decision variables can take on the values of: a. all positive integers b. all positive integers and zero c. all integer values and zero d. all integer values e. none of the answers provided are correct
b
6. Alternate optimal solutions has to do with: a. differing ways to set up the constraints that give the same optimal function value b. differing corner points that give the same optimal function value c. differing ways to set up the objective function formula d. all of the answers provided are correct
b
Rounding off the solution to an LP relaxed problem may yield: a.. an infeasible solution *b. a non-optimal solution c. a higher objective function value d. an unbounded solution e. A or B
b, e
10) A company wants to select 2 products from a set of four possible products. Which of the following constraints ensures that no more than 3 will be selected? A) XA + XB + XC + XD = 3 B) XA + XB + XC + XD ≥ 0 C) XA + XB + XC + XD ≤ 3 D) XA + XB + XC + XD ≥ 3 E) XA + XB + XC + XD ≠ 3
c
16. Consider the following linear programming model: Min 2X1 + 3X2 Subject to: X1 + 2X2 ≤ 1 X2 ≤ 1 X1 ≥ 0, X2 ≤ 0 This problem violates which of the following assumptions? a. additivity b. divisibility c. non-negativity d. proportionality e. linearity
c
27. In pricing out a new variable, the worth or value of resources consumed is typically measured by a. reduced costs b. the 100% rule c. shadow prices d. slack values e. surplus values
c
4. The assumption that precludes LP from having no synergy or economies of scale is: a. Linearity b. Sets c. Additivity d. Divisibility
c
5) The objective function of an assignment problem: A) maximization only B) minimization only C) may be either maximization or minimization. D) neither maximization nor minimization - it fits an equality
c
8. In the shortest-path LP model, the net flows take on the following values: a. +1 and -1 b. +1 only c. +1 and -1 and zero d. +1 and zero e. there is no general rule for the values of the net flows in the shortest-path models.
c
9. In the assignment models the net flows take on the following values: a. +1 and -1 b. +1 only c. +1 and -1 and zero d. +1 and zero e. there is no general rule for the values of the net flows in the assignment model
c
A company wants to select 2 products from a set of four possible products. Which of the following constraints ensures that no more than 3 will be selected? a. XA + XB + XC + XD = 3 b. XA + XB + XC + XD ≥ 0 c. XA + XB + XC + XD ≤ 3 d. XA + XB + XC + XD ≥ 3 e. XA + XB + XC + XD ≠ 3
c
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 nonnegative values
c
If a linear programming problem has alternate optimal solutions, then the ___________ will vary according to each alternate optimal point. a. objective function value b. objective function coefficients c. decision variable values d. two of the answers provided are correct e. none of the answers provided are correct - all values remain the same.
c
In a network diagram where noes "A" and "B" can start at the same time, the starting point that we would use would be noted on the diagram as: a. A-B b. A/B c. a dummy node d. we would just show A and B starting at the same time.
c
Maximal-flow models allow you to determine each of the following except: a. the maximum amount of throughput to a destination b. those that have capacitated arcs c. those that have uncapacitated arcs d. all of the answers are correct - the maximal-flow model gives all of this information. e. for systems that are one-way or two-way
c
Problems which can be stated as an assortment of desired objectives are known as: a. quadratic programming b. integer programming c. goal programming d. linear programming e. binary programming
c
The IP (Integer Programming) solution produces an objective function value: a. will be better (larger in a maximization problem for example) than the LP solution b. will be not as good as the LP solution c. can never be better than the LP solution d. it is not possible to compare the two solutions
c
The tool we discussed in class to build a data set for a pivot table from multiple sources was: a. Google drive or something like Google drive b. download and merge technique c. SQL d. just the simple download procedure
c
Which of the following is NOT a network flow model? A) Transportation model B) Assignment model C) Product mix model D) Shortest-path model E) Minimal-spanning tree model
c
13. In a balanced transshipment LP model, the net flow at the transshipment node could be: a. positive b. negative c. zero d. two of the options are correct e. all three of the options are correct
d
19. Consider the following linear programming model: Max X1 + X2 Subject to: X1 + X2 ≤ 2 X1 ≥ 1 X2 ≥ 3 X1, X2 ≥ 0 This linear programming model has a. alternate optimal solution b. unbounded solution c. redundant constraint d. infeasible solution e. unique solution
d
24. Impact of changes in RHS values of constraints is typically measured by the a. reduced cost b. RHS allowable increase value c. RHS allowable decrease value d. shadow price e. objective function coefficients
d
3. At start of the class we discussed the problems with getting good data for LP models, particularly with competing objectives. One of the tools we discussed to allow us to rank the objectives was: a. Numerating sets b. Dissemination c. Sizing d. Fuzzy pair-wise comparison
d
5. The ______________ is the magnitude of the change in the objective function value for a unit change in the RHS of a constraint a. constraint coefficient b. reduced cost c. flex value d. shadow price e. objective function marginal value
d
If a company produces Product A, then it must produce at least 200 units of Product A. Which of the following constraints model this condition? a. X1Y1 ≤ 200 b. X1 ≥ 200 + Y1 c. X1 ≤ 200Y1 d. X1 - 200Y1 ≥ 0 e. X1 > 200
d
The are problems in which all decision variables must have integer solutions: A) mixed binary IP problems B) pure binary IP problems C) mixed IP problems D) pure IP problems E) goal programming problems
d
The minimum amount the OFC of a variable should change in order to affect the optimal solution is the: a. objective function coefficient b. decision variable c. shadow price d. reduced cost c. allowable increase/decrease
d
The transportation model is an example of
decision making under certainty since the costs of each shipping route, the demand at each destination, and the supply at each source are all assumed to be known with certainty
The critical path consists of those activities that will cause a
delay in the entire project if they themselves are delayed. These critical path activities have zero slack. If they are delayed, the entire project is delayed. Critical path analysis is a way of determining the activities along the critical path and the earliest start time, earliest finish time, latest start time, and the latest finish time for every activity. It is important to identify these activities because if they are delayed, the entire project will be delayed
10. In the minimal spanning tree model the net flows take on the following values: a. +1 and -1 b. +1 only c. +1 and -1 and zero d. +1 and zero e. there is no general rule for the values of the net flows in the minimal spanning tree model
e
11. In the employee staffing LP problems, the RHS of the constraints are set to the following values: a. +1 and -1 b. +1 only c. +1 and -1 and zero d. +1 and zero e. there is no general rule for the values of the net flows in the employee staffing model
e
17. A redundant constraint is eliminated from a linear programming model. What effect will this have on the optimal solution? a. feasible region will decrease in size b. feasible region will increase in size c. a decrease in objective function value d. an increase in objective function value e. no change
e
20. Consider the following linear programming model Max 2X1 + 3X2 Subject to: X1 + X2 4 X1 2 X1, X2 0 This linear programming model has a. redundant constraints b. infeasible solution c. alternate optimal solution d. unique solution e. unbounded solution
e
26. Assume that the reduced cost of a decision variable is -$20 for a maximization problem. This implies that a. the objective function value will decrease by $20 if we do not produce any units of this product b. the objective function value will not change if we produce an additional unit of this product c. the objective function value will increase by $20 if we produce an additional unit of this product d. the shadow price value will decrease by $20 if we produce an additional unit of this product e. the objective function value will decrease by $20 if we produce an additional unit of this product
e
9) Rounding off the solution to an LP relaxed problem may yield: A) an infeasible solution B) a non-optimal solution C) a higher objective function value D) an unbounded solution E) A or B
e
A constraint has a slack of 5 units. This implies that: a. this constraint has exceeded its minimal requirement by 5 units b. this constraint has consumed 5 units of its resource c. this constraint has a surplus of 5 units d. this constraint is binding e. this constraint has 5 units of its resource unconsumed
e
If a company produces product A then it must also produce either product B or product C. Which of the following constraints enforces this condition? a. XA - XB - XC ≥ 0 b. XA + XB + XC ≤ 2 c. XA + (XB - XC) ≤ 0 d. XA + XB + XC ≥ 2 e. XA - XB - XC ≤ 0
e
If all the variables in a model are under the control of the decision maker, then the model is considered to be: A) probabilistic B) random C) mathematical D) schematic E) deterministic
e
The technique of randomly generating values for unknown elements in a model using random sampling is known as ________. A) optimization B) Markov analysis C) discrete-event simulation D) simulation gaming E) Monte Carlo simulation
e
Which of the following is not a network model: a. Transportation model b. Transshipment c. .Assignment model d. Maximal flow model e. Allocation model
e
Which of the following is not a property of an LP model: a. All problems have an objective function b. The objective function gives an optimal solution and possibly multiple optimal solutions. c. All problems have at least one constraint d. There must be at least two alternative decisions available e. Interactions are allowed
e
Which of the following models determines the path through the network that connects all the points? A) Transportation model B) Assignment model C) Product mix model D) Shortest-path model E) Minimal-spanning tree model
e
The queuing problem concerns the question of
finding the ideal level of service that an organization should provide. The three components of a queuing system are arrivals, waiting line, and service facility.
We use the 100% rule to verify
if the shadow prices in the current Sensitivity Report are still valid to analyze the impact of a proposed simultaneous change in input data values. To analyze a simultaneous change, we compute the ratio of each proposed change in a parameter's value to the maximum allowable change in its value, as given in the Sensitivity Report. The sum of these ratios must not exceed 1 (or 100%) in order for the information given in the current Sensitivity Report to be valid. If the sum of the ratios does exceed 1, the current information may still be valid; we just cannot guarantee its validity. However, if the ratio does not exceed 1, the information is defin
Refer to the figure. Excluding the non-negativity constraint, this model has: a. 6 decision variables b. 7 decision variables c. 8 decision variables including the dummy arc d. 5 decision variables e. none of the above
look at key
. A flow balance constraint calculates the net flow at a
node (that is, the difference between the total flow on all arcs entering the node and the total flow on all arcs leaving the node). At each source node, the net flow is expressed as a negative quantity, and represents the amount of flow created at the node. At each destination node, the net flow is expressed as a positive quantity, and represents the amount of flow consumed at the node. At each pure transshipment node, the net
Networks consist of _ that are connected by_
nodes, arcs
PERT and CPM are two popular _ techniques Pert is a _ technique, and cpm is a _technique
project management probabilistic, deterministic
The shadow price of a resource indicates the
the marginal value of each additional unit of that resource to the firm. In an LP model with several resources, this information helps the firm to prioritize its resources in terms of their marginal value.
The maximal-flow model can be used to determine the
the maximum number of cars that can flow through a road system, the number of gallons of chemicals that can flow through a chemical processing plant, the barrels of oil that can go through a pipeline network, the number of people that can use public transportation to get to work, the number of pieces of mail that can go through a mail service, and more. Any time that material or items flow through a network, the maximal-flow model can be used.
A change in an objective function coefficient changes
the slope of the objective function, with respect to that variable. The change in the slope may be sufficient to make a different corner point become the new optimal solution to the LP model.
