MGMT 101

Dual values are ___ for non-binding constraints because they have slacks

0

Infeasibility means that the number of solutions to the linear programming model that satisfies all constraints is

0

Note that slack variables have coefficients of

0 in the objective function

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

0.5B -0.5A - 0.5C <= 0

What constant for alpha would mimic the naive method?

1

What do you set the first and last node of a shortest route model to?

1

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

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 + 200(r)

If a 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

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

How do you solve a decision tree?

Any decision tree can be solved by rolling it back Start at the end of the tree and proceed towards the beginning Every time you encounter a chance node (circle), replace it with its expected value Every time you encounter a decision node (rectangle), choose the best alternative

Exponential smoothing

Applies differential weights to different time periods Pretty much does what weighted moving averages does except you only need to apply 1 weight.

Assignment problems

Assign one job to one machine, one person to one job, one salesperson to one territory. The key feature is that is involves one on each side of the assignment

What does a maximin approach assume?

Assume the worst and make the best of it (worst of d1 and d2, then the best between them)

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

Let x1 and x2 be binary (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

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

Multiple choice (choose 1 and only 1)

D1 + D2 + D3 = 1

K out of N constraint (want to choose 2; at most want to choose 2)

D1 + D2 + D3 = OR ≤ 2

Mutually exclusivity (choose one or the other but not more than 1, but you don't have to choose 1 at all)

D1 + D2 + D3 ≤ 1

Corequisite constraint (if you do D1 you have to do D2, and if you don't do D1 you can't do D2)

D1 = D2

Conditional constraint (can only do D1 if you do D2)

D1 ≤ D2

What happens when slack variables are added to each constraint and to the objective function?

Doing so transforms a linear program into its standard form

(EVPI/EVSI) uses Bayes Theorem

EVSI

Minimax regret

First translate consequences into opportunity losses (regrets) by comparing each consequence to the best for each state of nature Identify the highest regret for each alternative and ignore the rest/choose the alternative with the lowest of the highest regrets

The relationship d = 5000 − 25p describes what happens to demand (d) as price (p) varies. Here, price can vary between $10 and $50. How many units can be sold at the $10 price? How many can be sold at the $50 price?

For p = 10, d = 4750 For p = 50, d = 3750

Consider prices of $20, $30, and $40. Which of these three price alternatives will maximize total revenue? What are the values for demand and revenue at this price?

For p = 20, d = 4500, TR = $90,000 For p = 30, d = 4250, TR = $127,500 For p = 40, d = 4000, TR = $160,000 (maximum total revenue)

Moving averages

Forecast the next time period by averaging the preceding k time periods, and then move that average along the time series

What are the steps to problem solving?

Identify and define problem Determine alternative solutions Determine evaluation criteria Evaluate alternatives Choose best alternative implement the decision Evaluate the results IDDECE

Weighted moving averages

Instead of simply averaging, apply different weights to different time periods. Weights are positive numbers that will add to 1.

The critical path

Is the longest path

There are basically two ways to balance expected return and risk

Maximize expected returns subject to some maximum risk Minimize risk subject to some minimum expected return

What are the key objectives of an linear program of an optimal portfolio?

Maximizing expected rate of return and minimizing investment risk

A snack food manufacturer 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. Develop an objective function that would minimize the total cost.

Min 6x1 + 5.5x2

Model the expression for total revenue.

TR = p(5000 − 25p)

Maximizing expected values

Takes all consequences into consideration at their probability

Transportation problems

The most effective way to move products from a place of origin (supply) to a destination (demand)

How to develop a linear program?

Understand the problem Describe the objective Define the decision variables Describe each constraint Write the objective function in terms of decision variables

How to model seasonal patterns?

Using dummy variables in multiple regression models, treating the seasons as categorical varaibles

What is the formula for exponential smoothing?

What happened * alpha + (1 - alpha)*forecast for that time period

High values give a higher weight to the most recent time periods so are a) less smooth b) more smooth

a

What is management science?

a collection of quantitative methods to support managerial decision making based on the scientific method

The approach to determining the optimal decision strategy involves

a forward (left to right) pass through the decision tree

Uncertainty of a simulation must be described with

a particular probability distribution

What is a way to model the objective of a max flow problem?

add an additional arc from the destination node back to the origin node, which would have no capacity constraint, and maximize flow through this arc

Revenue management methodology was originally developed for

an airline

Applications are usually based on

an iterative process that involves managers and management science

Fixed costs

are independent of the decision variables

Decision criteria

are the ways to evaluate the choices faced by the decision maker

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

How are chance events often modeled?

as mutually exclusive and collectively exhaustive outcomes (states of nature)

A negative dual price for a constraint in a minimization problem means

as the right-hand side increases, the objective function value will decrease

Static models

assume each trial is independent

How can we address the problem with forecasting errors?

average absolute errors or average squared errors

How do we adjust for scale effects?

average absolute percentage errors

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

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 non-negative. d) should be summed to judge the goodness of a forecasting model.

b

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

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

In a transshipment problem, shipments

can occur between any two nodes

What are the two scenarios of traditional sensitivity analysis?

changes in objective function coefficients and changes to the right hand side values of constraints

What-if analysis

changes some of the input parameters to study the impact of these changes on the outputs

What is sensitivity analysis?

changes to the objective function or changes to the constraints and how these changes affect the optimal solution

Chance nodes are depicted with

circles

Fixed setup costs

costs you incur only if you decide to produce something and are independent of production quantity

Cyclical impacts are often based on

cyclical changes in the economy like recessions

Times series data

data that have been obtained in regular intervals

Relevant cost

depend on the decision variables

Index funds

designed to mimic the performance of the stock market as a whole

Consequence/payoff nodes are depicted with

diamonds

Waiting time (queueing models) are dynamic/static

dynamic

The word "uniform" in the term "uniform random numbers" means

each number has an equal probability of being drawn

The difference between the transportation and assignment problems is that

each supply and demand value is 1 in the assignment problem

Expected value of perfect information (EVPI)

expresses how much better we would be if we knew what was going to happen (uncertainty is known)

A four-period moving average forecast for period 10 would be found by averaging the values from periods 10, 9, 8, and 7 (T/F)

false

A path through a project network must reach every node (T/F)

false

A transportation problem with 3 sources and 4 destinations will have 7 decision variables (T/F)

false

All quarterly time series contain seasonality (T/F)

false

Alternative optimal solutions occur when there is no feasible solution to the problem. (T/F)

false

An alpha (α) value of 0.2 will cause an exponential smoothing forecast to react more quickly to a sudden drop in demand than will an α equal to 0.4 (T/F)

false

Any change to the objective function coefficient of a variable that is positive in the optimal solution will change the optimal solution (T/F)

false

Computer-generated random numbers are normally distributed (T/F)

false

Cyclical impacts are possible to predict (T/F)

false

Decision alternatives are structured so that several could occur simultaneously (T/F)

false

Decision variables limit the degree to which the objective in a linear programming problem is satisfied. (T/F)

false

Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940's. (T/F)

false

In an all-integer linear program all objective function coefficients and right-hand side values must be integer (T/F)

false

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution (T/F)

false

Inputs to a quantitative model must all be deterministic if the problem is to have a solution. (T/F)

false

Long term changes can only be linear (never nonlinear) (T/F)

false

Maximax, maximin, and minimax regret require probabilities (T/F)

false

Maximizing expected values accounts for risk (T/F)

false

Modern project management depends on either PERT or CPM (T/F)

false

Only binding constraints form the shape (boundaries) of the feasible region. (T/F)

false

Payoff tables can be used for more complicated, sequential decision situations (T/F)

false

Revenue management methodology was originally developed for the banking industry (T/F)

false

Rounding the solution of a regular linear program is the same as integer linear programming (T/F)

false

Sensitivity analysis cannot be used to examine how changes in any value impact the results of the analysis (in particular the preferred alternative) (T/F)

false

Simulation is an optimization technique (T/F)

false

The dual value associated with a constraint is the change in the value of the solution per unit decrease in the right-hand side of the constraint (T/F)

false

The earliest start time for an activity is equal to the smallest of the earliest finish times for all its immediate predecessors (T/F)

false

The field of management science concentrates on the use of qualitative methods to assist in decision making. (T/F)

false

The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is fully structured. (T/F)

false

The parameters of a simulation model are the controllable inputs (T/F)

false

The terms 'stochastic' and 'deterministic' have the same meaning in quantitative analysis. (T/F)

false

The variance in the project completion time is the sum of the variances of all activities in the project (T/F)

false

There is a dual value for every decision variable in a model (T/F)

false

Transshipment problems are less complicated (T/F)

false

Uncontrollable inputs are the decision variables for a model (T/F)

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 (T/F)

false

You must specify variables as binary in a shortest route problem (T/F)

false

You must specify variables as binary in an assignment problem (T/F)

false

If you increase expected return requirements (%), variance will probably

go up (correlated)

Media selection problems usually determine

how many times to use each media source

What is the risk premium

how much the company is willing to forgo in order to get rid of the risk

LP relaxation

ignore the integer constraints for a moment and treat the program as a regular linear programming situation

Range of feasibility is ___ for non-binding constraints

infinity

Cyclical impacts

irregular deviations from a trend

Slack

is the amount by which the left side of a <= constraint is smaller than the right side

Deterministic

known for sure

A simulation cosists of

many what-if analysis performed with different values for the uncertain input parameters

A model that uses a system of symbols to represent a problem is called

mathematical

For a maximization problem, the conservative approach is often referred to as the

maximin approach

Blending problems arise whenever a manager must decide how to

mix two or more resources to produce one or more products

Maximizing expected values is based on

monetary payoffs and probabilities

Low values give a higher weight to

more distant time period and are more smooth

What are the three smoothing techniques?

moving averages, weighted moving averages, and exponential smoothing

Infeasibility

not every constraint can be simultaneously satisfied. Thus, there is no feasible region and no possible (let alone optimal) solution

Unbounded situations

occurs if the constraints are not restrictive enough to prevent the objective function from becoming infinitely high or infinitely small

Sensitivity analysis information in computer output is based on the assumption of

one coefficient changes

Maximax

optimistic; Identify the best consequence for each alternative and ignore the others/choose the alternative with the best of the best consequence

Maximin

pessimistic/conservative; Identify the worst consequence for each alternative and ignore others/choose the alternative with the best of the worst consequence

American airlines

pioneered the use of linear programming to determine how many tickets should be sold at discount vs. full price

The measure of risk most often associated with the Markowitz portfolio model is the

portfolio variance

What is the problem with simply averaging forecast errors?

positive and negative errors cancel out and it can only give information about systematic bias (over/under predicting)

What is another term for sensitivity analysis?

post-optimality analysis

Arcs in a project network indicate

precedence relationships

A quantity that is difficult to measure with certainty is called a

probalistic input

Dual values will remain true as long as the hours remain within

range of feasibility

Decision nodes are depicted with

rectangles

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

Dynamic models

refer to simulations that change over time where trials are not independent

Long term changes are modeled using

regression analysis

Sesonal impacts

regular recurring patterns

Should fixed and/or relevant costs be reflected in the objective function?

relevant costs only

How to make the gamble of the decision maker indifferent

repeatedly change p

The overall goal of portfolio models is to create a portfolio that provides the best balance between

risk and return

Utility function: concave

risk aversion

Utility function: linear

risk neutraility

Calculate risk premium

risk premium = EV -certainty equivalent

Utility function: convex

risk taking

What is dual price also known as?

shadow price

Risk profiles

show the actual possible payoffs/consequences along with their corresponding probabilities

When analytical solutions are not available, ___ are used

simulations

Quantitative is for

solving the problem

Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in

standard form

In what state do we analyze dynamic models?

steady states, after some time has elapsed

Qualitative is for

structuring the problem

A cost that is incurred no matter what values the decision variables assume is

sunk cost

Decision variables

tell how much or how many of something to produce, invest, purchase, hire, etc.

What is the market measured by in index funds?

the S&P 500

Dual value

the change of the objective function for a 1-unit increase in the right hand side of a constraints

Supply chain models

the collection of all parties and activities that are involved in producing and distributing a product. The objective is typically to minimize cost

What will happen if we change both simultaneously?

the condition is no longer met and the optimal solution will change

Forecast error

the difference between the actual value (Yt) and the predicted value/forecast (Ft) for a certain time period t et = Yt - Ft

The higher the expected return of an investment

the higher the risk

Critical path is (slack)

the path consisting of all activities with zero slack

What is an expected value

the probability weighted average of all possible consequences; is not the actual payoff, just what we expect the payoff to be

Break-even point

the production volume where profit would be zero (revenues = cost)

Range of feasibility

the range of right hand side values for which the dual value is valid

Reduced cost

the reduced cost of a decision variable is the dual value of the non-negativity constraint (how the objective function would change if we needed one, not zero, units)

The optimal solution will not change (even though the value of the objective function might) as long as

the slope of the objective function does not make a different extreme point optimal

Utility measures

the total worth of a consequence, including attitudes towards risk that our decision maker may have

To solve our decision dilemma we will replace the original payoffs with

their corresponding utilities

What is a major problem with decision rules?

they ignore all but one of the consequences for each alternative. We could average them, but this would assume that each consequence is equally likely to occur, which is not true

What is Bayes Theorem used for?

to update prior probabilities into posterior probabilities; prior probabilities refer to the situation before information is obtained and posterior probabilities refer to the situation after information is obtained

Utility function

translates payoffs into their corresponding utilities

The problem which deals with the distribution of goods from several sources to several destinations is the

transportation probelm

A critical activity can be part of a noncritical path (T/F)

true

A larger value of k means smoother (T/F)

true

A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear (T/F)

true

A risk neutral decision maker will have a linear utility function (T/F)

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 (T/F)

true

All activities on a critical path have zero slack time (T/F)

true

Any of the numbers that go into a decision analysis are subject to some amount of imprecision (T/F)

true

Chance events are beyond your control (T/F)

true

Convex function types are easier to solve than others (T/F)

true

Decision alternatives are choosen from (T/F)

true

Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs (T/F)

true

EVPI is always greater than or equal to EVSI (T/F)

true

Each simulation run provides only a sample of how the real system will operate (T/F)

true

For any constraint, either its slack/surplus value must be zero or its dual price must be zero (T/F)

true

Forecasts can be based on judgements and opinions (qualitative) or data (quantitative) (T/F)

true

Harry Markowitz won the Nobel prize in economics for his path-breaking work in quantifying this tradeoff to come up with optimal portfolios (T/F)

true

Higher values of R indicate less risk aversion and will flatten the function (T/F)

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 (T/F)

true

If x1 + x2 ≤ 500y1 and y1 is a binary (0-1) variable, then if y1 is 0, x1 and x2 will be 0 (T/F)

true

In an all-integer linear program all decision variables must be integer (T/F)

true

In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values (T/F)

true

In portfolio models, risk is minimized by diversification (T/F)

true

In the case of functions with multiple local optima, most nonlinear optimization software methods can get stuck and terminate at a local optimum (T/F)

true

Integer LP allows for tremendous flexibility in modeling (especially in situations involving binary variables) (T/F)

true

Integer and binary programs are much more difficult to solve; algorithms much more complicated (T/F)

true

Integer linear programs are harder to solve than linear programs (T/F)

true

Maximizing expected values and maximizing expected utilities require probabilities (T/F)

true

Possible dependencies among uncertainties are difficult to model, we assume independency (T/F)

true

Program Evaluation and Review Technique (PERT) was developed in the 1950's by the Navy (T/F)

true

Ranges of optimality require that changes in objective function coefficients are made one at a time (T/F)

true

Revenue management methodology can be applied in the case of nonperishable assets (T/F)

true

Shortest route problems are a special case of transshipment models with one supply node(origin), one demand node (destination), and several transshipment nodes in between (T/F)

true

Simulation is an excellent technique to use when a situation is too complicated to use standard analytical procedures (T/F)

true

Simultaneous changes are much harder to handle (T/F)

true

Smoothing methods are more appropriate for a stable time series than when significant trend or seasonal patterns are present (T/F)

true

The Critical Path Method (CPM) was developed independently at DuPont and Remington Rand (T/F)

true

The assignment problem is a special case of the transportation problem in which all supply and demand values equal one (T/F)

true

The constraint 5x1 - 2x2 <= 0 passes through the point (x1 = 20, x2 = 50) (T/F)

true

The degree of risk is associated with the probability or magnitude of loss (T/F)

true

The direction of flow in the shortest-route problem is always out of the origin node and into the destination node (T/F)

true

The earliest finish time for the final activity is the project duration (T/F)

true

The exponential smoothing forecast for any period is a weighted average of all the previous actual values for the time series (T/F)

true

The field of management science approaches decision making rationally, with techniques based on the scientific method. (T/F)

true

The field of management science is another name for decision science and for operations research. (T/F)

true

The first step in the decision making process is to identify the problem. (T/F)

true

The length of time an activity can be delayed without affecting the project completion time is the slack (T/F)

true

The shortest-route problem is a special case of the transshipment problem where each supply = 1 and each demand = 1 (T/F)

true

The smoothing techniques can only forecast the very next time period (T/F)

true

The standard form of a linear programming problem will have the same solution as the original problem.( T/F)

true

The utility function for a risk avoider typically shows a diminishing marginal return for money (T/F)

true

Time series data can exhibit seasonal patterns of less than one month in duration (T/F)

true

Time series methods base forecasts only on past values of the variables (T/F)

true

To assign utilities, consider the best and worst payoffs in the entire decision situation (T/F)

true

Trials of a simulation show what would happen when values of the probabilistic input change (T/F)

true

Uncertainties and risks can result in good decisions leading to bad outcomes (T/F)

true

Utility measures account for risk (T/F)

true

When a route in a transportation problem is unacceptable, the corresponding variable can be removed from the LP formulation (T/F)

true

the value of the optimal solution of the LP relaxation is an upper/lower bound (depending on if you want to maximize or minimize) for the value of the the optimal solution of the mixed linear program (T/F)

true

Max flow problem

try to maximize the amount of flow that can move through a network

Stochastic/probabilstic

unknown

What bound does EVPI provide

upprt

Naive forecasting

uses the most recent values to predict the next time period

Alternative optimal solutions

when more than one combination of decision variables leads to the same, optimal value of the objective function

What is dynamic pricing?

when prices change depending on supply and demand

When are smoothing techniques popular?

when there are no significant trends or seasonal patterns

Where is the optimal solution of a linear program?

where the objective function is just about to leave the feasible region at an extreme point

A constraint with a positive slack value

will have a dual value of zero

The manufacturer needs at least 12000 units of corn. The Iowa cooperative can supply up to 8000 units, and the Illinois cooperative can supply at least 6000 units. Develop constraints for these conditions.

x1 + x 2 ≥ 12000 x1 ≤ 8000 x2 ≥ 6000