Deck 5: Advanced Linear Programming Applications

Question 1

Upon completion of a DEA model,all operating units that are relatively efficient are not necessarily identified.

Answer 1

True

Question 2

In a data envelopment model,dual prices inform reservation agents of the revenue loss associated with overbooking each origin-destination-itinerary fare (ODIF).

Answer 2

False

Question 3

The analysis of a two-person,zero-sum game begins with checking to see whether a pure strategy exists.

Answer 3

True

Question 4

Zero-sum means that what one player wins,the other player loses,and the gain and loss balance each other out.

Question 5

It is possible for a single DEA programming model to identify all operating units that are inefficient.

Question 6

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.

Question 7

Revenue management methodology was originally developed for the banking industry.

Question 8

DEA will show all but one operating unit to be relatively inefficient in the case where an operating unit produces the most of every output and also consumes the least of every input.

Question 9

In portfolio models,risk is minimized by diversification.

Question 10

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

A)short- and long-term investments.
B)gains and losses.
C)risk and return.
D)liquidity and stability.

Question 11

DEA is used to measure the relative efficiency of two (or more)units in different industries,such as a bank and a school.

Question 12

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 these are correct.

Question 13

Revenue management methodology was originally developed for a(n)

A)cruise line.
B)airline.
C)car rental company.
D)hotel chain.

Question 14

In a two-person,zero-sum,pure-strategy game,it can be advantageous for a player to switch from their strategy when the player discovers the other player's strategy in advance.

Question 15

Revenue management methodology enables an airline to maximize the number of full-fare seats it sells on each flight.

Question 16

If the inputs of the composite unit in DEA are greater than the inputs for an individual unit,then the composite is more efficient.

Question 17

The goal of portfolio models is to create a portfolio that provides the best balance between risk and return.

Question 18

If a pure strategy solution exists for a two-person,zero-sum game,it is the optimal solution to the game.

Question 19

In game theory,the player seeking to maximize the value of the game selects a maximax strategy.

Question 20

Revenue management methodology can be applied in the case of nonperishable assets.

Question 21

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 these are correct.

Question 22

Consider a two-person,zero-sum game where the payoffs listed below are the winnings for Player A.Identify the pure strategy solution.What is the value of the game?
​ ​

Question 23

Consider the following two-person,zero-sum game.Payoffs are the winnings for Company X.Formulate the linear program that determines the optimal mixed strategy for Company X.​

Question 24

Eastern Washington County School Corporation is interested in comparing educational performance at four elementary schools and has hired you to prepare a DEA model to do so.After detailed conversations with the corporation administrative staff and the building principals,you have isolated the following input and output measures: ​
Data are collected for each school on each measure. ​
Develop a DEA model that would evaluate the efficiency of Ralston Elementary School.

Question 25

Consider a two-person,zero-sum game where the payoffs listed below are the winnings for Company X.Identify the pure strategy solution.What is the value of the game?

Question 26

If it is an optimal solution 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-then the game

A)has a mixed strategy solution.
B)will have alternating winners.
C)will have no winner.
D)has a pure strategy solution.

Question 27

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.

Question 28

The output shows the solution to a DEA model where facilities in Seaview (S),Farmington (F),Lewiston (L),and San Domingo (D)are compared.The inputs,in order,are number of machines,size of workforce,and goodness of location.The outputs,in order,are production,quality rating,and on-time completion percentage.The model examines the efficiency of Lewiston. OPTIMAL SOLUTION
Objective Function Value = 0.510 ​ ​
a.Is the Lewiston plant efficient? Why or why not? If not,which plants should it emulate in order to improve?
b.How much more production does the composite facility provide than the Lewiston site?
c.What is the quality rating for the composite facility?

Question 29

Hervis Car Rental in Austin,Texas,has 50 high-performance Shelby-H Mustangs in its rental fleet.These cars will be in greater demand than usual during the last weekend in July when the Central Texas Mustang Club holds its annual rally in Austin.At times like this,Hervis uses a revenue management system to determine the optimal number of reservations to have available for the Shelby-H cars.Hervis has agreed to have at least 60% of its Shelby-H Mustangs available for rally attendees at a special rate.Although many of the rally attendees will request a Saturday and Sunday two-day package,some attendees may select a Saturday-only or a Sunday-only reservation.Customers not attending the rally may also request a Saturday and Sunday two-day package,or make a Saturday-only or Sunday-only reservation.Thus,six types of reservations are possible.The cost for each type of reservation is shown here. The anticipated demand for each type of reservation is as follows: Hervis Car Rental would like to determine how many Shelby-H Mustangs to make available for each type of reservation in order to maximize total revenue.
a.Define the decision variables.
b.Formulate a linear programming model for this revenue management application.

Question 30

Portfolio manager Max Gaines needs to develop an investment portfolio for his conservative clients.His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides the best return possible with a minimum risk.Formulate the maximin linear program.​ ​

Question 31

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.

Question 32

Shown below is the solution to the linear program for finding Player A's optimal mixed strategy in a two-person,zero-sum game. ​
a.What is Player A's optimal mixed strategy?
b.What is Player B's optimal mixed strategy?
c.What is Player A's expected gain?
d.What is Player B's expected loss?

Question 33

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.

Question 34

To develop a portfolio that provides the best return possible with a minimum risk,the linear programming model will have an objective function that

A)minimizes the maximum risk.
B)minimizes total risk.
C)maximizes return and minimizes risk.
D)maximizes the minimum return.

Question 35

Mountainside State Park has four visitor centers.To study the operation of these centers,a DEA model has been developed that compares inputs (size,number of staff,weekly hours of operation)and outputs (% of visitors attending educational program,daily sales in gift shop).The computer solution is shown below.What can you conclude about the efficiency of the North center?
LINEAR PROGRAMMING PROBLEM ​
OPTIMAL SOLUTION
Objective Function Value = 1.000 ​

Question 36

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.

Question 37

A DEA linear programming model involving four input measures and three output measures will have

A)7 constraints.
B)8 constraints.
C)12 constraints.
D)13 constraints.

Question 38

Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk.His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides an annual return of no less than 3%.Formulate the appropriate linear program.​

Question 39

LeapFrog Airways provides passenger service for Indianapolis,Baltimore,Memphis,Austin,and Tampa.LeapFrog has two WB828 airplanes,one based in Indianapolis and the other in Baltimore.Each morning,the Indianapolis-based plane flies to Austin with a stopover in Memphis,and the Baltimore-based plane flies to Tampa with a stopover in Memphis.Both planes have a coach section with a 120-seat capacity.​
LeapFrog uses two fare classes: a discount-fare D class and a full-fare F class.LeapFrog's products,each referred to as an origin-destination-itinerary fare (ODIF),are listed below with their fares and forecasted demand.​ ​
Develop a linear programming model for LeapFrog's problem situation and determine how many seats LeapFrog should allocate to each ODIF.​