Deck 5: Advanced Linear Programming Applications

Question 1

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

Answer 1

True

Question 2

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.

Answer 2

D

Question 3

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.

Answer 3

A

Question 4

DEA does not necessarily identify the operating units that are relatively efficient.

Question 5

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 6

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 7

Revenue management methodology was originally developed for

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

Question 8

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

Question 9

Revenue management methodology was originally developed for the banking industry.

Question 10

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

Question 11

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.

Question 12

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.

Question 13

In portfolio models, risk is minimized by diversification.

Question 14

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.

Question 15

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

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 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.

Question 18

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.

Question 19

It is possible for DEA to show all operating units to be relatively inefficient.

Question 20

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.

Question 21

List several industries in which revenue management has been applied and list several different types of decisions being made with the aid of the methodology.

Question 22

List several types of organizations with multiple operating units where data envelopment analysis might be applied and give examples of possible inputs and outputs for each organization.

Question 23

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
MIN
1E+0wn+0ws+0we+0ww
S.T.
1) -400E+400wn+1200ws+2400we+1500ww<0
2) -3E+3wn+6ws+10we+7ww<0
3) -56E+56wn+108ws+92we+108ww<0
4) -49E+49wn+83ws+56we+72ww>0
5) -38E+38wn+425ws+1200we+630ww>0
6) +1wn+1ws+1we+1ww=1
OPTIMAL SOLUTION
Objective Function Value = 1.000 $$\begin{array} { c c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { E } & 1.000 & 0.000 \\\text { wn } & 1.000 & 0.000 \\\text { ws } & 0.000 & 0.000 \\\text { we } & 0.000 & 0.000 \\\text { ww } & 0.000 & 0.000\end{array}$$ $$\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & 0.008 \\2 & 0.000 & 0.000 \\3 & 0.000 & 0.001 \\4 & 0.000 & - 0.034 \\5 & 0.000 & - 0.013 \\6 & 0.000 & - 1.000\end{array}$$

Question 24

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 work force, and goodness of location. The outputs, in order, are production, quality rating, and on-time completion percentage. The model examines the efficiency of Lewiston.
MIN
0S+0F+0L+0D+1E
S.T.
1) 1S+1F+1L+1D=1
2) 5S+22F+36L+15D-36E<0
3) 400S+1500F+3150L+1060D-3150E<0
4) 24S+13F+32L+17D-32E<0
5) 800S+2900F+1860L+1700D+0E>1860
6) 95S+92F+83L+94D+0E>83
7) 83S+85F+90L+91D+0E>90
OPTIMAL SOLUTION
Objective Function Value = 0.510 $$\begin{array} { c c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { S } & 0.000 & 0.385 \\\text { F } & 0.167 & 0.000 \\\text { L } & 0.000 & 0.490 \\\text { D } & 0.833 & 0.000 \\\text { E } & 0.510 & 0.000\end{array}$$ $$\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & 1.365 \\2 & 2.208 & 0.000 \\3 & 474.479 & 0.000 \\4 & 0.000 & 0.031 \\5 & 40.000 & 0.000 \\6 & 10.667 & 0.000 \\7 & 0.000 & - 0.021\end{array}$$
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 25

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 26

Describe the steps used to determine when a two-person, zero-sum game has a pure-strategy solution.

Question 27

The 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 measurements: $\begin{array}{ll}\text { Input Measures } & \text { Output Measures } \\\hline \text { Average classroom size } & \text { Percent of children in remedial classes } \\\text { Percent of students on reduced price lunch } & \text { Average first grade score on standard test } \\\text { Average number of parent volunteer hours per week } & \text { Average fifth grade score on standard test }\end{array}$ Data is collected for each school on each measure $$\begin{array} { l | c c c c } & & { \text { School } } \\& \text { Archer } & \text { Hayes } & \text { Ralston } & \text { Creekside } \\\hline \text { Inputs } & & & & \\\text { Classroom size } & 21 & 28 & 32 & 20 \\\text { \% reduced lunch } & 10 & 8 & 25 & 2 \\\text { Avg. vol. hours } & 30 & 46 & 15 & 64 \\\text { Outputs } & & & & \\\text { \% remediation } & 15 & 12 & 19 & 3 \\\text { 1st grade score } & 83 & 84 & 62 & 85 \\\text { 5th grade score } & 76 & 72 & 53 & 79\end{array}$$ Develop the DEA model that would evaluate the efficiency of Ralston Elementary School.

Question 28

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. $$\begin{array} { c | c c c } && { \text { Company Y Strategies } } \\\text { Company X Strategies } & y _ { 1 } & y _ { 2 } & y _ { 3 } \\\hline x _ { 1 } & 4 & 3 & 9 \\x _ { 2 } & 2 & 5 & 1 \\x _ { 3 } & 6 & 1 & 7\end{array}$$

Question 29

Explain the differences between the LP formulations for a conservative portfolio and moderate-risk portfolio.

Question 30

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 31

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 32

Hervis Car Rental in Austin, TX 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 33

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 34

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 35

Write a summary of the DEA approach and explain how you would interpret the solution.