CH 05 - Advanced Linear Programming Applications. Questions and Answers

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/ 1. Revenue management methodology was originally developed for the banking industry. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.02 - 5.2 ... NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.2 Revenue Management KEYWORDS: Bloom's: Remember 2. The goal of portfolio models is to create a portfolio that provides the best balance between risk and return. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.03 - 5.3 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.3 Portfolio Models and Asset Allocation KEYWORDS: Bloom's: Remember 3. DEA is used to measure the relative efficiency of two (or more) units in different industries, such as a bank and a school. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.01 - 5.1 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.1 Data Envelopment Analysis KEYWORDS: Bloom's: Remember 4. If the inputs of the composite unit in DEA are greater than the inputs for an individual unit, then the composite is more efficient. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.01 - 5.1 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.1 Data Envelopment Analysis KEYWORDS: Bloom's: Understand 5. It is possible for a single DEA programming model to identify all operating units that are inefficient. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.01 - 5.1 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.1 Data Envelopment Analysis KEYWORDS: Bloom's: Understand 6. Upon completion of a DEA model, all operating units that are relatively efficient are not necessarily identified. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.01 - 5.1 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.1 Data Envelopment Analysis KEYWORDS: Bloom's: Understand 7. 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. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.01 - 5.1 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.1 Data Envelopment Analysis KEYWORDS: Bloom's: Understand 8. 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. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.04 - 5.4 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.4 Game Theory KEYWORDS: Bloom's: Understand 9. If a pure strategy solution exists for a two-person, zero-sum game, it is the optimal solution to the game. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.04 - 5.4 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.4 Game Theory KEYWORDS: Bloom's: Understand 10. 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. a. b. ANSWER: POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.05.04 - 5.4 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.4 Game Theory KEYWORDS: Bloom's: Understand 11. In portfolio models, risk is minimized by diversification. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.03 - 5.3 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.3 Portfolio Models and Asset Allocation KEYWORDS: Bloom's: Remember 12. Revenue management methodology can be applied in the case of nonperishable assets. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.02 - 5.2 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.2 Revenue Management KEYWORDS: Bloom's: Remember 13. In a data envelopment model, dual prices inform reservation agents of the revenue loss associated with overbooking each origin-destination-itinerary fare (ODIF). a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.02 - 5.2 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.2 Revenue Management KEYWORDS: Bloom's: Understand 14. In game theory, the player seeking to maximize the value of the game selects a maximax strategy. a. b. ANSWER: POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.05.04 - 5.4 NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 5.4 Game Theory KEYWORDS: Bloom's: Understand 15. The analysis of a two-person, zero-sum game begins with checking to see whether a pure strategy exists. a. b. 16. Revenue management methodology enables an airline to maximize the number of full-fare seats it sells on each flight. a. b. 17. Zero-sum means that what one player wins, the other player loses, and the gain and loss balance each other out. a. b. Multiple Choice 18. Revenue management methodology was originally developed for a(n) a. cruise line. b. airline. c. car rental company. d. hotel chain. 19. 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. 20. 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. 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. 22. 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. 23. 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. None of these are correct. 24. 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. 25. 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. 26. 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. 27. 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. 28. 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. 29. 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. Subjective Short Answer 30. 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: Input Measures Output Measures Average classroom size Percent of children in remedial classes Percent of students on reduced price lunch Average first grade score on standard test Average number of parent volunteer hours per week Average fifth grade score on standard test Data are collected for each school on each measure. School Archer Hayes Ralston Creekside Inputs Classroom size 21 28 32 20 % reduced lunch 10 8 25 2 Avg. vol. hours 30 46 15 64 Outputs % remediation 15 12 19 3 1st grade score 83 84 62 85 5th grade score 76 72 53 79 Develop a DEA model that would evaluate the efficiency of Ralston Elementary School. 31. 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 Variable Value Reduced Cost E 1.000 0.000 wn 1.000 0.000 ws 0.000 0.000 we 0.000 0.000 ww 0.000 0.000 Constraint Slack/Surplus 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 32. 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. 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 Variable Value Reduced Cost S 0.000 0.385 F 0.167 0.000 L 0.000 0.490 D 0.833 0.000 E 0.510 0.000 Constraint Slack/Surplus 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 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? 33. 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? Player B Strategies Player A Strategies b1 b2 b3 a1 5 5 4 a2 1 6 2 a3 7 2 3 34. 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? Company Y Strategies Company X Strategies y1 y2 y3 x1 3 5 9 x2 8 4 3 x3 7 6 7 35. 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. Company Y Strategies Company X Strategies y1 y2 y3 x1 4 3 9 x2 2 5 1 x3 6 1 7 36. Shown below is the solution to the linear program for finding Player A's optimal mixed strategy in a two-person, zero-sum game. OBJECTIVE FUNCTION VALUE = 3.500 VARIABLE VALUE REDUCED COSTS PA1 0.050 0.000 PA2 0.600 0.000 PA3 0350 0.000 GAINA 3.500 0.000 CONSTRAINT SLACK/SURPLUS DUAL PRICES 1 0.000 −0.500 2 0.000 −0.500 3 0.000 0.000 4 0.000 3.500 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? 37. 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. Annual Returns (Planning Scenarios) Mutual Fund Year 1 Year 2 Year 3 Year 4 International Stock 22.37 26.73 6.46 3.19 Large-Cap Blend 14.88 18.61 10.52 5.25 Mid-Cap Blend 19.45 18.04 5.91 1.94 Small-Cap Blend 13.79 11.33 2.07 6.85 Intermediate Bond 7.29 8.05 9.18 3.92 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. Annual Returns (Planning Scenarios) Mutual Fund Year 1 Year 2 Year 3 Year 4 International Stock 22.37 26.73 6.46 3.19 Large-Cap Blend 14.88 18.61 10.52 5.25 Mid-Cap Blend 19.45 18.04 5.91 1.94 Small-Cap Blend 13.79 11.33 2.07 6.85 Intermediate Bond 7.29 8.05 9.18 3.92 39. 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. Two-Day Saturday- Sunday- Package Only Only Rally $125 $75 $65 Regular 150 85 75 The anticipated demand for each type of reservation is as follows: Two-Day Saturday- Sunday- Package Only Only Rally 20 10 15 Regular 10 20 25 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. 40. 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. ODIF Origin Destination Fare Class ODIF Code Fare Demand 1 Indianapolis Memphis D IMD 175 44 2 Indianapolis Austin D IAD 275 25 3 Indianapolis Tampa D ITD 285 40 4 Indianapolis Memphis F IMF 395 15 5 Indianapolis Austin F IAF 425 10 6 Indianapolis Tampa F ITF 475 8 7 Baltimore Memphis D BMD 185 26 8 Baltimore Austin D BAD 315 50 9 Baltimore Tampa D BTD 290 42 10 Baltimore Memphis F BMF 385 12 11 Baltimore Austin F BAF 525 16 12 Baltimore Tampa F BTF 490 9 13 Memphis Austin D MAD 190 58 14 Memphis Tampa D MTD 180 48 15 Memphis Austin F MAF 310 14 16 Memphis Tampa F MTF 295 11 Develop a linear programming model for LeapFrog's problem situation and determine how many seats LeapFrog should allocate to each ODIF. [Show More]

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