Lesson Topics. A.11 Other Advanced Applications Review Questions

Transcription

1 Lesson Topics Data Envelopment Analysis measures the relative efficiency of operating units with the same goals and objectives, and the same types of resources. Applies to hospitals, banks, courts, Revenue Management (6) Problems are Resource Allocation Problems when inputs are fixed. Revenue Management Problems thus help airlines determine how many seats to sell at a discount. 1

2 Revenue Management Each of the following review questions apply the theory of Revenue Management to the managerial decision of how best to divide products into categories. 2

3 Revenue Management Question. Disneyland can comfortably accommodate up to 10,000 customers on any particular day. During the Saturday and Sunday before kids go back to school, Disney uses a revenue management system to determine the optimal number of tickets to make available so that the park never has more than 10,000 customers. Although many people going to Disneyland will buy a Saturday-and-Sunday two-day ticket, they may also select a Saturday-only or Sunday-only ticket. Disney has agreed to have at least 60% of each type of ticket (two-day, Saturday-only, Sunday-only) available to local residents at a special price. Thus, six types of tickets are possible. The price Disney charges for each type of ticket is shown here: Two-Day Saturday Sunday Ticket Only Only Local resident $125 $75 $65 Non resident $150 $85 $75 The anticipated demand for each type of ticket is as follows: Two-Day Saturday Sunday Ticket Only Only Local resident 5,000 6,000 2,000 Non resident 2,000 3,000 3,000 Disney would like to determine how many of each type of ticket to sell in order to maximize revenue. Formulate Disney s problem as a linear program, but you need not solve for the optimum. Tip: Your written answer should define the decision variables, and formulate the objective and constraints. 3

4 Answer to Question: Define the decision variables: LOTW = number of tickets available for local residents for two days NRTW = number of tickets available for non-residents for two days LOSA = number of tickets available for local residents for Saturday only NRSA = number of tickets available for non-residents for Saturday only LOSU = number of tickets available for local residents for Sunday only NRSU = number of tickets available for non-residents for Sunday only Formulate the objective: Max 125LOTW + 150NRTW + 75LOSA + 85NRSA + 65LOSU + 75NRSU Formulate the constraints: LOTW + NRTW + LOSA + NRSA < 10,000 LOTW + NRTW + LOSU + NRSU < 10,000 (Saturday Capacity) (Sunday Capacity) LOTW >.6(LOTW+NRTW) LOSA >.6(LOSA+NRSA) LOSU >.6(LOSU+NRSU) LOTW < 5,000 NRTW < 2,000 LOSA < 6,000 NRSA < 3,000 LOSU < 2,000 NRSU < 3,000 (60% two-day tickets for local residents) (60% Saturday-only tickets for local residents) (60% Sunday-only tickets for local residents) (Two-day local demand) (Two-day non-resident demand) (Saturday-only local demand) (Saturday-only non-resident demand) (Sunday-only local demand) (Sunday-only non-resident demand) LOTW, NRTW, LOSA, NRSA, LOSU, NRSU > 0 (Non-negativity) 4

5 Revenue Management Question. Disneyland can comfortably accommodate up to 10,000 customers on any particular day. During the Saturday and Sunday before kids go back to school, Disney uses a revenue management system to determine the optimal number of tickets to make available so that the park never has more than 10,000 customers. Although many people going to Disneyland will buy a Saturday-and-Sunday two-day ticket, they may also select a Saturday-only or Sunday-only ticket. Disney has agreed to have at least 30% of each type of ticket (two-day, Saturday-only, Sunday-only) available to local residents at a special price. Thus, six types of tickets are possible. The price Disney charges for each type of ticket is shown here: Two-Day Saturday Sunday Ticket Only Only Local resident $125 $75 $65 Non resident $150 $85 $75 The anticipated demand for each type of ticket is as follows: Two-Day Saturday Sunday Ticket Only Only Local resident 5,000 6,000 2,000 Non resident 2,000 3,000 3,000 Disney would like to determine how many of each type of ticket to sell in order to maximize revenue. Formulate Disney s problem as a linear program, but you need not solve for the optimum. Tip: Your written answer should define the decision variables, and formulate the objective and constraints. 5

6 Answer to Question: Define the decision variables: LOTW = number of tickets available for local residents for two days NRTW = number of tickets available for non-residents for two days LOSA = number of tickets available for local residents for Saturday only NRSA = number of tickets available for non-residents for Saturday only LOSU = number of tickets available for local residents for Sunday only NRSU = number of tickets available for non-residents for Sunday only Formulate the objective: Max 125LOTW + 150NRTW + 75LOSA + 85NRSA + 65LOSU + 75NRSU Formulate the constraints: LOTW + NRTW + LOSA + NRSA < 10,000 (Saturday Capacity) LOTW + NRTW + LOSU + NRSU < 10,000 (Sunday Capacity) LOTW >.3(LOTW+NRTW) (30% two-day tickets for local residents) LOSA >.3(LOSA+NRSA) (30% Saturday-only tickets for local residents) LOSU >.3(LOSU+NRSU) (30% Sunday-only tickets for local residents) LOTW < 5,000 (Two-day local demand) NRTW < 2,000 (Two-day non-resident demand) LOSA < 6,000 (Saturday-only local demand) NRSA < 3,000 (Saturday-only non-resident demand) LOSU < 2,000 (Sunday-only local demand) NRSU < 3,000 (Sunday-only non-resident demand) LOTW, NRTW, LOSA, NRSA, LOSU, NRSU > 0 (Non-negativity) 6

7 Revenue Management Question. Avis Car Rental in Austin, TX has 50 highperformance 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, Avis uses a revenue management system to determine the optimal number of reservations to have available for the Shelby-H cars. Avis 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 Regular Avis 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. Formulate a linear-programming model for this revenue-management application. Then, solve the problem with the Management Scientist. Tip: Your written answer should define the decision variables, formulate the objective and constraints, and solve for the optimum. --- You will not earn full credit if you just solve for the optimum; you must also define the decision variables, and formulate the objective and constraints. 7

8 Answer to Question: RATW = number of reservations available for rally attendees for two days RGTW = number of reservations available for regular customers for two days RASA = number of reservations available for rally attendees for Saturday only RGSA = number of reservations available for regular customers for Saturday only RASU = number of reservations available for rally attendees for Sunday only RGSU = number of reservations available for regular customers for Sunday only Max 125RATW + 150RGTW + 75RASA + 85RGSA + 65RASU + 75RGSU s.t. RATW + RGTW + RASA + RGSA < 50 (Shelby-H Saturday Capacity) RATW + RGTW + RASU + RGSU < 50 (Shelby-H Sunday Capacity) RATW + RASA > 30 (60% Saturday Capacity for Rally attendees) RATW + RASU > 30 (60% Sunday Capacity for Rally attendees) RATW < 20 (Two-Day Package Rally Demand) RGTW < 10 (Two-Day Package Regular Demand) RASA < 10 (Saturday-Only Rally Demand) RGSA < 20 (Saturday-Only Regular Demand) RASU < 15 (Sunday-Only Rally Demand) RGSU < 25 (Sunday-Only Regular Demand) RATW,RGTW,RASA,RGSA,RASU,RGSU > 0 (Non-negativity) 8

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10 Revenue Management Each of the following review questions apply the theory of Revenue Management to the managerial decision of how best to allocate hotel rooms. 10

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12 Revenue Management Question. Evans Enterprises has bought a prime parcel of beachfront property and plans to build a luxury hotel. After meeting with the architectural team, the Evans family has drawn up some information to make preliminary plans for construction. Excluding the suites, which are not part of this decision, the hotel will have four kinds of rooms: beachfront non-smoking, beachfront smoking, lagoon view non-smoking, and lagoon view smoking. In order to decide how many of each of the four kinds of rooms to plan for, the Evans family will consider the following information. After adjusting for expected occupancy, the average nightly revenue for a beachfront non-smoking room is $175. The average nightly revenue for a lagoon view non-smoking room is $130. Smokers will be charged an extra $15. Construction costs vary. The cost estimate for a lagoon view room is $12,000 and for a beachfront room is $15,000. Air purifying systems and additional smoke detectors and sprinklers ad $3000 to the cost of any smoking room. Evans Enterprises has raised $6.3 million in construction guarantees for this portion of the building. There will be at least 100 but no more than 180 beachfront rooms. Design considerations require that the number of lagoon view rooms be at least 1.5 times the number of beachfront rooms, and no more than 2.5 times that number. Industry trends recommend that the number of smoking rooms be no more than 50% of the number of non-smoking rooms. Formulate and solve a linear programming model to maximize revenue. Tip: Your written answer should define the decision variables, formulate the objective and constraints, and solve for the optimum. --- You will not earn 12

13 full credit if you just solve for the optimum; you must also define the decision variables, and formulate the objective and constraints. 13

14 Answer to Question: Let BN = the number of beachfront non-smoking rooms BS = the number of beachfront smoking rooms LN = the number of lagoon view non-smoking rooms LS = the number of lagoon view smoking rooms Max 175BN + 190BS + 130LN + 145LS s.t BN BS LN LS < 6,300,000 BN + BS > 100 BN + BS < BN - 1.5BS + LN + LS > 0-2.5BN - 2.5BS + LN + LS < 0 -.5BN + BS -.5LN + LS < 0 BN, BS, LN, LS > 0 14

15 Revenue Management Question. Evans Enterprises has bought a prime parcel of beachfront property and plans to build a luxury hotel. After meeting with the architectural team, the Evans family has drawn up some information to make preliminary plans for construction. The hotel will have four kinds of rooms: beachfront non-smoking, beachfront smoking, lagoonview non-smoking, and lagoon-view smoking. In order to decide how many of each of the four kinds of rooms to plan for, the Evans family will consider the following information. After adjusting for expected occupancy, the average nightly revenue for a beachfront non-smoking room is $150. The average nightly revenue for a lagoon view non-smoking room is $200. Smokers will be charged an extra 10 percent. Construction costs vary. The cost estimate for a lagoon view room is $12,000 and for a beachfront room is $15,000. Air purifying systems and additional smoke detectors and sprinklers ad $3000 to the cost of any smoking room. Evans Enterprises has raised $6.3 million in construction guarantees for the building. There will be at least 100 but no more than 180 beachfront rooms. Design considerations require that the number of lagoon view rooms be at least 1.5 times the number of beachfront rooms, and no more than 2.5 times that number. Industry trends recommend that the total number of smoking rooms be no more than 30% of the number of non-smoking rooms. Formulate a linear programming model to maximize revenue. Formulate the problem, but you need not solve for the optimum. Tip: Your written answer should define the decision variables, and formulate the objective and constraints. 15

16 Answer to Question: Let BN = the number of beachfront non-smoking rooms BS = the number of beachfront smoking rooms LN = the number of lagoon view non-smoking rooms LS = the number of lagoon view smoking rooms Max 150BN + 165BS + 200LN + 220LS s.t BN BS LN LS < 6,300,000 BN + BS > 100 BN + BS < BN - 1.5BS + LN + LS > 0-2.5BN - 2.5BS + LN + LS < 0 -.3BN + BS -.3LN + LS < 0 BN, BS, LN, LS > 0 16

17 Revenue Management Question. Evans Enterprises has bought a prime parcel of beachfront property and plans to build a luxury hotel. After meeting with the architectural team, the Evans family has drawn up some information to make preliminary plans for construction. Excluding the suites, which are not part of this decision, the hotel will have four kinds of rooms: beachfront non-smoking, beachfront smoking, lagoon view nonsmoking, and lagoon view smoking. In order to decide how many of each of the four kinds of rooms to plan for, the Evans family will consider the following information. After adjusting for expected occupancy, the average nightly revenue for a beachfront non-smoking room is $175. The average nightly revenue for a lagoon view non-smoking room is $130. Smokers will be charged an extra $15. Construction costs vary. The cost estimate for a lagoon view room is $12,000 and for a beachfront room is $15,000. Air purifying systems and additional smoke detectors and sprinklers ad $3000 to the cost of any smoking room. Evans Enterprises has raised $6.3 million in construction guarantees for this portion of the building. There will be at least 120 but no more than 190 beachfront rooms. Design considerations require that there be at least as many lagoon view rooms as beachfront rooms. Industry trends recommend that the number of smoking rooms be no more than 40% of the number of non-smoking rooms. Formulate a linear programming model to maximize revenue. Formulate the problem, but you need not solve for the optimum. Tip: Your written answer should define the decision variables, and formulate the objective and constraints. 17

18 Answer to Question: Let BN = the number of beachfront non-smoking rooms BS = the number of beachfront smoking rooms LN = the number of lagoon view non-smoking rooms LS = the number of lagoon view smoking rooms Max 175BN + 190BS + 130LN + 145LS s.t BN BS LN LS < 6,300,000 BN + BS > 120 BN + BS < BN - BS + LN + LS > 0 -.4BN + BS -.4LN + LS < 0 BN, BS, LN, LS > 0 18