Problem 5-05 Leisure Air, a regional airline, provides service for Pittsburgh, N
ID: 3073024 • Letter: P
Question
Problem 5-05
Leisure Air, a regional airline, provides service for Pittsburgh, Newark, Charlotte, Myrtle Beach, and Orlando. Leisure Air has two Boeing 737-400 airplanes, one based in Pittsburgh and the other in Newark. Both airplanes have a coach section with a 132-seat capacity. Each morning the Pittsburgh-based plane flies to Orlando with a stopover in Charlotte, and the Newark-based plane flies to Myrtle Beach, also with a stopover in Charlotte. At the end of the day, both planes return to their home bases. We restrict our attention to the Pittsburgh-Charlotte, Charlotte-Orlando, Newark-Charlotte, and Charlotte-Myrtle Beach flight legs for the morning flights.
Leisure Air uses two fare classes: a discount-fare Q class and a full-fare Y class. Reservations using the discount-fare Q class must be made 14 days in advance and must include a Saturday night stay in the destination city. Reservations using the full-fare Y class may be made any time, with no penalty for changing the reservation at a later date. Leisure Air established fares and developed forecasts of customer demand for each of 16 ODIFs. These data are shown in the table below.
But because demand cannot be forecasted perfectly, the number of seats actually sold for each origin-destinationitinerary fare (ODIF) may turn out to be smaller or larger than forecasted. Suppose that Leisure Air believes that economic conditions have improved and that its original forecast may be too low. To account for this possibility, Leisure Air is considering switching the Boeing 737-400 airplanes that are based in Pittsburgh and Newark with Boeing 757-200 airplanes that Leisure Air has available in other markets. The Boeing 757-200 airplane has a seating capacity of 158 in the coach section.
A. Because of scheduling conflicts in other markets, suppose that Leisure Air is only able to obtain one Boeing 757-200. Should the larger plane be based in Pittsburgh or in Newark? Answer: Newark
The total revenue of basing the larger plane in Newark is bigger than basing the larger plane in Pittsburgh.
B. Based upon your answer in part (a), determine a new allocation for the ODIFs.
Original allocation:
SOLVE: Using a larger plane based in Newark, the optimal allocations are:
Briefly summarize the major differences between the new allocation using one Boeing 757-200 and the original allocation summarized above.
SOLVE: The main differences between the original allocations and the new allocations are in the variables:
SOLVE: C. Suppose that two Boeing 757-200 airplanes are available. Determine a new allocation for the ODIF’s using the two larger airplanes. Using a larger plane based in Pittsburgh and a larger plane based in Newark, the optimal allocations are:
Briefly summarize the major differences between the new allocation using two Boeing 757-200 airplanes and the original allocation shown in part (b).
SOLVE: The main differences between the allocations in part b and the new allocations are in the variables:
SOLVE: This solution provides an in (increase or decrease) in revenue of $ ___________ .
SOLVE: D. Consider the new solution obtained in part (b). Which ODIF has the highest bid price?
SOLVE: What is the interpretation for this bid price?
SOLVE: The bid price for this solution is $_______ which means that if there was one more (Y or Q) class seat revenue would (increase or decrease) by $_________ .
Class ODIF
Code Fare($) Forecasted
Demand 1 Pittsburgh Charlotte Q PCQ 178 33 2 Pittsburgh Myrtle Beach Q PMQ 268 44 3 Pittsburgh Orlando Q POQ 228 45 4 Pittsburgh Charlotte Y PCY 380 16 5 Pittsburgh Myrtle Beach Y PMY 456 6 6 Pittsburgh Orlando Y POY 560 11 7 Newark Charlotte Q NCQ 199 26 8 Newark Myrtle Beach Q NMQ 249 56 9 Newark Orlando Q NOQ 349 39 10 Newark Charlotte Y NCY 385 15 11 Newark Myrtle Beach Y NMY 444 7 12 Newark Orlando Y NOY 580 9 13 Charlotte Myrtle Beach Q CMQ 179 64 14 Charlotte Myrtle Beach Y CMY 380 8 15 Charlotte Orlando Q COQ 224 46 16 Charlotte Orlando Y COY 582 10
Explanation / Answer
To develop a linear programming model that can be used to determine how many seats Leisure Air should allocate to each fare class, we need to define 16 decision variables, one for each origin-destination-itinerary fare alternative. Using P for Pittsburgh, N for Newark, C for Charlotte, M for Myrtle Beach, and O for Orlando, the decision variables take the following form:
PCQ = number of seats allocated to Pittsburgh–Charlotte Q class
PMQ = number of seats allocated to Pittsburgh–Myrtle Beach Q class
POQ = number of seats allocated to Pittsburgh–Orlando Q class
PCY = number of seats allocated to Pittsburgh–Charlotte Y class
NCQ = number of seats allocated to Newark–Charlotte Q class
COY = number of seats allocated to Charlotte–Orlando Y class
The objective is to maximize total revenue. Using the fares shown in Table, we can write the objective function for the linear programming model as follows:
Max 178PCQ + 268PMQ + 228POQ + 380PCY + 456PMY + 560POY + 199NCQ + 249NMQ + 349NOQ + 385NCY + 444NMY + 580NOY + 179CMQ + 380CMY + 224COQ + 582COY
Next, we must write the constraints. We need two types of constraints: capacity and demand.
We begin with the capacity constraints.
Consider the Pittsburgh–Charlotte flight leg in Figure. The Boeing 737-400 airplane has a 132-seat capacity. Three possible final destinations for passengers on this flight (Charlotte, Myrtle Beach, or Orlando) and two fare classes (Q and Y) provide six ODIF alternatives:
(1) Pittsburgh–Charlotte Q class,
(2) Pittsburgh–Myrtle Beach Q class,
(3) Pittsburgh–Orlando Q class,
(4) Pittsburgh–Charlotte Y class,
(5) Pittsburgh–Myrtle Beach Y class, and
(6) Pittsburgh–Orlando Y class. Thus, the number of seats allocated to
the Pittsburgh–Charlotte flight leg is PCQ PMQ POQ PCY PMY POY. With the capacity of 132 seats, the capacity constraint is as follows:
PCQ + PMQ + POQ + PCY + PMY + POY … 132 Pittsburgh– Charlotte
The capacity constraints for the Newark–Charlotte, Charlotte–Myrtle Beach, and Charlotte– Orlando flight legs are developed in a similar manner. These three constraints are as follows:
NCQ +NMQ +NOQ +NCY +NMY + NOY <= 132
The demand constraints limit the number of seats for each ODIF based on the forecasted demand. Using the demand forecasts in Table 5.3, 16 demand constraints must be added to the model. The first four demand constraints are as follows:
PCQ <= 33
PMQ <= 44
POQ <= 45
PCY <= 16
Pittsburgh – Charlotte Q class
Pittsburgh– Myrtle Beach Q class
Pittsburgh – Orlando Q class
Pittsburgh– Charlotte Y class
The complete linear programming model with 16 decision variables, 4 capacity constraints, and 16 demand constraints is as follows:
Max 178PCQ + 268PMQ + 228POQ + 380PCY + 456PMY + 560POY+ 199NCQ + 249NMQ + 349NOQ + 385NCY + 444NMY + 580NOY + 179CMQ + 380CMY + 224COQ + 582COY
The optimal solution to the Leisure Air revenue management problem is shown. The value of the optimal solution is $103,103. The optimal solution shows that
PCQ 33, PMQ 44, POQ 22, PCY 16, and so on.
Thus, to maximize revenue,
Leisure Air should allocate 33 Q class seats to Pittsburgh–Charlotte, 44 Q class seats to
Pittsburgh–Myrtle Beach, 22 Q class seats to Pittsburgh–Orlando, 16 Y class seats to
Pittsburgh–Charlotte, and so on.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.