Leisure Air, a regional airline, provides service forPittsburgh, Newark, Charlotte, Myrtle Beach, and Orlando. LeisureAir has two Boeing 737-400 airplanes, one based in Pittsburgh andthe other in Newark. Both airplanes have a coach section with a132-seat capacity. Each morning the Pittsburgh-based plane flies toOrlando with a stopover in Charlotte, and the Newark-based planeflies to Myrtle Beach, also with a stopover in Charlotte. At theend of the day, both planes return to their home bases. We restrictour attention to the Pittsburgh-Charlotte, Charlotte-Orlando,Newark-Charlotte, and Charlotte-Myrtle Beach flight legs for themorning flights.
Leisure Air uses two fare classes: a discount-fare Q class and afull-fare Y class. Reservations using the discount-fare Q classmust be made 14 days in advance and must include a Saturday nightstay in the destination city. Reservations using the full-fare Yclass may be made any time, with no penalty for changing thereservation at a later date. Leisure Air established fares anddeveloped forecasts of customer demand for each of 16 ODIFs. Thesedata are shown in the table below.
FARE AND DEMAND DATA FOR 16 LEISURE AIRORIGIN-DESTINATION-ITINERARY FARES (ODIFs) |
ODIF | Origin | Destination | Fare
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 |
But because demand cannot be forecasted perfectly, the number ofseats 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 haveimproved and that its original forecast may be too low. To accountfor this possibility, Leisure Air is considering switching theBoeing 737-400 airplanes that are based in Pittsburgh and Newarkwith Boeing 757-200 airplanes that Leisure Air has available inother markets. The Boeing 757-200 airplane has a seating capacityof 158 in the coach section.
a. Because of scheduling conflicts in othermarkets, suppose that Leisure Air is only able to obtain one Boeing757-200. Should the larger plane be based in Pittsburgh or inNewark?
Newark
Explain.
The total revenue of basing the larger plane in Newark isbigger than basing the larger plane inPittsburgh.
b. Based upon your answer in part (a),determine a new allocation for the ODIFs.
Original allocation:
THE SOLUTION FOR THE LEISURE AIR REVENUE MANAGEMENT PROBLEM |
Optimal Objective Value = 103103.0000 | | |
Variable | | Value | | Reduced Cost |
PCQ | | 33.00000 | | 0.00000 |
PMQ | | 44.00000 | | 0.00000 |
POQ | | 22.00000 | | 0.00000 |
PCY | | 16.00000 | | 0.00000 |
PMY | | 6.00000 | | 0.00000 |
POY | | 11.00000 | | 0.00000 |
NCQ | | 26.00000 | | 0.00000 |
NMQ | | 36.00000 | | 0.00000 |
NOQ | | 39.00000 | | 0.00000 |
NCY | | 15.00000 | | 0.00000 |
NMY | | 7.00000 | | 0.00000 |
NOY | | 9.00000 | | 0.00000 |
CMQ | | 31.00000 | | 0.00000 |
CMY | | 8.00000 | | 0.00000 |
COQ | | 41.00000 | | 0.00000 |
COY | | 10.00000 | | 0.00000 |
| | | | |
Constraint | | Slack/Surplus | | Dual Value |
1 | | 0.00000 | | 4.00000 |
2 | | 0.00000 | | 70.00000 |
3 | | 0.00000 | | 179.00000 |
4 | | 0.00000 | | 224.00000 |
5 | | 0.00000 | | 174.00000 |
6 | | 0.00000 | | 85.00000 |
7 | | 23.00000 | | 0.00000 |
8 | | 0.00000 | | 376.00000 |
9 | | 0.00000 | | 273.00000 |
10 | | 0.00000 | | 332.00000 |
11 | | 0.00000 | | 129.00000 |
12 | | 20.00000 | | 0.00000 |
13 | | 0.00000 | | 55.00000 |
14 | | 0.00000 | | 315.00000 |
15 | | 0.00000 | | 195.00000 |
16 | | 0.00000 | | 286.00000 |
17 | | 33.00000 | | 0.00000 |
18 | | 0.00000 | | 201.00000 |
19 | | 5.00000 | | 0.00000 |
20 | | 0.00000 | | 358.00000 |
c.
Using a larger plane based in Newark, the optimal allocationsare:
PCQ | = | PMQ | = | POQ | = |
PCY | = | PMY | = | POY | = |
NCQ | = | NMQ | = | NOQ | = |
NCY | = | NMY | = | NOY | = |
CMQ | = | CMY | = | | |
COQ | = | COY | = | | |
d.
Briefly summarize the major differences between the new allocationusing one Boeing 757-200 and the original allocation summarizedabove.
The main differences between the original allocations and the newallocations are in the variables:
CMQ, COQ, PMQ, NMQ, and POQ
e. Suppose that two Boeing 757-200 airplanesare available. Determine a new allocation for the ODIF’s using thetwo larger airplanes. Using a larger plane based in Pittsburgh anda larger plane based in Newark, the optimal allocations are:
PCQ | = | PMQ | = | POQ | = |
PCY | = | PMY | = | POY | = |
NCQ | = | NMQ | = | NOQ | = |
NCY | = | NMY | = | NOY | = |
CMQ | = | CMY | = | | |
COQ | = | COY | = | | |
f.
Briefly summarize the major differences between the new allocationusing two Boeing 757-200 airplanes and the original allocationshown in part (b).
The main differences between the allocations in part b and the newallocations are in the variables:
CMQ, COQ, NMQ, and POQ
This solution provides an increase in revenue of$ .
g. Consider the new solution obtained in part(b). Which ODIF has the highest bid price?
COY
What is the interpretation for this bid price?
The bid price for this solution is $ which meansthat if there was one more Y class seat revenuewould increase by $ .
