""Need help with business case"
3. Business case: revenue management at East-West airlines
(a) Compute shadow prices for each of the 16 demand and 4 capacity constraints.
(b) Boston-Chicago Q-class demand has std. deviation ? = 5.3. Compare allowable decrease and increase for this constraint with 1.28? (10% critical value for the normal distribution). Does the allowable increase for the demand constraints exceed the 1.28?? How about the allowable decrease? If the threshold of 1.28? is not exceeded, there is at least 10% chance that the shadow price for the constraint may be inappropriate.
(c) Suppose that you are considering introducing a business class ticket for the BostonChicago itinerary. Two business class seats use the same space as three Q or Y class seats. What is the minimal price you should charge for a business class seat in order to increase profits?
(d) In the absence of business class, you are considering to reduce the price for Q-class ticket on the Boston-Chicago flight. How much can you reduce it without having to re-optimize the ticket sales?
Instructions. Please upload a picture le or a pdf of your solution on Canvas by the due time. You can use pen/pencil and paper and then scan/take a picture of your solution. Alternatively, you can use a tablet (such as ipad or microsoft surface) to digitally write your solution by hand. Typed solutions will not be accepted. 1. Comprehension check Read Chapter 3 and solve the following problems in the end of the chapter. Copy the answers from Excel to your solution. You do not need to submit the XLS le. (a) Problem 3.28 (b) Problem 3.4-2 2. Business case: revenue management at East-West airlines Suppose that East-West airlines is a small airline that offers passanger air transportation between two major east coast cities, namely Boston and New York; two major west coast cities , namely San Iii-anciSCO and Los Angeles; and one major midwest city, namely Chicago. EastWest operates a hub in Chicago, at which passengers can change planes to their nal destination. East-West Airlines owns and operates two identical Boeing 757 aircraft, each with capacity of 200 seats. The daily schedule of these airlines is shown in Table 10.1. Eastwest offers both discounted (Q-class) and unrestricted (Yclass) fares. Discounted tick- ets must be purchased fourteen days in advance of ight departure. A Qclass ticket is non-refundable, non-changeable. Unrestricted fare tickets can be purchased any time up until the departure time of the ight. A Yclass ticket is fully refundable. For the purpose of this HA, we will focus exclusively on the westbound operations. Table 10.2 shows the westbound itineraries that East-West airlines. Table 10.3 show expected demand (a) for each pair of departure-destination (disregard a). The goal of the airline company is to choose the numblr of tickets for each class and each itinerary to maximize the revenue. Each ight can carry up to 200 passengers. There are no direct ights from East Coast to West Coast, so the ights to Chicago will carry some passenger that will transfer on another plane to the West coast destination. (a) Dene decision variables (b) Dene an objective function (c) Dene constraints (d) Find optimal number of tickets for each combination of class and itinerary and the corresponding maximal revenue using Excel. TABLE 10.1 Aircraft Departs: Arrives: The daily flight Number City Time City Time schedule for East- BOSTON 8:00AM EST CHICAGO 10:15AM CST West Airlines. CHICAGO 10:45AM CST SAN FRANCISCO 12:15PM PST NNNNHH SAN FRANCISCO 5:30PM PST CHICAGO 10:45PM CST CHICAGO 11:59PM CST BOSTON 4:30AM EST NEW YORK 7:45AM EST CHICAGO 10:15AM CST CHICAGO 10:45AM CST LOS ANGELES 12:15PM PST LOS ANGELES 5:30PM PST CHICAGO 10:45PM CST CHICAGO 11:59PM CST NEW YORK 4:45AM EST TABLE 10.2 Itinerary Q-Class Y-Class Prices of Q-Class From: To: Fare Price Fare Price and Y-Class fares for BOSTON CHICAGO $200 $230 the westbound BOSTON SAN FRANCISCO $320 $420 itineraries of East- BOSTON LOS ANGELES $400 $490 West Airlines. NEW YORK CHICAGO $250 $290 NEW YORK SAN FRANCISCO $410 $550 NEW YORK LOS ANGELES $450 $550 CHICAGO SAN FRANCISCO $200 $230 CHICAGO LOS ANGELES $250 $300 TABLE 10.3 2-Class demand Y-Class demand Itinerary (Number of Passengers) (Number of Passengers) The mean and standard deviation From: To: of the demand for BOSTON CHICAGO 25.0 5.3 20.0 5.2 travel on Mondays BOSTON SAN FRANCISCO 55.0 5.1 40.0 6.0 BOSTON LOS ANGELES 65.0 9.3 25.0 4.8 on westbound NEW YORK CHICAGO 24.0 4.4 16.0 3.0 flights at East-West NEW YORK SAN FRANCISCO 65.0 8.4 50.0 6.9 Airlines. NEW YORK LOS ANGELES 40.0 5.1 35.0 6.3 CHICAGO SAN FRANCISCO 21.0 6.2 20.0 3.7 CHICAGO LOS ANGELES 25.0 5.2 14.0 2.4
