# Question

Flight 120 between Seattle and San Francisco is a popular flight among both leisure and business travelers. The airplane holds 112 passengers in a single cabin. Both a discount 7-day advance fare and a full-price fare are offered. The airline’s management is trying to decide (1) how many seats to allocate to its discount 7-day advance fare and (2) how many tickets to issue in total (recognizing that there will be some no-shows).

The discount ticket sells for $150 and is nonrefundable. Demand for the 7-day advance fares is typically between 50 and 150, but is most likely to be near 90. (Assume a triangular distribution.) The full-price fare (no advance purchase requirement and fully refundable prior to check-in time) is $400. Excluding customers who purchase this ticket and then cancel prior to check-in time, demand is equally likely to be anywhere between 30 and 70 for these tickets (with essentially all of the demand occurring within one week of the flight). The average no-show rate is 5 percent for the nonrefundable discount tickets and 15 percent for the refundable full-price tickets, where the latter no-shows occur too late to qualify for a refund. (The latter no-shows typically are business people whose plans have changed and whose firm bears the cost of the wasted ticket.) Assume a binomial distribution for the actual number of no-shows of each type for a particular flight. If more ticketed passengers show up than there are seats available, the extra passengers must be bumped from the flight. A bumped passenger is rebooked on another flight and given a voucher for a free ticket on a future flight. The total cost to the airline for bump- ing a passenger is $600. There is a fixed cost of $10,000 to operate each flight. There are two decisions to be made. First, prior to one week before the flight, how many tickets should be made available at the discount fare? Too many and the airline risks losing out on fullfare passengers. Too few and the airline may have a less-than-full flight. Second, how many tickets should be issued in total? Too many and the airline risks needing to bump passengers. Too few and the airline risks having a less-than-full flight.

(a) Suppose that the airline makes available a maximum of 75 tickets for the discount fare and a maximum of 120 tickets in total. Use ASPE to generate a 1,000 trial forecast of the distribution of the profit, the number of seats filled, and the number of passengers bumped.

(b) Generate a two-dimensional parameter analysis report that gives the mean profit for all combinations of the following values of the two decision variables: (1) the maximum number of tickets made available at the discount fare is a multiple of 10 between 50 and 90, and (2) the maximum number of tickets made available for either fare is 112, 117, 122, 127, or 132.

(c) Use ASPE’s Solver to try to determine the maximum number of discount fare tickets and the maximum total number of tickets to make available so as to maximize the airline’s mean profit.

The discount ticket sells for $150 and is nonrefundable. Demand for the 7-day advance fares is typically between 50 and 150, but is most likely to be near 90. (Assume a triangular distribution.) The full-price fare (no advance purchase requirement and fully refundable prior to check-in time) is $400. Excluding customers who purchase this ticket and then cancel prior to check-in time, demand is equally likely to be anywhere between 30 and 70 for these tickets (with essentially all of the demand occurring within one week of the flight). The average no-show rate is 5 percent for the nonrefundable discount tickets and 15 percent for the refundable full-price tickets, where the latter no-shows occur too late to qualify for a refund. (The latter no-shows typically are business people whose plans have changed and whose firm bears the cost of the wasted ticket.) Assume a binomial distribution for the actual number of no-shows of each type for a particular flight. If more ticketed passengers show up than there are seats available, the extra passengers must be bumped from the flight. A bumped passenger is rebooked on another flight and given a voucher for a free ticket on a future flight. The total cost to the airline for bump- ing a passenger is $600. There is a fixed cost of $10,000 to operate each flight. There are two decisions to be made. First, prior to one week before the flight, how many tickets should be made available at the discount fare? Too many and the airline risks losing out on fullfare passengers. Too few and the airline may have a less-than-full flight. Second, how many tickets should be issued in total? Too many and the airline risks needing to bump passengers. Too few and the airline risks having a less-than-full flight.

(a) Suppose that the airline makes available a maximum of 75 tickets for the discount fare and a maximum of 120 tickets in total. Use ASPE to generate a 1,000 trial forecast of the distribution of the profit, the number of seats filled, and the number of passengers bumped.

(b) Generate a two-dimensional parameter analysis report that gives the mean profit for all combinations of the following values of the two decision variables: (1) the maximum number of tickets made available at the discount fare is a multiple of 10 between 50 and 90, and (2) the maximum number of tickets made available for either fare is 112, 117, 122, 127, or 132.

(c) Use ASPE’s Solver to try to determine the maximum number of discount fare tickets and the maximum total number of tickets to make available so as to maximize the airline’s mean profit.

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