South Central Airlines (SCA) operates a commuter flight between Atlanta and Charlotte. The regional jet holds 48 passengers and currently SCA only books up to 48 reservations. Past data shows that SCA always sells all 48 reservations, but on average, two passengers do not show up. As a result, with 48 reservations, the flight is often being flown with empty seats. To capture additional profit, SCA is considering an overbooking strategy in which they would accept 50 reservations even though the airplane holds only 48 passengers. SCA believes that it will be able to always book all 50 reservations. The probability distribution for the number of passengers showing up when 50 reservations are accepted is estimated as follows:
Passengers
Showing Up |
Probability |
| 46 |
0.06 |
| 47 |
0.25 |
| 48 |
0.5 |
| 49 |
0.15 |
| 50 |
0.04 |
SCA receives a marginal profit of $100 for each passenger who books a reservation (regardless whether they show up or not). The airline will also incur a cost for any passenger denied seating on the flight. This cost covers added expenses of rescheduling the passenger as well as loss of goodwill, estimated to be $160 per passenger. Develop a spreadsheet simulation model for this overbooking system. Simulate the number of passengers showing up for a flight (Do 100 simulations). Assume the airline collects revenue from every ticket booked, even if the passenger doesn't show up.
| (a) |
What is the average net profit for each flight with the overbooking strategy? |
| If required, round your answer to the nearest dollar. |
| $ |
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| (b) |
What is the probability that the net profit with the overbooking strategy will be less than the net profit without overbooking (48*$100 = $4,800)? |
| If required, round your answer to two decimal places. |
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| (c) |
Explain how your simulation model could be used to evaluate other overbooking levels such as 51, 53, and 54 and for recommending a best overbooking strategy. |
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The input in the box below will not be graded, but may be reviewed and considered by your instructor.
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