Question

Overbooking On a given Vancouver-Toronto flight there are 245 seats. Suppose the ticket price is $459 on average and the number of passengers who reserve a seat but do not show up for departure is normally distributed with mean 27 and standard deviation 17. You decide to overbook the flight and estimate that the average loss from a passenger who will have to be 'bumped' (if the number of passengers exceeds the number of seats) is $735. Part a: 4 points What is the under-stocking cost Cu? Locally stored answer: Part b: 4 points What is the over-stocking cost Co? Locally stored answer: Part c: 4 points What is the service level or critical fractile? (Please state a probability with 4 decimal places and not a percentage). Locally stored answer:

Answer 1

The under-stocking cost (Cu) for not selling a ticket when there is demand is $459, and the over-stocking cost (Co) is $735 for having to bump a passenger. The service level or critical fractile, calculated using Cu / (Cu + Co), is approximately 0.3844.

Step-by-step explanation:

The student is asking about the costs associated with overbooking for an airline and how to calculate service levels based on a normal distribution of passenger no-shows. We can calculate under-stocking cost (Cu), over-stocking cost (Co), and the critical fractile or service level for the airline's scenario.

• Part a: The under-stocking cost, Cu, is the opportunity cost of not selling a ticket when there is demand. Since the ticket price is $459, Cu would be $459, as that is the revenue lost by not having a passenger for an empty seat.
• Part b: The over-stocking cost, Co, is the cost incurred from having to bump a passenger. Since the average loss from bumping a passenger is $735, Co would be $735.
• Part c: To find the service level or critical fractile, we use the formula Cu / (Cu + Co). Substituting the values we have 459 / (459 + 735) = 459 / 1194. Calculating this gives a critical fractile of approximately 0.3844 (when rounded to four decimal places).