Define the underage cost and overage cost

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Reference no: EM133447369

Case: A group wants to start an airline. They buy one airplane that has n seats. They estimate that two types of travelers will purchase tickets for a certain flight on a certain date:

Leisure, who are willing to pay only the discounted fare $d ;
Business, who are willing to pay the full fare $f (where f > d ).
it is decided that the number of leisure travelers requesting tickets for this flight will be greater than n for sure, while the number of business travelers requesting tickets is random. Assume that leisure purchase tickets before business (In practice, this is roughly true, which is why airfares increase as the flight date gets closer).

THEY wants to sell as many seats as possible to business travelers since their WTP is higher. Although, since the number of such travelers is random and these customers arrive near the flight's departure date, a good strategy is to assign a certain number of seats Q for full fares and the remainder, n - Q for discount fares.

The discount fares are sold first: The first n-Q customers the request a ticket will be charged $d per ticket and the remaining (at most Q) customers will be the full price $f. Because leisure are only willing to pay $d, they will not want to buy a full-fare ticket. therefore, if there are less than Q ticket requests from business, some seats will not be sold (and BuzzAir regrets not selling them to leisure travelers). Conversely, it is possible that some of the seats sold to leisure travelers for $d could have been sold to business travelers who would have been willing to pay $f.

QUESTION:

1.) We know that finding a full fare Q is a Newsvendor problem. Define the underage cost, overage cost, and uncertainty. What is the critical ratio?

2.) Demand for the flight is normally distributed with a mean of 40 and SD of 18. There are n seats=100, d=$175, f=$400. What is the optimal quantity of f (full fare)seats?

Reference no: EM133447369

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