A hotel near St. Thomas always fills up on the evening before football games. Hi

Question

A hotel near St. Thomas always fills up on the evening before football games. Historical data tells us that when the hotel is fully booked, the number of last minute cancellations has a mean of 6 and a standard deviation of 4. The average room rate $100. When the hotel is overbooked, the policy is to find a room in a nearby hotel and pay the room for the customer. This usually costs the hotel on average $200 since rooms booked on such late notice are very expensive.

a) How many rooms should the hotel overbook?

b) For the hotel to be 90% sure that they do not have a single room unoccupied, how many rooms should the hotel overbook?

Explanation / Answer

The cost of underestimating the demand is Cu and cost of overestimating demand is Co Cu = $200 (Nearby Accomodation) Co = $100 (Lost Sales) Service Level = Cu / (Cu + Co) = 200 / (200 + 100) = 200/300 = 0.6667 Z Value at above service level = 0.430727 Overbooking = Mean + Z Value * Std Deviation = 6 + 4 * 0.430727 = 6 + 1.7223 = 8 Hotel should overbook by 8 rooms b. Z Value at 90% = 1.28155 Overbooking = Mean + Z Value * Std Deviation = 6 + 4 * 1.28155 = 6 + 5.126 = 11 Hotel should overbook by 11 rooms

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