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QUESTION
Hilton hotel very busy around graduation time and is almost always fully booked. From experience, the manager believes that when the hotel is fully booked, the number of no-shows have a distribution shown in the attached spreadsheet:
Hotel-Hilton-spreadsheet (XLSX)
The average room rate is £80 (assume this is the profit as marginal costs are 0). When a customer is denied a room due to overbooking, it costs the hotel roughly £200 (goodwill, finding other accommodation).
How many rooms should the hotel overbook during the graduation period?
Fill up the other costs in the table (using Excel formulas) and then pick the overbooking limit that minimises the total cost. (Hint: Fill the appropriate calculation for one cell and copy and paste to the rest. The Expected Total Cost is the weighted average of the costs for each row, weighted by the probabilities).
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