Use the following information to determine the optimal overbooking policy for a

Question

Use the following information to determine the optimal overbooking policy for a motel at a rural town in South Carolina. The motel’s capacity is 30 rooms. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per room is $110, and the cost of lost goodwill per guest due to overbooking is approximately $60. No-Shows Probability 0 0.25 1 0.35 2 0.15 3 0.25 Calculate the total expected profit with 33 reservations (which means 3 overbookings). $3,300.00 $3,204.00 $2,897.50 $2,883.50 $2,827.00

Explanation / Answer

Profit per room = $110

Cost per loss of goodwill = $60

For an alternative of 3 overbookings, there are 4 states of nature that can exist, i.e. 0 no-shows, 1 no-shows, 2 no shows or 3 no shows

For 0 no-shows, the cost will be due to loss of goodwill of 3 customers, i.e. 3 * 60 = $180

For 1 no-shows, the cost will be due to loss of goodwill of 2 customers, i.e. 2 * 60 = $120

For 2 no-shows, the cost will be due to loss of goodwill of 1 customers, i.e. 1 * 60 = $60

For 3 no-shows, the cost will be due to loss of goodwill of 0 customers, i.e. 0 * 60 = $0

The probability of 0 no-shows = 0.25

The probability of 1 no-shows = 0.35

The probability of 2 no-shows = 0.15

The probability of 3 no-shows = 0.25

The total expected loss due to overbooking= 0.25 * 180 + 0.35 * 120 + 0.15 * 60 + 0.25 * 0 = $96

Total profit from filling all the 30 rooms = $110 * 30 = $3300

Total expected profit = Total profit from filling all the 30 rooms? - Expected loss due to overbooking policy

= 3300 - 96

= $3204

Hence the correct answer is option B.

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