4 Marks Question 5 The Bloomberg Resort rents weekly Guest Houses by the Bali sh

Question

4 Marks Question 5 The Bloomberg Resort rents weekly Guest Houses by the Bali shore. These Guest Houses rent for $1500 per week, and guest typically spend another $500 as profit to the firm during their stay. If no Guest House is available for a customer with reservation, he has to be transported to another Guest House, and Bloomberg picks up the cost of the other Guest House $750 per week plus $200 as transportation charge. No-shows by customers' average three a week, evenly distributed between 0 and 6. How many Guest Houses should Bloomberg overbook?

Explanation / Answer

Co = cost of overage (customers denied advance reservation) = $1500 + $500 = $2,000

Cs = cost of stockouts (customers with reservations are turned away because no rooms are left) = $750 + $200 = $950

Critical ratio (CR) = Co / (Co + Cs) = 2000 / 2950 = 0.677

From the marginal cost approach,  Accept bookings until,

CR <= P(Overbookings >= No-shows)

At the point of optimality, P(Overbookings >= No-shows) = CR = 0.667

So, the optimal overbooking = Mean no. of noshows + 0.667 x (Max no-show - Min no-show)

= 3 + 0.667 * (6 - 0)

= 7

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