On the Hotel Overbooking Problem—An Inventory System with Stochastic Cancellations

摘要: M hotel rooms are available at a date n periods from now. Reservations made by customers for that date, which is the peak of high season. Typically, such time period, policy overbooking exercised management. Customers, however, may cancel their previously confirmed reservations any prior to arrival, with no penalty. On other hand, new requests particular generated anew. At end each period management reviews both “inventory” level remaining uncanceled and total number not-yet-confirmed requests. decision regarding inventory start next period. A one three actions: i keep its present i.e., declining all requests; ii increase confirming some and, if necessary, trying obtain additional extra cost; iii decrease canceling incurring penalty cancellation. Each occupied room target day carries given profit, while unhonored reservation incurs The problem find optimal over-booking strategy will maximize net profit. For criteria, maximization expected discounted it shown 3-region as follows: For there exist upper lower bounds an intermediate point that, greater than bound, should be decreased bound; b below two cases occur: discrepancy requests, acquired equal smaller but not exceed point; c between possibilities: above none confirmed, point, provided point.