【正文】
? Demand for low fare rooms is abundant. ? Let D be uncertain demand for high fare rooms. ? Suppose D has Poisson distribution with mean . ? Assume most of the high fare (business) demand occurs only within a few days of the actual stay. ? Objective: ? Maximize expected revenues by controlling the number of low fare rooms you sell. Slide ??, Yield management decisions ? The booking limit is the number of rooms you are willing to sell in a fare class or lower. ? The protection level is the number of rooms you reserve for a fare class or higher. ? Let Q be the protection level for the high fare class. ? Q is in effect while you sell low fare tickets. ? Since there are only two fare classes, the booking limit on the low fare class is 118 – Q: ? You will sell no more than 118Q low fare tickets because you are protecting (or reserving) Q seats for high fare passengers. 0 118 Q seats protected for high fare passengers Sell no more than the low fare booking limit, 118 Q Slide ??, The connection to the newsvendor ? A single decision is made before uncertain demand is realized. ? There is an overage cost: ? If D Q then you protected too many rooms (you over protected) ... ? … so some rooms are empty which could have been sold to a low fare traveler. ? There is an underage cost: ? If D Q then you protected too few rooms (you under protected) … ? … so some rooms could have been sold at the high fare instead of the low fare. ? Choose Q to balance the overage and underage costs. Slide ??, Optimal protection level ? Overage cost: ? If D Q we protected too many rooms and earn nothing on Q D rooms. ? We could have sold those empty rooms at the low fare, so Co = rL. ? Underage cost: ? If D Q we protected too few rooms. ? D – Q rooms could have been sold at the high fare but were sold instead at the low fare, so Cu = rH rL ? Optimal high fare protection level: ? Optimal low fare booking limit = 118 – Q* ? Choosing the optimal high fare protection level is a Newsvendor problem with properly chosen underage and overage costs. HLHuourrrCCCQF ????)(*Slide ??, Hyatt example ? Critical ratio: ? Poisson distribution with mean : ? Answer: 24 rooms should be protected for high fare travelers. Similarly, a booking limit of 11824 = 94 rooms should be applied to low fare reservations. 2 2 5 1 5 9 6 6 0 . 2 9 3 32 2 5 2 2 5u h lo u hC r rC C r? ?? ? ? ??Q F ( Q ) Q F ( Q ) Q F ( Q )10 0 .0 0 0 1 20 0 .0 9 2 0 30 0 .7 3 6 511 0 .0 0 0 4 21 0 .1 3 1 4 31 0 .7 9 2 712 0 .0 0 0 9 22 0 .1 8 0 2 32 0 .8 4 0 613 0 .0 0 1 9 23 0 .2 3 8 1 33 0 .8 8 0 314 0 .0 0 3 9 24 0 .3 0 4 0 34 0 .9 1 2 115 0 .0 0 7 7 25 0 .3 7 6 0 35 0 .9 3 7 016 0 .0 1 4 0 26 0 .4 5 1 6 36 0 .9 5 5 817 0 .0 2 4 2 27 0 .5 2 8 0 37 0 .9 6 9 718 0 .0 3 9 6 28 0 .6 0 2 5 38 0 .9 7 9 719 0 .0 6 1 8 29 0 .6 7 2 6 39 0 .9 8 6 7Slide ??, Related calculations ? How many