You are managing the Killington Inn, a ski lodge dedicated to the needs of skiers in the central Vermont ski complex (the mountains of Killington, Okemo, etc.). Each year the Inn advertises and sells weekend ski packages that include two nights lodging (Friday, Saturday) plus unlimited skiing for two at all nearby mountains. The packages sell for $459 if booked early and $599 if booked late. The Inn currently has 30 rooms available for these weekend ski packages. Demand for late bookers (class 1) follows a Poisson distribution with mean L = 20. Calculate the optimal protection level for class 1 using Littlewood’s two‐class model.
**Littlewood’s Two‐Class Model with Upgrades**
One of the interesting wrinkles one can add to Littlewood’s model is the possibility of upgrades. When a class 2 request is denied in period 2 (because we have hit the booking limit for class 2capacity), a customer may then make a class 1 request. If some customers upgrade to class 1,then protecting capacity has some additional benefit to its expected value. Suppose a customer requests class 1 with probability q if class 2 is closed. Then the payoffs andprobabilities associated with denying a class 2 request in period 2 when capacity is x are
Payoff |
Probability |
p1 |
q |
p1Prob (D1>= x) |
1-q |
Observe that the payoff is p1 if the customer upgrades and p1Prob(D1 ³ x)the traditional expected payoff without upgrades) if they do not. (Note: D1 is considered “pure” demand for class 1 in period 1 and does not include this upgrade demand). Therefore, the expected value of rejecting a class 2 request when capacity is x is
qp1+(1-q)p1Prob(D1>=x)
Thus one only accepts class 2 requests in period 2 if it exceeds this value. Observe that this
expected value is slightly larger than that used in the two‐class model without upgrades. This
makes sense because a class 2 request that is denied will sometimes (with probability q) be
transformed into a higher priced outcome in this model. After a little algebra, the optimal
protection level is seen to be y*1 = F1-1 (p1-p2/(1-q)p1))