Question

1. A package holiday company is about to block book hotel rooms for the coming season. The number of holidays actually booked is equally likely to be any number between 0 and 99 (for simplicity rather than reality). Each room booked costs the company $250 and they can sell them for $350. How many rooms should the company book if unsold rooms have no value?

Answer 1

Cost of underage, C_u = Selling price - Cost = 350 - 250 = 100
Cost of overage, C_o = Cost - Salvage value = 250 - 0 = 250

So,

The newsvendor critical fractile, CF = C_u / (C_o + C_u) = 100 / (250+100) = 0.286

For the booking numbers to become optimal, the cumulative in-stock probability must be equal to CF.

So,

Optimal booking number = 0 + 0.286*(99 - 0) = 28.3 i.e. 28 rooms when rounded off