Consider a company with N warehouses and a certain amount (W units) of stock of a particular SKU to allocate among the warehouses. The next allocation will not be made until one period from now. Let ifx(x0) = probability density of demand in a period for warehouse i(i = 1, 2, ... , N)

Develop a rule for allocating the W units of stock under each of the following costing assumptions (treated separately):

a. A cost Hi incurred at warehouse i if any shortage occurs.

b. A cost Bi is charged per unit short at warehouse i.? Lp852