On Warehousing Problems

An entrepreneur operates a warehouse of a given capacity for storing a seasonal product. At the beginning of each of a number of consecutive periods (“months”), the product can be bought for storage at a known cost per unit or sold from storage at a known quantity-dependent price per unit. For a given month, the selling price per unit is supposed to have a constant value up to a certain number of units and a lesser constant value for additional units sold. What pattern of buying, storing, and selling should the entrepreneur adopt to maximize his profit?

In this paper, a warehousing problem of this kind is shown to be a generalized Hitchcock distribution problem with mixed boundary conditions and non-positive flows along certain routes. This fact suggests a simple procedure for solving problems of this kind. The procedure readily allows the inclusion of storage costs, which were neglected by Charnes and Cooper.