An Inverse Warehousing Problem for Imperfect Markets

This paper focuses upon the problem of a monopolist who has no control over the rate of arrivals into inventory and who ships his product to distant markets where the price per unit is a randomly shifting inverse function of the quantity shipped. It is assumed that the firm seeks to minimize its expected losses over a many-period horizon where the quantity shipped during any period is subject to last minute reconsideration.

Given certain assumptions about the cost and revenue functions and the level of inventory, it will be shown that the optimal shipping quantity is a linear function of the storage level and that the solution of the many-period nonstationary problem can be expressed in closed form.