Inventory Replenishment for Profit Maximization over a Finite Horizon under One-time Cost Changes

Abstract

This article considers the optimal inventory ordering, purchasing and holding policies of the profit-maximization problem, as against the well-known cost-minimization case, over a finite horizon of length H, under two special conditions. First, there is change in at least one of the inventory costs, that is, in the cost of ordering and/or purchasing/holding, at some point, T_c < H, during the planning horizon. Second, it is not necessary to satisfy the demand, at a rate of R units per year, for the entire horizon. Rather, the objective is to meet the demand for a period of length H₁ ≤ H. In fact, if the retailer does not have the obligation to meet the entire demand, this article shows the conditions wherein it may be more profitable to meet only a portion or may be even none of the demand. Further, such a determination can be made up front, with H₁ as a decision variable and the optimal policies of the cost-minimization models, by fulfilling the entire demand, will result in lower profits. Numerical examples are included to identify the demand fulfilment and the profit differences between the cost-minimization and profit-maximization optimal policies, under the different one-time cost changes.