Optimization of an inventory system with partial backlogging from a financial investment perspective

Abstract

In some real inventory systems, item sales can be adjusted to a stable demand rate along the inventory cycle.For instance, home appliances, electrical products, lounge furniture, home water supply, etc., are items with astable demand rate. In this work, we analyze an inventory system for an item of this type, where the demandrate is constant. Shortages are allowed, and it is assumed that a fraction of demand during the stock-outperiod is backlogged. It is supposed that the shortage costs (backorder cost and lost sales cost) have an affinestructure: a fixed cost plus a linear cost that depends on the period of time where shortages exist. In thispaper, instead of the maximization of the profit per unit time, or the minimization of the average inventorycost per unit time, the objective is the maximization of the return on inventory investment, which is a quotientdefined as the average profit divided by the average inventory cost. The optimal inventory policy is obtainedin a closed form under this new perspective. Moreover, it is shown that the optimal policy that maximizes thereturn on inventory investment is, in general, different from the one that maximizes the profit per unit time. Inaddition, the new optimal perspective offers some advantages. The optimal inventory policy that maximizesthe return on investment does not depend on the unit selling price. Therefore, the inventory manager does notneed to change his/her inventory policy if this price changes. These advantages are not usually present whenthe objective is the maximization of the profit per unit time. Numerical examples are provided to illustratethe theoretical results developed in this work. A sensitivity analysis of the optimal policy with respect to thesystem input parameters is also developed.