Inventory Replenishment for Profit Maximization over a Finite Horizon

摘要

This paper shows the potential differences between the profit-maximizing and the cost-minimizing solutions to the deterministic finite-horizon inventory problem. First, it presents a counterexample to the proposition that both types of solutions are alike. Then, it provides a formal proof of the proposition that the cost minimization solution to the finite- horizon deterministic inventory problem does not necessarily correspond to the profit maximization solution. It also supplies the conditions under which both solutions coincide and both differ and presents practical instances of such solutions. The main difference lies in that it may be more profitable not to meet the demand for the entire planning horizon than to incur in lost sales. We provide a simple search procedure to reach the optimal solution. The analysis also provides a tool for managers to evaluate both extendible and abandoning options. A numerical example serves to illustrate the characteristics of the problem.