A Probabilistic Production and Inventory Problem

Abstract

R. Howard (R. Howard.1960. Dynamic Programming and Markov Processes . John Wiley and Sons, Inc., New York.) and A. Manne (A. Manne. 1960. Linear programming and sequential decisions. Management Science , April.) have suggested two methods for optimizing average costs per unit time by means of a sequential decision rule. This rule gives order quantities as a function of initial stock levels, and is based upon the assumption of a Markov process which is both homogenous and discrete. The formulation does not include any restrictive hypothesis on the structure of costs. This paper presents a synthesis of both dynamic and linear programming methods applicable to the same kind of model for the case of time discounting.