CHARACTERISTICS OF DYNAMIC MAXIMIN ORDERING POLICY

Abstract

It is the purpose of this article to attempt a further extension of our previous studies [l1J [12]. The problem which is the concern of our study is the following type. There is a certain one-stage profit function P(x, y, z), where x, y, and z denote the initial stock, starting stock, and demand of the merchandise, respectively. The exact probability distribution on z is unknown, but z can be assumed to exist in the closed interval [Zmin, Zmax]. The demand interval assumed is identical at any stage in future. Under the assumption of maximin profit principle, our problem is reduced to one of the multi-stage games, and the solution to our problem is to solve the functional equation of the form (Ll) f(x)=Val[P(x, y, z)-,-aflMax(v-z, O))J where f(x) is the total present value of securable profit starting with initial stock x and using a maximin ordering policy in an unlimited number of stages, and a is a discount factor such that O~a~1. (By a maximin ordering policy we mean an ordering policy which is optimal in the sense of the maximin profit principle, i. e., an ordering policy which maximizes the se curable profit assuming that the least favourable situation will occur under the prescribed assumptions.) The method of successive approximations is fully utilized to obtain the solution of this equation. Hence, we analyse the following sequence of (1.2) (1.3) equations. fJ(x)=VaIP(x, y, z) fn(x)=Val[P(x, y, z)-!--afn-dMax(y-z,O))J for n=2, 3,. ..... , where fn(x) is the total present value of securable profit starting with initial stock x and using a maximin ordering policy

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