Costs of Incorrect Data in Optimal Inventory Computations

Abstract

Consider an infinite-stage inventory process in which the cost of ordering an amount y of stock is ky , and the penalty cost incurred in meeting an excess demand y over the stock on hand is py + q ; also, the process assumes that demands at successive stages are random variables drawn from a fixed probability distribution. Then, under conditions described in the paper, the extra costs incurred in using a policy that, instead of minimizing the statistical expectation of the total cost of the process, minimizes that of a process whose parameters are different from those of the process under consideration are determined. That is, in determining the policy, it is incorrectly assumed that (i) the penalty cost is p ′ y + q , (ii) the penalty cost is py + q ', or (iii) the fixed discount ratio per period of time is a ′ instead of a .