Costs of Incorrect Data in Optimal Inventory Computations

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.