The Near-Myopic Nature of the Lagged-Proportional-Cost Inventory Problem with Lost Sales

A considerable literature has been devoted to periodic-review inventory problems with proportional ordering costs and known independent demand distributions, because of the optimality under broad conditions of “base-stock” policies. An important exception is the case when order delivery is lagged and excess demand is simply lost, which is more complicated. By further restricting holding and penalty costs to be proportional, the author has extended preliminary work by Karlin and Scarf to obtain good bounds for both the optimal order policy and the associated minimum-expected-discounted-cost function for the stationary problem. These bounds possess a “newsboy” interpretation primarily in terms of costs to be incurred specifically for the review period (the period marked by the arrival of this order). In fact, the upper ordering bound is precisely the “myopic” policy in Veinott's sense. (However, the myopic policy is not base stock.) Experimental results for the one- and two-period lag problems strongly support the heuristic argument that myopic policies should, in fact, be very nearly optimal. An extension of the model to a partial backlogging situation is presented for which optimal policies may also be safely conjectured to be “myopoid.” It is hoped that interest will be stimulated toward investigating myopic policies as approximate solutions to a large class of proportional cost problems.