Managing inventory with multiple products, lags in delivery, resource constraints, and lost sales: A mathematical programming approach

This paper develops an order-up-to S inventory model that is designed to ha ndle multiple items, resource constraints, lags in delivery, and lost sales without sacrificing computational simplicity. Mild conditions are shown to ensure that the expected average holding cost and the expected average sho rtage cost are separable convex functions of the order-up-to levels. We dev elop nonparametric estimates of these costs and use them in conjunction wit h Linear programming to produce what is termed the "LP policy." The LP poli cy has two major advantages over traditional methods: first, it can be comp uted in complex environments such as the one described above; and second, i t does not require an explicit functional form of demand, something that is difficult to specify accurately in practice. In two numerical experiments designed so that optimal policies could be computed, the LP policy fared we ll, differing from the optimal profit by an average of 2.20% and 1.84%, res pectively. These results compare quite favorably with the errors incurred i n traditional methods when a correctly specified distribution uses estimate d parameters. Our findings support the effectiveness of this mathematical p rogramming technique for approximating complex, real-world inventory contro l problems.