An Asymptotically Optimal Heuristic for Multi-Item Inventory Models with Joint Inventory Constraints

Abstract

We analyze a periodic review stochastic inventory model with T periods and I items. At the beginning of each period, the inventory position of each item can be adjusted by placing an order or by salvaging some of the inventory. There is a limited capacity for the total inventory held at the end of each period. Orders arrive and salvage batches deplete the inventory after a given lead time. In addition to variable order and salvaging costs, there are linear or convex holding and backlogging costs. In every period, the probability of the aggregate inventory level exceeding the prevailing inventory capacity must be smaller than a given tolerance.

In this paper we show that when demands are independent across items or when each item is correlated with at most O(1) other items, a simple structured policy can be found which is asymptotically optimal when the number of items I grows to infinity. We achieve these results by showing that the problem, specified with chance constraints on the overflow probability in each period, can be sandwiched in between two problems with sets of expected value constraints.

Keywords: Dynamic Programming, Inventory Production, Optimal Control