On capacitated multi-item inventory problems

Multi-item capacity constrained inventory problems have been widely discussed in the literature. While determining an optimal solution for such problems is extremely difficult, a number of optimization and heuristic approaches based on certain assumptions have been developed. Based on the timings of the orders, these approaches can be classified into two categories – staggering and non-staggering. Most of these approaches assume stationary order quantities. There is only one heuristic known so far which allows non-stationary order quantities. In this paper, an optimal solution procedure for two items is developed. Also, an improvement over the non-stationary heuristic is proposed, and numerical examples are presented to compare the improved heuristic with the original one in terms of the ordering patterns of the items. The average annual costs computed for different approaches are also compared. Finally, it is concluded that though determining an optimal solution is very difficult, development of heuristics employing better starting solutions may be attempted, which will give near-optimal results.