A comparison of simple heuristics for multi-product dynamic demand lot-sizing with limited warehouse capacity

The paper analyzes the problem of the replenishment of multiple products to satisfy dynamic demands when the warehouse capacity or the available inventory budget is limited. In this context the timing of replenishment lot-sizes has to be staggered to account for the capacity conflict and to provide an effective space sharing in addition to the solution of the trade-off between setup and inventory holding costs. We analyze three simple heuristics. First, we review a forward algorithm that successively builds lots by extending replenishments according to a cost-based priority rule. The second heuristic solves the lot-sizing problems independently for each product in a first step and then resolves capacity violations by a smoothing mechanism. Further, this paper adapts a heuristic for single-item uncapacitated lot-sizing that successively improves an initial lot-for-lot schedule by combining replenishments according to a cost savings-based priority rule to the multi-item capacitated problem. The performance of the three simple methods is compared in an extensive numerical study and benchmarked against the solution of a mixed-integer programming approach. The results show the different ability of the approaches to simultaneously account for the individual lot-sizing problems and the lot-staggering problem across multiple products. Especially the savings approach appears to provide better results for a broad range of problems, especially for large, tightly capacitated problems with high demand variability.