The Dynamic Lot-Sizing Problem for Multiple Items Under Limited Capacity

This paper addresses the problem of scheduling the timing and quantities of production of n different products over m periods for a single production facility with a prespecified capacity. We assume that the demand is deterministic and can vary from one period to another and from one product to another. The objective is to minimize the sum of production setup and inventory holding costs. For medium-size problems, optimal solution algorithms do not yet exist and therefore heuristic solution algorithms are of interest. Most of the existing heuristics make use of the “forward-pass” concept in one way or the other. Forward pass means we begin by determining the lot sizes for earlier periods before moving to study the later periods. In this paper we study the forward-pass approach as well as a different solution approach which we call the four-step algorithm. We develop the feasibility conditions for pure forward-pass algorithms. Finally, we perform a comparative evaluation study.