A heuristic solution procedure for the multi‐item, single‐level, limited capacity, lot‐sizing problem

Abstract

Abstract The problem to be considered is that of determining lot‐sizes for a group of products which are produced at a single workcentre. It is assumed that the requirements for each product are known, period by period, out to the end of some common time horizon. (A reasonable assumption in a Material Requirements Planning context when we are dealing with components of one or more other items already scheduled.) For each product there is a fixed setup cost incurred each time production takes place. Unit production and holding costs are linear. The time required to set up the machine is assumed to be negligible. All costs and production rates can vary from product to product but not with respect to time. In each period there is a finite amount of machine time available that can vary from period to period. The objective is to determine lot‐sizes so that 1) costs are minimized, 2) no backlogging occurs and 3) capacity is not exceeded. An exact solution to this complex problem is out of the question. Therefore, a simple heuristic has been developed which guarantees a feasible solution, if one exists. Results of a large number of test problems, including three supplied by industrial sources, are presented. The results indicate that the heuristic will usually generate a very good solution with a relatively small amount of computational effort.