Multi-level lot sizing in material requirements planning: an empirical investigation

Abstract

The research report in this paper was a result of a recent article by Yelle [8]. He reports computational results using all combinations of four single level heuristic lot sizing rules, which are applied sequentially to a two level problem in a Material Requirements Planning (MRP) environment. To test the impact of the different combinations of these lot sizing rules he employed six different demand patterns for the end-items which range from level demand to demand which is intermittent throughout the planning horizon. In our research we utilized the same data as Yelle and conducted a more extensive analysis by adding (a) two more recent and powerful single level heuristic rules, namely, the least unit cost heuristic and Silver and Meal's least-cost per period heuristic, (b) the very well known single level optimum method of Wagner-Whitin[7], and (c) a multi-level heuristic proposed recently by McLaren and Whybark [4]. The results show a significant improvement in many cases over the best solutions reported by Yelle. Further in this paper, we also provide a much simpler mathematical formulation of the multi-level lot sizing problem than found in the literature. This formulation was advantageously used to determine optimum solutions using IBM's Mathematical Programming System Extended (MPSX) to the aforementioned problems.