Capacitated Lot-sizing with Linked Production Quantities of Adjacent Periods

One of the most important tasks operations manager are confronted with is to determine production quantities over a medium-size planning horizon such that demand is met, scarce production facilities are not overloaded and that the sum of holding and setup costs is minimized. For the single machine case the well-known Capacitated Lot-Sizing Problem (CLSP) has been proposed to determine minimum cost solutions. The CLSP is based on the assumption that for each lot produced in a period setup cost is incurred. But in practice the machine setup can be preserved over idle time very often. In such cases the setup cost of a CLSP solution can be reduced by linking the production quantities of an item which is scheduled in two adjacent periods. Therefore we propose the CLSP with linked lot-sizes of adjacent periods. The problem is formulated as a mixed-integer programming model. For the heuristic solution we present a priority rule based scheduling procedure which is backward-oriented, i.e. at rst lot-sizes are xed in the last period, then in the last but one period, and so on. The priority rule consists of a convex combination of estimated holding and setup cost savings. Since the solution quality depends on realisation of the convex combination we perform a simple local search method on the parameter space to obtain low cost solutions. We show by a computational study that our procedure is more eecient than a two stage approach which rst solves the CLSP with the Dixon-Silver or the Kirca-KK okten heuristic and performs linking of lots afterwards.