Capacitated lot-sizing with linked production quantities of adjacent periods

The well-known Capacitated Lot-Sizing Problem (CLSP) is based on the assumption that for each lot in a period setup costs are incurred. The setup costs 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 (semi-sequencing), denoted by CLSPLA. The CLSPLA is formulated as a mixed-integer programming model. For the heuristic solution of the CLSPLA we provide a method which is backward oriented, denoted by BACLSPLA. We apply a priority rule which consists of a convex combination of holding and setup costs. The convex combination as well as the solution quality depend on a parameter value from [0,1]. We perform a simple parameter value search to obtain a low costs solution. The CLSP may be solved by the famous Dixon-Silver heuristic. A CLSP-schedule (of the Dixon-Silver heuristic) can be transformed into a CLSPLA solution. A computational study shows, that BACLSPLA, i.e. the integration of (semi-) sequencing, is more efficient.