Impact analysis of setup carryover and crossover on lot sizing problems

Abstract

This paper presents a literature classification and a detailed computational study analysing the impact of considering the possibility of setup carryover and crossover when solving the lot sizing problem. This problem is an extension of the standard Capacitated Lot Sizing Problem. A setup carryover is defined as the possibility to begin a period with production (instead of setup) of the item that was being produced at the end of the previous period. A setup crossover allows the opportunity to start a setup operation in one period and continue it to the following one, i.e. the setup operation can span over two periods. We adapt and compare two formulations proposed in the literature that have not been compared each other. Furthermore, some formulations proposed in the literature for modelling the setup crossover with a reduced number of binary variables, are extended to the addressed problem. Finally, a relax-and-fix and fix-and-optimise (RF-FO) heuristic is also applied to solve some difficult instances. Computational results are presented based on random generated data.