New construction heuristic for capacitated lot sizing problems

Abstract

We consider the classical single-level multi-item capacitated lot-sizing problem (CLSP) which is the core model for production planning. It is NP-hard and if setup operations consume capacity the feasibility problem itself is NP-complete. Several construction heuristics have been proposed in the research literature, but none of them achieves a sufficient solution quality and generality at the same time - meaning that they can be applied to different variations of the problem easily. We propose a general two-step construction heuristic (2-SCH) which sorts the customer orders in the first step and iteratively adds them to a preliminary production plan in the second step. Hence, various problem classes can be solved easily and fast. Computational experiments on the CLSP without setup times show that the 2-SCH outperforms the well-known Dixon–Silver (Dixon & Silver, 1981) and the ABC heuristics Maes and Van Wassenhove (1986) and provides better results than the genetic programming approach proposed recently by Hein et al. (2018). We also apply it to the CLSP with setup times where it outperforms the construction heuristic proposed by Trigeiro (1989). Finally, we show the flexibility of the 2-SCH by applying it to the CLSP with backorders and the multi-level CLSP as well as the single-level CLSP in an online environment.