Single machine multi-product capacitated lot sizing with sequence-dependent setups

Abstract

In production planning in the glass container industry, machine-dependent setup times and costs are incurred for switch overs from one product to another. The resulting multi-item capacitated lot-sizing problem has sequence-dependent setup times and costs. We present two novel linear mixed-integer programming formulations for this problem, incorporating all the necessary features of setup carryovers. The compact formulation has polynomially many constraints, whereas the stronger formulation uses an exponential number of constraints that can be separated in polynomial time. We also present a five-step heuristic that is effective both in finding a feasible solution (even for tightly capacitated instances) and in producing good solutions to these problems. We report computational experiments.

Keywords:

• Capacitated lot sizing and scheduling
• Sequence-dependent setup
• Integer programming
• Heuristics

Acknowledgements

The authors are grateful to Professor Stephen C. Graves from the Sloan School of Management for his helpful comments. The first author is also grateful to the Portuguese Foundation for Science and Technology for awarding him a PhD grant (SFRH/BD/23987/2005).