Models for capacitated lot-sizing problem with backlogging, setup carryover and crossover

Abstract

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.

Keywords:

• lot sizing
• setup carryover
• setup crossover
• mixed integer linear programming

Acknowledgements

The authors thank the anonymous referees for their valuable comments. This research was funded by FAPESP (2010/06901-1 and 2010/10133-0) and CNPq (590003/2009-7 and 300713/2010-0) from Brazil, FP7-PEOPLE-2009-IRSES project no. 246881 from European Commission and by the North Portugal Regional Operational Programme (ON.2 – O Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF), project BEST-CASE.