Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries

Abstract

In this paper, we propose three novel mathematical models for the two-stage lot-sizing and scheduling problems present in many process industries. The problem shares a continuous or quasi-continuous production feature upstream and a discrete manufacturing feature downstream, which must be synchronized. Different time-based scale representations are discussed. The first formulation encompasses a discrete-time representation. The second one is a hybrid continuous-discrete model. The last formulation is based on a continuous-time model representation. Computational tests with state-of-the-art MIP solver show that the discrete-time representation provides better feasible solutions in short running time. On the other hand, the hybrid model achieves better solutions for longer computational times and was able to prove optimality more often. The continuous-type model is the most flexible of the three for incorporating additional operational requirements, at a cost of having the worst computational performance.

Keywords:

• lot sizing and scheduling
• two-stage production system
• mixed-integer program
• time scale

Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments. This research was funded by FAPESP (2008/09953-2), CNPq (300713/2010-0) and CAPES (CAPES BEX-1545/11-6) from Brazil, and FP7-PEOPLE-2009-IRSES project no. 246881 and Erasmus Mundus External Cooperation Windows Programme from European Commission.