Synchronisation of scarce resources for a parallel machine lotsizing problem

Abstract

In this paper we present a novel approach to tackling the synchronisation of a secondary resource in lot-sizing and scheduling problems. This kind of problem occurs in various manufacturing processes (e.g. wafer testing in the semiconductor industry, production and bottling of soft drinks). We consider a scenario of parallel unrelated machines that have to be equipped with a tool or need a special kind of resource for processing. Our approach allows tracing the assignment of these secondary resources across different machines and synchronising their usage independently of the time period. We present extensions of the general lot-sizing and scheduling problem and of the capacitated lot-sizing problem. We prove that the latter model is a special case of the first, but it performs computationally much better.

Keywords:

• lot sizing
• production planning
• scheduling
• mixed integer linear programming

Acknowledgements

This work was partly financed by the Austrian Science Foundation under contract number J2815-N13 and by FP7-PEOPLE-2009-IRSES project No. 246881. The authors would like to thank Maria Antónia Carravilla and José Fernando Oliveira for many helpful discussions and comments on this work.