Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic

  • Authors:

  • Florian Sahling;Lisbeth Buschkühl;Horst Tempelmeier;Stefan Helber

  • Affiliations:

  • Department of Production Management, Leibniz University Hannover, Germany;Department of Supply Chain Management and Production, University of Cologne, Germany;Department of Supply Chain Management and Production, University of Cologne, Germany;Department of Production Management, Leibniz University Hannover, Germany

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2009

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Abstract

This paper presents a new algorithm for the dynamic multi-level capacitated lot sizing problem with setup carry-overs (MLCLSP-L). The MLCLSP-L is a big-bucket model that allows the production of any number of products within a period, but it incorporates partial sequencing of the production orders in the sense that the first and the last products produced in a period are determined by the model. We solve a model which is applicable to general bill-of-material structures and which includes minimum lead times of one period and multi-period setup carry-overs. Our algorithm solves a series of mixed-integer linear programs in an iterative so-called fix-and-optimize approach. In each instance of these mixed-integer linear programs a large number of binary setup variables is fixed whereas only a small subset of these variables is optimized, together with the complete set of the inventory and lot size variables. A numerical study shows that the algorithm provides high-quality results and that the computational effort is moderate.