Journal of the Operational Research Society

, Volume 57, Issue 4, pp 389–399

On alternative mixed integer programming formulations and LP-based heuristics for lot-sizing with setup times

Theoretical Paper

DOI: 10.1057/palgrave.jors.2601996

Cite this article as:
Denizel, M. & Süral, H. J Oper Res Soc (2006) 57: 389. doi:10.1057/palgrave.jors.2601996


We address the multi-item, capacitated lot-sizing problem (CLSP) encountered in environments where demand is dynamic and to be met on time. Items compete for a limited capacity resource, which requires a setup for each lot of items to be produced causing unproductive time but no direct costs. The problem belongs to a class of problems that are difficult to solve. Even the feasibility problem becomes combinatorial when setup times are considered. This difficulty in reaching optimality and the practical relevance of CLSP make it important to design and analyse heuristics to find good solutions that can be implemented in practice. We consider certain mixed integer programming formulations of the problem and develop heuristics including a curtailed branch and bound, for rounding the setup variables in the LP solution of the tighter formulations. We report our computational results for a class of instances taken from literature.


capacitated lot-sizing reformulation valid inequalities heuristics 

Copyright information

© Palgrave Macmillan Ltd 2005

Authors and Affiliations

  1. 1.Sabancı UniversityOrhanlıTurkey
  2. 2.Middle East Technical UniversityAnkaraTurkey

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