On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

  • Authors:

  • Tao Wu;Leyuan Shi;Joseph Geunes;Kerem Akartunalı

  • Affiliations:

  • Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, USA 53706;Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, USA 53706 and Department of Industrial Engineering and Management, Peking University, Beijing, China 100 ...;Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA 32611;Department of Management Science, University of Strathclyde, Glasgow, UK G1 1QE

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2012

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Abstract

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (驴, S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures.