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Reformulation and a Lagrangian heuristic for lot sizing problem on parallel machines

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Abstract

We consider the capacitated lot sizing problem with multiple items, setup time and unrelated parallel machines. The aim of the article is to develop a Lagrangian heuristic to obtain good solutions to this problem and good lower bounds to certify the quality of solutions. Based on a strong reformulation of the problem as a shortest path problem, the Lagrangian relaxation is applied to the demand constraints (flow constraint) and the relaxed problem is decomposed per period and per machine. The subgradient optimization method is used to update the Lagrangian multipliers. A primal heuristic, based on transfers of production, is designed to generate feasible solutions (upper bounds). Computational results using data from the literature are presented and show that our method is efficient, produces lower bounds of good quality and competitive upper bounds, when compared with the bounds produced by another method from the literature and by high-performance MIP software.

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Acknowledgments

The authors would like to thank the referees for their very helpful feedback, resulting in a better paper, and are also grateful to Franklina M. B. Toledo for making available the code of her heuristic. This research was funded by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) (Processes numbers 2010/16727-9 and 2011/22647-0).

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  1. Departamento de Matemática Aplicada, IBILCE, UNESP-Univ. Estadual Paulista, 15054-000, São José do Rio Preto, SP, Brazil

    Diego Jacinto Fiorotto & Silvio Alexandre de Araujo

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  1. Diego Jacinto Fiorotto
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  2. Silvio Alexandre de Araujo
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Correspondence to Silvio Alexandre de Araujo.

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Fiorotto, D.J., de Araujo, S.A. Reformulation and a Lagrangian heuristic for lot sizing problem on parallel machines. Ann Oper Res 217, 213–231 (2014). https://doi.org/10.1007/s10479-014-1570-1

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