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On the computational complexity of uncapacitated multi-plant lot-sizing problems

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Abstract

Production and inventory planning have become crucial and challenging in nowadays competitive industrial and commercial sectors, especially when multiple plants or warehouses are involved. In this context, this paper addresses the complexity of uncapacitated multi-plant lot-sizing problems. We consider a multi-item uncapacitated multi-plant lot-sizing problem with fixed transfer costs and show that two of its very restricted special cases are already NP-hard. Namely, we show that the single-item uncapacitated multi-plant lot-sizing problem with a single period and the multi-item uncapacitated two-plant lot-sizing problem with fixed transfer costs are NP-hard. Furthermore, as a direct implication of the proven results, we also show that a two-echelon multi-item lot-sizing with joint setup costs on transportation is NP-hard.

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Acknowledgements

The authors are thankful to two anonymous reviewers for their comments which helped improving the quality of this paper. Work of Rafael A. Melo was supported by the State of Bahia Research Foundation (FAPESB); and the Brazilian National Council for Scientific and Technological Development (CNPq).

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Authors and Affiliations

  1. Departamento de Estatística e Matemática Aplicada, Universidade Federal do Ceará, Fortaleza, Brazil

    Jesus O. Cunha

  2. Departamento de Engenharia de Produção, Universidade Federal da Paraíba, João Pessoa, Brazil

    Hugo H. Kramer

  3. Computational Intelligence and Optimization Research Laboratory (CInO), Departamento de Ciência da Computação, Universidade Federal da Bahia, Salvador, Brazil

    Rafael A. Melo

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  1. Jesus O. Cunha
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  2. Hugo H. Kramer
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  3. Rafael A. Melo
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Correspondence to Rafael A. Melo.

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Cunha, J.O., Kramer, H.H. & Melo, R.A. On the computational complexity of uncapacitated multi-plant lot-sizing problems. Optim Lett 15, 803–812 (2021). https://doi.org/10.1007/s11590-020-01615-x

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