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Computational complexity of finding Pareto efficient outcomes for biobjective lot‐sizing models

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  • H. Edwin Romeijn
  • Dolores Romero Morales
  • Wilco Van den Heuvel

Abstract

In this article, we study a biobjective economic lot‐sizing problem with applications, among others, in green logistics. The first objective aims to minimize the total lot‐sizing costs including production and inventory holding costs, whereas the second one minimizes the maximum production and inventory block expenditure. We derive (almost) tight complexity results for the Pareto efficient outcome problem under nonspeculative lot‐sizing costs. First, we identify nontrivial problem classes for which this problem is polynomially solvable. Second, if we relax any of the parameter assumptions, we show that (except for one case) finding a single Pareto efficient outcome is an N P ‐hard task in general. Finally, we shed some light on the task of describing the Pareto frontier. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 386–402, 2014

Suggested Citation

  • H. Edwin Romeijn & Dolores Romero Morales & Wilco Van den Heuvel, 2014. "Computational complexity of finding Pareto efficient outcomes for biobjective lot‐sizing models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 386-402, August.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:5:p:386-402
    DOI: 10.1002/nav.21590
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    Cited by:

    1. Wilco van den Heuvel & Semra Ağralı & Z. Caner Taşkın, 2023. "A Decomposition Algorithm for Single and Multiobjective Integrated Market Selection and Production Planning," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1439-1453, November.
    2. M. Turkensteen (Marcel) & van den Heuvel, W., 2019. "The trade-off between costs and carbon emissions from lot-sizing decisions," Econometric Institute Research Papers EI2019-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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