Computational complexity of finding Pareto efficient outcomes for biobjective lot‐sizing models |
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| Authors: | H Edwin Romeijn Dolores Romero Morales Wilco Van den Heuvel |
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| Affiliation: | 1. Department of Industrial and Operations Engineering, University of Michigan, , Ann Arbor, Michigan, 48109‐2117;2. Sa?d Business School, University of Oxford, , United Kingdom;3. Econometric Institute, Erasmus University Rotterdam, , 3000 DR Rotterdam, The Netherlands |
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| 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  ‐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 |
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| Keywords: | lot‐sizing biobjective expenditure Pareto efficient outcomes complexity analysis |
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