Computational complexity of finding Pareto efficient outcomes for biobjective lot‐sizing models. (4th July 2014)

• Record Type: Journal Article
• Authors: Romeijn, H. Edwin; Morales, Dolores Romero; Van den Heuvel, Wilco
• Is Part Of: Naval research logistics. Volume 61:Number 5(2014:Aug.)
• Page Start: 386
• Page End: 402
• Publication Date: 2014-07-04
• Subjects: lot‐sizing -- biobjective -- expenditure -- Pareto efficient outcomes -- complexity analysis; Logistics, Naval -- Periodicals; Supplies and stores -- Periodicals; 359.07
• DOI: 10.1002/nav.21590
• Languages: English
• ISSNs: 0894-069X

Abstract

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