Bin Packing Problem with Time Lags

Orlando Rivera Letelier (), François Clautiaux () and Ruslan Sadykov ()
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Orlando Rivera Letelier: Doctoral Program in Industrial Engineering and Operations Research, Universidad Adolfo Ibáñez, Peñalolén, Santiago 7941169, Chile
François Clautiaux: Inria Centre at the University of Bordeaux, 33405 Talence, France; Institut de Mathématiques de Bordeaux (IMB) UMR 5251 (Unité Mixte de Recherche 5251 du Centre Nationale de la Recherche Scientifique), University of Bordeaux, 33405 Talence, France
Ruslan Sadykov: Inria Centre at the University of Bordeaux, 33405 Talence, France; Institut de Mathématiques de Bordeaux (IMB) UMR 5251 (Unité Mixte de Recherche 5251 du Centre Nationale de la Recherche Scientifique), University of Bordeaux, 33405 Talence, France

INFORMS Journal on Computing, 2022, vol. 34, issue 4, 2249-2270

Abstract: We introduce and motivate several variants of the bin packing problem where bins are assigned to time slots, and minimum and maximum lags are required between some pairs of items. We suggest two integer programming formulations for the general problem: a compact one and a stronger formulation with an exponential number of variables and constraints. We propose a branch-cut-and-price approach that exploits the latter formulation. For this purpose, we devise separation algorithms based on a mathematical characterization of feasible assignments for two important special cases of the problem: when the number of possible bins available at each period is infinite and when this number is limited to one and time lags are nonnegative. Computational experiments are reported for instances inspired from a real-case application of chemical treatment planning in vineyards, as well as for literature instances for special cases of the problem. The experimental results show the efficiency of our branch-cut-and-price approach, as it outperforms the compact formulation on newly proposed instances and is able to obtain improved lower and upper bounds for literature instances. Summary of Contribution: The paper considers a new variant of the bin packing problem, which is one of the most important problems in operations research. A motivation for introducing this variant is given, as well as a real-life application. We present a novel and original exact branch-cut-and-price algorithm for the problem. We implement this algorithm, and we present the results of extensive computational experiments. The results show a very good performance of our algorithm. We give several research directions that can be followed by subsequent researchers to extend our contribution to more complex and generic problems.

Keywords: integer programming; algorithms; cutting planes; branch and bound; production-scheduling; cutting stock; relaxation (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:34:y:2022:i:4:p:2249-2270

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