Practical constraints in the container loading problem: Comprehensive formulations and exact algorithm
•An exact iterative algorithm solves the container loading problem.•Cuts to break symmetric solutions and an enhanced linear relaxation are proposed.•Twelve real constraints are modeled with integer linear and constraint programming paradigms.•The exact algorithm solves more than 70% of the instance...
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| Vydané v: | Computers & operations research Ročník 128; s. 105186 |
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| Jazyk: | English |
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Elsevier Ltd
01.04.2021
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| ISSN: | 0305-0548, 1873-765X |
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| Abstract | •An exact iterative algorithm solves the container loading problem.•Cuts to break symmetric solutions and an enhanced linear relaxation are proposed.•Twelve real constraints are modeled with integer linear and constraint programming paradigms.•The exact algorithm solves more than 70% of the instances within one hour.•For some real constraints, more than 90% of the instances are solved.
This paper addresses the Single Container Loading Problem. We present an exact approach that considers the resolution of integer linear programming and constraint programming models iteratively. A linear relaxation of the problem based on packing in planes is proposed. Moreover, a comprehensive set of mathematical formulations for twelve practical constraints that arise in this problem are discussed. These constraints include complete shipment, conflicting items, priorities, weight limit, cargo stability, load-bearing, multi-drop, load-balancing, manual loading, grouping, separation, and multiple orientations. Extensive computational experiments are carried out on instances from the literature to show the performance of the proposed approach and state how each practical constraint affects the container’s occupancy, the approach runtime, and the number of packing patterns evaluated. In general, the approach could optimally solve instances with around ten items types and a total of 110 items, besides obtaining the optimal solution for more than 70% of all instances. |
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| AbstractList | •An exact iterative algorithm solves the container loading problem.•Cuts to break symmetric solutions and an enhanced linear relaxation are proposed.•Twelve real constraints are modeled with integer linear and constraint programming paradigms.•The exact algorithm solves more than 70% of the instances within one hour.•For some real constraints, more than 90% of the instances are solved.
This paper addresses the Single Container Loading Problem. We present an exact approach that considers the resolution of integer linear programming and constraint programming models iteratively. A linear relaxation of the problem based on packing in planes is proposed. Moreover, a comprehensive set of mathematical formulations for twelve practical constraints that arise in this problem are discussed. These constraints include complete shipment, conflicting items, priorities, weight limit, cargo stability, load-bearing, multi-drop, load-balancing, manual loading, grouping, separation, and multiple orientations. Extensive computational experiments are carried out on instances from the literature to show the performance of the proposed approach and state how each practical constraint affects the container’s occupancy, the approach runtime, and the number of packing patterns evaluated. In general, the approach could optimally solve instances with around ten items types and a total of 110 items, besides obtaining the optimal solution for more than 70% of all instances. |
| ArticleNumber | 105186 |
| Author | Junqueira, Leonardo Alves de Queiroz, Thiago Nascimento, Oliviana Xavier do |
| Author_xml | – sequence: 1 givenname: Oliviana Xavier do surname: Nascimento fullname: Nascimento, Oliviana Xavier do email: olivianaxn@gmail.com organization: Institute of Mathematics and Technology, Federal University of Goiás – Campus Catalão, Av. Dr. Lamartine Pinto de Avelar, 1120, 75704-020 Catalão-GO, Brazil – sequence: 2 givenname: Thiago surname: Alves de Queiroz fullname: Alves de Queiroz, Thiago email: taq@ufg.br organization: Institute of Mathematics and Technology, Federal University of Goiás – Campus Catalão, Av. Dr. Lamartine Pinto de Avelar, 1120, 75704-020 Catalão-GO, Brazil – sequence: 3 givenname: Leonardo surname: Junqueira fullname: Junqueira, Leonardo email: junqueira@usp.br organization: Department of Production Engineering, Polytechnic School, University of São Paulo, Av. Prof. Luciano Gualberto, 1380, 05508-010 São Paulo-SP, Brazil |
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