Volume 55, Number 3, May-June 2021
|Page(s)||1949 - 1970|
|Published online||28 June 2021|
Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources
Instituto de Matemática, UFMS – Universidade Federal de Mato Grosso do Sul, Campo Grande, MS, Brazil.
2 Instituto de Ciâncias Matemáticas e de Computação, USP – Universidade de São Paulo, São Carlos, SP, Brazil.
3 Departamento de Matemática, UNESP – Universidade Estadual Paulista, São José do Rio Preto 15054-000, SP, Brazil
* Corresponding author: firstname.lastname@example.org
Accepted: 29 May 2021
The purpose of this paper is to propose mathematical models to represent a lot sizing and scheduling problem on multiple production lines that share scarce resources and to investigate the computational performance of the proposed models. The main feature that differentiates this problem from others in the literature is that the decision on which lines to organize should be taken considering the availability of the necessary resources. The optimization criterion is the minimization of the costs incurred in the production process (inventory, backlogging, organization of production lines, and sequence-dependent setup costs). Nine mixed integer optimization models to represent the problem are given and, also, the results of an extensive computational study carried out using a set of instances from the literature. The computational study indicates that an efficient formulation, able to provide high quality solutions for large sized instances, can be obtained from a classical model by making the binary production variables explicit, using the facility location reformulation as well as the single commodity flow constraints to eliminate subsequences. Moreover, from the results, it is also clear that the consideration of scarce resources makes the problem significantly more difficult than the traditional one.
Mathematics Subject Classification: 90C11
Key words: Lot sizing and scheduling / parallel production lines / scarce resources / mixed integer programming models
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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