A mixed integer formulation and an efficient metaheuristic for the unrelated parallel machine scheduling problem: Total tardiness minimization

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE EURO Journal on Computational Optimization Pub Date : 2022-01-01 DOI:10.1016/j.ejco.2022.100034

Héctor G.-de-Alba , Samuel Nucamendi-Guillén , Oliver Avalos-Rosales

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引用次数: 1

Abstract

In this paper, the unrelated parallel machine scheduling problem with the objective of minimizing the total tardiness is addressed. For such a problem, a mixed-integer linear programming (MILP) formulation, that considers assignment and positional variables, is presented. In addition, an iterated local search (ILS) algorithm that produces high-quality solutions in reasonable times is proposed for large size instances. The ILS robustness was determined by comparing its performance with the results provided by the MILP. The instances used in this paper were constructed under a new approach which results in tighter due dates than the previous generation method for this problem. The proposed MILP formulation was able to solve instances of up to 150 jobs and 20 machines. Regarding the ILS, it yielded high-quality solutions in a reasonable time, solving instances of a size up to 400 jobs and 20 machines. Experimental results confirm that both approaches are efficient and promising.

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不相关并行机调度问题的混合整数公式和有效的元启发式:总延误最小化

研究了以总延迟最小为目标的不相关并行机调度问题。针对这类问题，给出了考虑赋值和位置变量的混合整数线性规划(MILP)公式。此外，针对大型实例，提出了一种迭代局部搜索算法，可以在合理的时间内生成高质量的解。通过将其性能与MILP提供的结果进行比较来确定ILS的鲁棒性。本文中使用的实例是在一种新的方法下构造的，与以前的生成方法相比，该方法的交货期更短。提出的MILP公式能够解决多达150个工作和20台机器的实例。对于ILS，它在合理的时间内产生了高质量的解决方案，解决了多达400个作业和20台机器的实例。实验结果证实了这两种方法的有效性和前景。

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来源期刊

EURO Journal on Computational Optimization OPERATIONS RESEARCH & MANAGEMENT SCIENCE-

CiteScore

3.50

自引率

0.00%

发文量

审稿时长

60 days

期刊介绍： The aim of this journal is to contribute to the many areas in which Operations Research and Computer Science are tightly connected with each other. More precisely, the common element in all contributions to this journal is the use of computers for the solution of optimization problems. Both methodological contributions and innovative applications are considered, but validation through convincing computational experiments is desirable. The journal publishes three types of articles (i) research articles, (ii) tutorials, and (iii) surveys. A research article presents original methodological contributions. A tutorial provides an introduction to an advanced topic designed to ease the use of the relevant methodology. A survey provides a wide overview of a given subject by summarizing and organizing research results.