Efficient arc-flow formulations for makespan minimisation on parallel machines with a common server

IF 4.1 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research Pub Date : 2024-11-17 DOI:10.1016/j.cor.2024.106911

Alessandro Druetto , Andrea Grosso , Jully Jeunet , Fabio Salassa

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引用次数: 0

Abstract

We consider the problem of scheduling non preemptively a set of jobs on parallel identical machines with prior setup operations on a single shared server, where the objective is to minimise the makespan. We develop an arc-flow formulation to the problem with two multigraphs, one for the machines and one for the server, with a same set of nodes representing points in time, and arcs associated with job execution, and with machines or server idleness. The resulting formulation, called Flow–Flow formulation (FFF), and its tuned version (FFT) are compared with the best existing model in the literature, a time-indexed variable formulation (

F 2

), on benchmark instances with up to 200 jobs and 10 machines. Computational results showed that our Flow–Flow models outperformed

F 2

especially for instances with more than 50 jobs and optimally solved a majority of problems with 150 and 200 jobs for which

F 2

found only very few optimal solutions.

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在带共用服务器的并行计算机上实现最小间隔的高效弧流计算公式

我们考虑的问题是在并行的相同机器上对一组作业进行非抢占式调度，并在单个共享服务器上进行事先设置操作，目标是最小化作业间隔。我们用两个多图（一个是机器多图，另一个是服务器多图）对该问题进行了弧流表述，其中同一组节点代表时间点，弧与作业执行相关，弧与机器或服务器闲置相关。在多达 200 个作业和 10 台机器的基准实例上，我们将得出的公式（称为流-流公式（FFF））及其调整版本（FFT）与文献中现有的最佳模型（时间索引变量公式（F2））进行了比较。计算结果表明，Flow-Flow 模型的性能优于 F2，尤其是在作业量超过 50 个的实例中，并且优化解决了作业量为 150 和 200 个的大多数问题，而 F2 只找到了极少数的最优解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computers & Operations Research 工程技术-工程：工业

CiteScore

8.60

自引率

8.70%

发文量

292

审稿时长

8.5 months

期刊介绍： Operations research and computers meet in a large number of scientific fields, many of which are of vital current concern to our troubled society. These include, among others, ecology, transportation, safety, reliability, urban planning, economics, inventory control, investment strategy and logistics (including reverse logistics). Computers & Operations Research provides an international forum for the application of computers and operations research techniques to problems in these and related fields.