A Max-Plus algebra approach for generating a non-delay schedule

IF 0.5 Q4 ECONOMICS

Croatian Operational Research Review Pub Date : 2019-07-01 DOI:10.17535/CRORR.2019.0004

Tena Žužek, A. Peperko, J. Kušar

引用次数: 3

Abstract

. A Max-Plus algebra is one of the promising mathematical approaches that can be used for scheduling operations. It was already applied for the presentation of Johnson’s algorithm and for solving cyclic jobshop problems, but it had not yet been applied for non-delay schedules. In this article, max-plus algebra is used to formally present the generation of a non-delay schedule for the ﬁrst time. We present a simple algorithm for generating matrices of starting and ﬁnishing times of operations, using max-plus algebra formalism. We apply the LRPT (Longest Remaining Processing Time) rule as the priority rule, and the SPT (Shortest Processing Time) rule as the tie-breaking rule. The algorithm is applicable for any other pair of priority rules with a few minor adjustments.

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生成非延迟调度的一种Max-Plus代数方法

Max Plus代数是可用于调度操作的有前途的数学方法之一。它已经被应用于Johnson算法的表示和求解循环jobshop问题，但尚未被应用于非延迟调度。在本文中，首次使用max-plus代数来正式表示无延迟调度的生成。我们提出了一个简单的算法来生成运算开始和结束时间的矩阵，使用最大加代数形式。我们应用LRPT（最长剩余处理时间）规则作为优先级规则，SPT（最短处理时间）法则作为平局打破规则。该算法适用于任何其他对优先级规则，只需进行一些小的调整。

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

Croatian Operational Research Review ECONOMICS-

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

22 weeks

期刊介绍： Croatian Operational Research Review (CRORR) is the journal which publishes original scientific papers from the area of operational research. The purpose is to publish papers from various aspects of operational research (OR) with the aim of presenting scientific ideas that will contribute both to theoretical development and practical application of OR. The scope of the journal covers the following subject areas: linear and non-linear programming, integer programing, combinatorial and discrete optimization, multi-objective programming, stohastic models and optimization, scheduling, macroeconomics, economic theory, game theory, statistics and econometrics, marketing and data analysis, information and decision support systems, banking, finance, insurance, environment, energy, health, neural networks and fuzzy systems, control theory, simulation, practical OR and applications. The audience includes both researchers and practitioners from the area of operations research, applied mathematics, statistics, econometrics, intelligent methods, simulation, and other areas included in the above list of topics. The journal has an international board of editors, consisting of more than 30 editors – university professors from Croatia, Slovenia, USA, Italy, Germany, Austria and other coutries.