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

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

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-plu...

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Main Authors: Tena Žužek, Aljoša Peperko, Janez Kušar
Format: Article
Language:English
Published: Croatian Operational Research Society 2019-01-01
Series:Croatian Operational Research Review
Online Access:https://hrcak.srce.hr/file/324105
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spelling doaj-5cf20f0a0ef04d3e8636deca097bf5892020-11-24T21:54:47ZengCroatian Operational Research SocietyCroatian Operational Research Review1848-02251848-99312019-01-01101354410.17535/crorr.2019.0004222082A Max-Plus algebra approach for generating a non-delay scheduleTena Žužek0Aljoša Peperko1Janez Kušar2Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, SloveniaFaculty of Mechanical Engineering, University of Ljubljana, Ljubljana, SloveniaFaculty of Mechanical Engineering, University of Ljubljana, Ljubljana, SloveniaA 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.https://hrcak.srce.hr/file/324105
collection DOAJ
language English
format Article
sources DOAJ
author Tena Žužek
Aljoša Peperko
Janez Kušar
spellingShingle Tena Žužek
Aljoša Peperko
Janez Kušar
A Max-Plus algebra approach for generating a non-delay schedule
Croatian Operational Research Review
author_facet Tena Žužek
Aljoša Peperko
Janez Kušar
author_sort Tena Žužek
title A Max-Plus algebra approach for generating a non-delay schedule
title_short A Max-Plus algebra approach for generating a non-delay schedule
title_full A Max-Plus algebra approach for generating a non-delay schedule
title_fullStr A Max-Plus algebra approach for generating a non-delay schedule
title_full_unstemmed A Max-Plus algebra approach for generating a non-delay schedule
title_sort max-plus algebra approach for generating a non-delay schedule
publisher Croatian Operational Research Society
series Croatian Operational Research Review
issn 1848-0225
1848-9931
publishDate 2019-01-01
description 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.
url https://hrcak.srce.hr/file/324105
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AT aljosapeperko amaxplusalgebraapproachforgeneratinganondelayschedule
AT janezkusar amaxplusalgebraapproachforgeneratinganondelayschedule
AT tenazuzek maxplusalgebraapproachforgeneratinganondelayschedule
AT aljosapeperko maxplusalgebraapproachforgeneratinganondelayschedule
AT janezkusar maxplusalgebraapproachforgeneratinganondelayschedule
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