Optimizing preventive maintenance over a finite planning horizon in a semi-Markov framework

IF 1.9 3区工程技术 Q3 MANAGEMENT

IMA Journal of Management Mathematics Pub Date : 2021-08-01 DOI:10.1093/imaman/dpaa026

Antonio Sánchez Herguedas;Adolfo Crespo Márquez;Francisco Rodrigo Muñoz

{"title":"Optimizing preventive maintenance over a finite planning horizon in a semi-Markov framework","authors":"Antonio Sánchez Herguedas;Adolfo Crespo Márquez;Francisco Rodrigo Muñoz","doi":"10.1093/imaman/dpaa026","DOIUrl":null,"url":null,"abstract":"This paper describes the optimization of preventive maintenance (PM) over a finite planning horizon in a semi-Markov framework. In this framework, the asset may be operating, and providing income for the asset owner, or not operating and undergoing PM, or not operating and undergoing corrective maintenance following failure. PM is triggered when the asset has been operating for τ time units. A number m of transitions specifies the finite horizon. This system is described with a set of recurrence relations, and their z-transform is used to determine the value of τ that maximizes the average accumulated reward over the horizon. We study under what conditions a solution can be found, and for those specific cases the solution τ* is calculated. Despite the complexity of the mathematical solution, the result obtained allows the analyst to provide a quick and easy-to-use tool for practical application in many real-world cases. To demonstrate this, the method has been implemented for a case study, and its accuracy and practical implementation were tested using Monte Carlo simulation and direct calculation.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":"33 1","pages":"75-99"},"PeriodicalIF":1.9000,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaman/dpaa026","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Management Mathematics","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/9623703/","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MANAGEMENT","Score":null,"Total":0}

引用次数: 1

Abstract

This paper describes the optimization of preventive maintenance (PM) over a finite planning horizon in a semi-Markov framework. In this framework, the asset may be operating, and providing income for the asset owner, or not operating and undergoing PM, or not operating and undergoing corrective maintenance following failure. PM is triggered when the asset has been operating for τ time units. A number m of transitions specifies the finite horizon. This system is described with a set of recurrence relations, and their z-transform is used to determine the value of τ that maximizes the average accumulated reward over the horizon. We study under what conditions a solution can be found, and for those specific cases the solution τ* is calculated. Despite the complexity of the mathematical solution, the result obtained allows the analyst to provide a quick and easy-to-use tool for practical application in many real-world cases. To demonstrate this, the method has been implemented for a case study, and its accuracy and practical implementation were tested using Monte Carlo simulation and direct calculation.

查看原文本刊更多论文

在半马尔可夫框架中在有限规划范围内优化预防性维护

本文在半马尔可夫框架中描述了有限规划范围内预防性维修（PM）的优化。在这个框架中，资产可能正在运营，并为资产所有者提供收入，或者没有运营并进行PM，或者没有在故障后运营并进行纠正性维护。当资产已经运行τ时间单位时，PM被触发。转换的数量m指定了有限的视界。该系统用一组递推关系来描述，并使用它们的z变换来确定τ的值，该值最大化了地平线上的平均累积奖励。我们研究在什么条件下可以找到解，并在这些特定情况下计算解τ*。尽管数学解决方案很复杂，但所获得的结果使分析师能够在许多现实世界的案例中为实际应用提供一个快速且易于使用的工具。为了证明这一点，该方法已经实现了一个案例研究，并使用蒙特卡罗模拟和直接计算测试了其准确性和实际实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

IMA Journal of Management Mathematics OPERATIONS RESEARCH & MANAGEMENT SCIENCE-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The mission of this quarterly journal is to publish mathematical research of the highest quality, impact and relevance that can be directly utilised or have demonstrable potential to be employed by managers in profit, not-for-profit, third party and governmental/public organisations to improve their practices. Thus the research must be quantitative and of the highest quality if it is to be published in the journal. Furthermore, the outcome of the research must be ultimately useful for managers. The journal also publishes novel meta-analyses of the literature, reviews of the "state-of-the art" in a manner that provides new insight, and genuine applications of mathematics to real-world problems in the form of case studies. The journal welcomes papers dealing with topics in Operational Research and Management Science, Operations Management, Decision Sciences, Transportation Science, Marketing Science, Analytics, and Financial and Risk Modelling.