{"title":"Two-agent scheduling in a two-machine open shop","authors":"Peihai Liu, Manzhan Gu, Xiwen Lu","doi":"10.1007/s10479-023-05780-x","DOIUrl":null,"url":null,"abstract":"<div><p>This paper considers several two-machine open shop problems with two agents. Each agent has an independent set of nonpreemptive jobs, and the objective is to find either a schedule minimizing a linear combination of the makespans of both agents, a schedule minimizing the makespan of one agent with the makespan of the other agent not exceeding a threshold, or all Pareto-optimal schedules with respect to the makespans of both agents. We present a number of results for the problems above, including a polynomial algorithm and a pseudo-polynomial algorithm for special cases, non-approximability, two approximation algorithms, and a fully polynomial-time approximation scheme. Finally, we run numerical experiments to show the effectiveness of the pseudo-polynomial algorithm and the approximation algorithms.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"333 1","pages":"275 - 301"},"PeriodicalIF":4.5000,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-023-05780-x","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
This paper considers several two-machine open shop problems with two agents. Each agent has an independent set of nonpreemptive jobs, and the objective is to find either a schedule minimizing a linear combination of the makespans of both agents, a schedule minimizing the makespan of one agent with the makespan of the other agent not exceeding a threshold, or all Pareto-optimal schedules with respect to the makespans of both agents. We present a number of results for the problems above, including a polynomial algorithm and a pseudo-polynomial algorithm for special cases, non-approximability, two approximation algorithms, and a fully polynomial-time approximation scheme. Finally, we run numerical experiments to show the effectiveness of the pseudo-polynomial algorithm and the approximation algorithms.
期刊介绍：
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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