{"title":"Classification and comparison of integer programming formulations for the single-machine sequencing problem","authors":"","doi":"10.1016/j.cor.2024.106844","DOIUrl":null,"url":null,"abstract":"<div><p>It is natural to formulate sequencing problems as integer programming models. However, there are a number of possible formulations the practical value of which can be significantly different. In this paper, we first propose a novel classification of integer programming formulations for single-machine sequencing. Next, we present associated mixed-integer linear programming models for total tardiness minimization. Finally, we conduct an extensive computational study on randomly generated instances. For the unweighted case, the position-indexed formulation with linearly many constraints outperforms others, whereas for the weighted case, it is best to use the sparse reformulation of the time-indexed formulation. Integer programming turns out to be a viable option for many practical problem sizes.</p></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":null,"pages":null},"PeriodicalIF":4.1000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Operations Research","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0305054824003162","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
It is natural to formulate sequencing problems as integer programming models. However, there are a number of possible formulations the practical value of which can be significantly different. In this paper, we first propose a novel classification of integer programming formulations for single-machine sequencing. Next, we present associated mixed-integer linear programming models for total tardiness minimization. Finally, we conduct an extensive computational study on randomly generated instances. For the unweighted case, the position-indexed formulation with linearly many constraints outperforms others, whereas for the weighted case, it is best to use the sparse reformulation of the time-indexed formulation. Integer programming turns out to be a viable option for many practical problem sizes.
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.