{"title":"EPTAS for load balancing problem on parallel machines with a non-renewable resource","authors":"G. Jaykrishnan, Asaf Levin","doi":"10.1016/j.disopt.2023.100775","DOIUrl":null,"url":null,"abstract":"<div><p>The problem considered is the non-preemptive scheduling of independent jobs that consume a resource (which is non-renewable and replenished regularly) on parallel uniformly related machines. The input defines the speed of machines, size of jobs, the quantity of the resource required by the jobs, the replenished quantities, and replenishment dates of the resource. Every job can start processing only after the required quantity of the resource is allocated to the job. The objective function is a generalization of makespan minimization and minimization of the <span><math><msub><mrow><mi>l</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span><span>-norm of the vector of loads of the machines. We present an EPTAS for this problem. Prior to our work only a PTAS was known in this non-renewable resource settings only for the special case of our problem of makespan minimization on identical machines.</span></p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"48 ","pages":"Article 100775"},"PeriodicalIF":0.9000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572528623000178","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The problem considered is the non-preemptive scheduling of independent jobs that consume a resource (which is non-renewable and replenished regularly) on parallel uniformly related machines. The input defines the speed of machines, size of jobs, the quantity of the resource required by the jobs, the replenished quantities, and replenishment dates of the resource. Every job can start processing only after the required quantity of the resource is allocated to the job. The objective function is a generalization of makespan minimization and minimization of the -norm of the vector of loads of the machines. We present an EPTAS for this problem. Prior to our work only a PTAS was known in this non-renewable resource settings only for the special case of our problem of makespan minimization on identical machines.
期刊介绍：
Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
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