{"title":"The Problem of One Machine with Equal Processing Time and\nPreemption","authors":"K. A. Lyashkova, V. V. Servakh","doi":"10.1134/S1990478924030098","DOIUrl":null,"url":null,"abstract":"<p> We consider the problem of minimizing the weighted average execution time of\nequal-length jobs performance on one machine at the specified time of job arrival and the\npossibility of their interruption. The computational complexity of this problem is currently\nunknown. The article proposes an algorithm for preprocessing input data that allows reducing the\nproblem to a narrower and more regular class of examples. The properties of optimal solutions are\nsubstantiated. Based on them, an algorithm for constructing a finite subset of solutions containing\nan optimal schedule has been developed. A parametric analysis of the schedules in this subset has\nbeen carried out that makes it possible to form a subclass of schedules that are optimal at some\nvalues of weights. A polynomially solvable case of the problem is isolated.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"479 - 488"},"PeriodicalIF":0.5800,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924030098","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the problem of minimizing the weighted average execution time of
equal-length jobs performance on one machine at the specified time of job arrival and the
possibility of their interruption. The computational complexity of this problem is currently
unknown. The article proposes an algorithm for preprocessing input data that allows reducing the
problem to a narrower and more regular class of examples. The properties of optimal solutions are
substantiated. Based on them, an algorithm for constructing a finite subset of solutions containing
an optimal schedule has been developed. A parametric analysis of the schedules in this subset has
been carried out that makes it possible to form a subclass of schedules that are optimal at some
values of weights. A polynomially solvable case of the problem is isolated.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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