The Problem of One Machine with Equal Processing Time and Preemption

K. A. Lyashkova, V. V. Servakh
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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.

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来源期刊
Journal of Applied and Industrial Mathematics
Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering
CiteScore
1.00
自引率
0.00%
发文量
16
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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