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Optimality Region for Job Permutation in Single-Machine Scheduling with Uncertain Processing Times

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Abstract

The problem of scheduling optimally a given set of jobs on a single machine is studied. The lower and upper bounds on the admissible duration of each job are known. The optimality criterion of the schedule is the minimum total completion time of a given set of jobs. Some properties of the optimality region for a job permutation are investigated. Polynomial algorithms for constructing the optimality region for a job permutation and also for calculating the volume of this region are developed. The existence conditions of an empty optimality region for a job permutation are determined. A criterion for the existence of a job permutation with the maximum possible volume of the optimality region is established.

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Authors and Affiliations

  1. United Institute of Informatics Problems, National Academy of Sciences of Belarus, Minsk, Belarus

    Yu. N. Sotskov

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  1. Yu. N. Sotskov
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Correspondence to Yu. N. Sotskov.

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This paper was recommended for publication by A. A. Lazarev, a member of the Editorial Board

Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 5, pp. 60–90.

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Sotskov, Y.N. Optimality Region for Job Permutation in Single-Machine Scheduling with Uncertain Processing Times. Autom Remote Control 81, 819–842 (2020). https://doi.org/10.1134/S0005117920050045

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