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Mathematics 2019, 7(3), 301; https://doi.org/10.3390/math7030301

Two-Machine Job-Shop Scheduling with Equal Processing Times on Each Machine

1
V.A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Profsoyuznaya st. 65, 117997 Moscow, Russia
2
Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, PSF 4120, 39016 Magdeburg, Germany
*
Author to whom correspondence should be addressed.
Received: 23 January 2019 / Revised: 28 February 2019 / Accepted: 19 March 2019 / Published: 25 March 2019
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
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Abstract

In this paper, we consider a two-machine job-shop scheduling problem of minimizing total completion time subject to n jobs with two operations and equal processing times on each machine. This problem occurs e.g., as a single-track railway scheduling problem with three stations and constant travel times between any two adjacent stations. We present a polynomial dynamic programming algorithm of the complexity O ( n 5 ) and a heuristic procedure of the complexity O ( n 3 ) . This settles the complexity status of the problem under consideration which was open before and extends earlier work for the two-station single-track railway scheduling problem. We also present computational results of the comparison of both algorithms. For the 30,000 instances with up to 30 jobs considered, the average relative error of the heuristic is less than 1 % . In our tests, the practical running time of the dynamic programming algorithm was even bounded by O ( n 4 ) . View Full-Text
Keywords: scheduling; total completion time; job-shop scheduling; total completion time; job-shop
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Gafarov, E.; Werner, F. Two-Machine Job-Shop Scheduling with Equal Processing Times on Each Machine. Mathematics 2019, 7, 301.

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