Apply Ordinal Optimization to Optimize the Job-Shop Scheduling Under Uncertain Processing Times

2021 ◽  
Author(s):  
Shih-Cheng Horng ◽  
Shieh-Shing Lin
Keyword(s):  
Job Shop ◽  
Job Shop Scheduling ◽  
Ordinal Optimization ◽  
Shop Scheduling ◽  
Processing Times

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

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 301 ◽  
Author(s):  
Evgeny Gafarov ◽  
Frank Werner
Keyword(s):  
Dynamic Programming ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Scheduling Problem ◽  
Single Track ◽  
Shop Scheduling ◽  
Processing Times ◽  
Equal Processing Times

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 ) .

Job Shop Scheduling with Unit Processing Times

2006 ◽  
Vol 31 (2) ◽  
pp. 381-389 ◽  
Author(s):  
Nikhil Bansal ◽  
Tracy Kimbrel ◽  
Maxim Sviridenko
Keyword(s):  
Job Shop ◽  
Job Shop Scheduling ◽  
Shop Scheduling ◽  
Processing Times ◽  
Unit Processing Times ◽  
Unit Processing
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