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Open AccessArticle

Minimizing Makespan in A Two-Machine Flowshop Problem with Processing Time Linearly Dependent on Job Waiting Time

by Dar-Li Yang 1,2 and Wen-Hung Kuo 1,*
1
Department of Information Management, National Formosa University, Yun-Lin 632, Taiwan
2
Smart Machine and Intelligent Manufacturing Research Center, National Formosa University, Yun-Lin 632, Taiwan
*
Author to whom correspondence should be addressed.
Sustainability 2019, 11(24), 6885; https://doi.org/10.3390/su11246885
Received: 12 September 2019 / Revised: 20 November 2019 / Accepted: 24 November 2019 / Published: 4 December 2019
(This article belongs to the Special Issue Scheduling Problems in Sustainability)
This paper is aimed at studying a two-machine flowshop scheduling where the processing times are linearly dependent on the waiting times of the jobs prior to processing on the second machine. That is, when a job is processed completely on the first machine, a certain delay time is required before its processing on the second machine. If we would like to reduce the actual waiting time, the processing time of the job on the second machine increases. The objective is to minimize the makespan. When the processing time is reduced, it implies that the consumption of energy is reduced. It is beneficial to environmental sustainability. We show that the proposed problem is NP-hard in the strong sense. A 0-1 mixed integer programming and a heuristic algorithm with computational experiment are proposed. Some cases solved in polynomial time are also provided. View Full-Text
Keywords: flowshop scheduling; sustainability; NP-hard; integer programming; heuristic algorithm flowshop scheduling; sustainability; NP-hard; integer programming; heuristic algorithm
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Yang, D.-L.; Kuo, W.-H. Minimizing Makespan in A Two-Machine Flowshop Problem with Processing Time Linearly Dependent on Job Waiting Time. Sustainability 2019, 11, 6885.

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