Flowshop scheduling with learning effect and job rejection

• Published in: Journal of scheduling Vol. 23; no. 6; pp. 631 - 641
• Main Authors: Mor, Baruch, Mosheiov, Gur, Shapira, Dana
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2020; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Business and Management; Calculus of Variations and Optimal Control; Optimization; Completion time; Dynamic programming; Job shops; Learning; Operations Research/Decision Theory; Optimization; Production scheduling; Rejection; Scheduling; Supply Chain Management; Upper bounds; Scheduling; Learning effect; Dynamic programming; Proportionate flowshop; Job rejection
• ISSN: 1094-6136; 1099-1425
• DOI: 10.1007/s10951-019-00612-y

We study scheduling problems on a proportionate flowshop. Three objective functions are considered: minimum makespan, minimum total completion time, and minimum total load. We consider a learning process; thus, the processing time of a job processed later in sequence is reduced. The scheduler has the option of job rejection; i.e., only a subset of the jobs are processed and the rejected jobs are penalized. An upper bound on the total permitted rejection cost is assumed. Since the single-machine versions of these problems were shown to be NP -hard, we focus on the introduction of pseudopolynomial dynamic programming algorithms, indicating that the problems are NP -hard in the ordinary sense. We provide an extensive numerical study verifying that the proposed solution algorithms are very efficient and instances containing up to 80 jobs are solved in no more than 5 ms.