Regular scheduling measures on proportionate flowshop with job rejection

• Published in: Computational & applied mathematics Vol. 39; no. 2
• Main Authors: Mor, Baruch, Shapira, Dana
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.05.2020; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Applied physics; Completion time; Computational mathematics; Computational Mathematics and Numerical Analysis; Dynamic programming; Job shops; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Polynomials; Production scheduling; Rejection; Run time (computers); Scheduling; Upper bounds; Regular performance measures; Scheduling; Dynamic programming; Proportionate flowshop; Job rejection; 90B35
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-020-1130-z

In this article, we study the method of job rejection in the setting of proportionate flowshop, and focus on minimizing regular performance measures, subject to the constraint that the total rejection cost cannot exceed a given upper bound. In particular, we study total completion time, maximum tardiness, total tardiness, and total weighted number of tardy jobs. All the addressed problems are NP-hard as their single machine counterpart are known to be NP-hard. To the best of our knowledge, there are no detailed solutions in scheduling literature to the first two problems, whereas the last two problems were never addressed to date. For each problem, we provide a pseudo-polynomial dynamic programming solution algorithm, and furthermore, we enhance the reported running time of the first two problems. Our extensive numerical study validates the efficiency of the provided solutions.