TY - JOUR
T1 - Improved algorithms for scheduling on proportionate flowshop with job-rejection
AU - Mor, Baruch
AU - Shapira, Dana
N1 - Publisher Copyright:
© 2019, © 2019 Operational Research Society.
PY - 2019/11/2
Y1 - 2019/11/2
N2 - The rejection method is an option commonly used in manufacturing systems as a tool to overcome overloaded assembly lines. The operations manager is given the ability to refuse to produce, or alternately to outsource some of the products. A flowshop environment is a setting of machines in series such that each job should be processed on each of the machines. In a recent paper, Shabtay and Oron (2016), the two disciplines are combined, and the makespan criteria is studied, which is one of the fundamental measures in scheduling theory that reveals the utilization of the system. The problems considered are minimizing the makespan subject to a constraint on the maximal rejection cost E, and minimizing the rejection cost given that the makespan cannot exceed a given upper bound, K. The computational complexity of the pseudo polynomial dynamic programming (DP) algorithms presented by Shabtay and Oron are O(n2E) and O(n2K), respectively, where n is the number of jobs. In this paper, we consider the same problems, and our contributions are enhanced DP algorithms, which run in O(nE) and O(nK) time, in correspondence, implying an improvement of a factor of n. Furthermore, we supply empirical results based on the experimental simulations. This study, therefore, has both theoretical significance and practical implications, as our numerical study proves that the introduced DP algorithms are capable of solving large-size instances.
AB - The rejection method is an option commonly used in manufacturing systems as a tool to overcome overloaded assembly lines. The operations manager is given the ability to refuse to produce, or alternately to outsource some of the products. A flowshop environment is a setting of machines in series such that each job should be processed on each of the machines. In a recent paper, Shabtay and Oron (2016), the two disciplines are combined, and the makespan criteria is studied, which is one of the fundamental measures in scheduling theory that reveals the utilization of the system. The problems considered are minimizing the makespan subject to a constraint on the maximal rejection cost E, and minimizing the rejection cost given that the makespan cannot exceed a given upper bound, K. The computational complexity of the pseudo polynomial dynamic programming (DP) algorithms presented by Shabtay and Oron are O(n2E) and O(n2K), respectively, where n is the number of jobs. In this paper, we consider the same problems, and our contributions are enhanced DP algorithms, which run in O(nE) and O(nK) time, in correspondence, implying an improvement of a factor of n. Furthermore, we supply empirical results based on the experimental simulations. This study, therefore, has both theoretical significance and practical implications, as our numerical study proves that the introduced DP algorithms are capable of solving large-size instances.
KW - Scheduling
KW - job-rejection
KW - makespan
KW - proportionate flowshop
UR - http://www.scopus.com/inward/record.url?scp=85057832831&partnerID=8YFLogxK
U2 - 10.1080/01605682.2018.1506540
DO - 10.1080/01605682.2018.1506540
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AN - SCOPUS:85057832831
SN - 0160-5682
VL - 70
SP - 1997
EP - 2003
JO - Journal of the Operational Research Society
JF - Journal of the Operational Research Society
IS - 11
ER -