Improved algorithm for minimizing total late work on a proportionate flow shop and extensions to job rejection and generalized due dates

Gerstl et al (2019) studied the problem of minimizing the total late work (TLW) on an m-machine proportionate flow shop. They solved the case where the total late work refers to the last operation of the job (i.e., the operation performed on the last machine of the flow shop). As the problem is know...

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Bibliographic Details
Published in:	Computers & operations research Vol. 181; p. 107046
Main Authors:	Mor, Baruch, Geng, Xin-Na
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.09.2025
Subjects:	Dynamic programming Generalized due dates Job rejection Proportionate flow shop Scheduling Total late work Scheduling Generalized due dates Dynamic programming Total late work Proportionate flow shop Job rejection
ISSN:	0305-0548
Online Access:	Get full text
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Summary:	Gerstl et al (2019) studied the problem of minimizing the total late work (TLW) on an m-machine proportionate flow shop. They solved the case where the total late work refers to the last operation of the job (i.e., the operation performed on the last machine of the flow shop). As the problem is known to be NP-hard, the authors proved two crucial properties of an optimal schedule and introduced a pseudo-polynomial dynamic programming (DP) algorithm. In this research, we revisit the same problem and present enhanced algorithms by the factor of (n+m), where n is the number of jobs and m is the number of machines. Furthermore, based on the improved algorithm, we extend the fundamental problem to consider optional job rejection. We focus on minimizing the TLW subject to an upper bound on the total rejection cost and introduce DP algorithms. Next, we address the problem of minimizing the TLW with generalized due dates, with an upper bound on the permitted rejection cost, and likewise introduce DP algorithms. We conducted an extensive numerical study to evaluate the efficiency of all DP algorithms. •We revisit the problem of minimizing the total late work (TLW).•The machine setting is an m-machine proportionate flow shop.•We present enhanced DP algorithms by the factor of (n + m).•We then extend the fundamental problem by assuming job rejection.•We assume an upper bound on the total rejection cost.•Next, we extend by combining job rejection and generalized due dates.
ISSN:	0305-0548
DOI:	10.1016/j.cor.2025.107046