Two-machine flow shop scheduling with a common due date to maximize total early work

Xin Chen, Qian Miao, Bertrand M.T. Lin, Malgorzata Sterna and Jacek Blazewicz

European Journal of Operational Research, 2022, vol. 300, issue 2, 504-511

Abstract: This paper considers scheduling in a two-machine flow shop to maximize the total early work subject to a common due date. The early work of a job is a parameter defined as the total amount of the job that is processed before the specified due date. We mainly focus on the unweighted model in this paper, and propose a dynamic programming approach running in O(n2d2) time (compared with the previous result in O(n2d4) time for the weighted case discussed in the literature). Then we analyse the problem from an approximation point of view, in which we first show that Johnson’s algorithm, one of the most classical ones in flow shop scheduling, can only achieve the worst performance ratio for the considered problem (although it is an optimal one for makespan minimization). With the motivation of proposing better approximation algorithms, we further design a fully polynomial time approximation scheme (FPTAS). Finally, we point out that the approximation results also work for the weighted model - if a specific constraint is satisfied.

Keywords: Combinatorial optimization; Flow shop scheduling; Early and late work; Dynamic programming; FPTAS (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:300:y:2022:i:2:p:504-511

DOI: 10.1016/j.ejor.2021.07.055

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