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

•Two-machine ow shop scheduling to maximize total early work is considered.•A dynamic programming approach running in O(n2d2) time is proposed.•A fully polynomial time approximation scheme (FPTAS) is developed.•The approximation results work for the weighted model - if a specific constraint is satis...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:European journal of operational research Jg. 300; H. 2; S. 504 - 511
Hauptverfasser: Chen, Xin, Miao, Qian, Lin, Bertrand M.T., Sterna, Malgorzata, Blazewicz, Jacek
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 16.07.2022
Schlagworte:
Combinatorial optimization
Dynamic programming
Early and late work
Flow shop scheduling
FPTAS
Early and late work
Dynamic programming
Combinatorial optimization
FPTAS
Flow shop scheduling
ISSN:0377-2217, 1872-6860
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:•Two-machine ow shop scheduling to maximize total early work is considered.•A dynamic programming approach running in O(n2d2) time is proposed.•A fully polynomial time approximation scheme (FPTAS) is developed.•The approximation results work for the weighted model - if a specific constraint is satisfied. 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2021.07.055