Two-stage flexible flow shop scheduling subject to fixed job sequences

• Published in: The Journal of the Operational Research Society Vol. 67; no. 3; pp. 506 - 515
• Main Authors: Hwang, F J, Lin, Bertrand M T
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 01.03.2016; Palgrave Macmillan; Palgrave Macmillan UK; Taylor & Francis Ltd
• Subjects: Algorithms; Bottlenecks; Business and Management; Business metrics; dedicated machines; Dynamic programming; Employment; fixed job sequences; General Paper; General Papers; Job shops; Lateness; Machinery; Management; Mathematical theorems; Objective functions; Operations research; Operations Research/Decision Theory; Performance metrics; Production scheduling; Recursion; regular objective functions; Run time; Scheduling; Studies; two-stage flexible flow shop; dynamic programming; regular objective functions; two-stage flexible flow shop; dedicated machines; fixed job sequences
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/jors.2015.61

This paper investigates the scheduling problem in a two-stage flexible flow shop, which consists of m stage-1 parallel dedicated machines and a stage-2 bottleneck machine, subject to the condition that n l jobs per type l∈{1, ..., m} are processed in a fixed sequence. Four regular performance metrics, including the total completion time, the maximum lateness, the total tardiness, and the number of tardy jobs, are considered. For each considered objective function, we aim to determine an optimal interleaving processing sequence of all jobs coupled with their starting times on the stage-2 bottleneck machine. The problem under study is proved to be strongly NP-hard. An O(m 2 Π l=1 m n l 2 ) dynamic programming algorithm coupled with numerical experiments is presented.