Flow shop scheduling with general position weighted learning effects to minimise total weighted completion time

Abstract

This article considers the flow shop problem of minimising the total weighted completion time in which the processing times of jobs are variable according to general position weighted learning effects. Two simple heuristics are proposed, and their worst-case error bounds are analysed. In addition, some complex heuristics (including simulated annealing algorithms) and a branch-and-bound algorithm are proposed as solutions to this problem. Finally, computational experiments are performed to examine the effectiveness and efficiency of the proposed algorithms.

Keywords:

• Scheduling
• simulated annealing
• learning effect
• flow shop
• branch-and-bound algorithm

Disclosure statement

No potential conflict of interest was reported by the author(s).

Table A9. Tests of between-subjects effects to SA1 for large-sized instances.

Table A10. Tests of between-subjects effects to SA2 for large-sized instances.

Additional information

Funding

This work was supported by the MOE Project of Humanities and Social Science of China (grant no. 19YJE630002), and the National Natural Science Foundation of China (grant nos. 71971165, 71832011, 71872033 and 71401033). Feng Liu is also supported by the the China Postdoctoral Science Foundation (grant no. 2019T120212) and the Dalian High Level Talents Innovation Support Plan.