On scheduling of step-improving jobs to minimize the total weighted completion time

Abstract

Kim et al. (2022) studied single-machine scheduling of step-improving jobs with a common discount factor to minimize the total weighted completion time. This study proposes a pseudo-polynomial algorithm to solve the problem. We then consider the general problem in which the discount factors are job dependent. It is proven that there is an optimal solution in which the early normal jobs are sequenced in the WSPT order and the late discounted jobs are sequenced in the WSPT order. Based on two WSPT lists, a dynamic programming solution algorithm is proposed. The run time is pseudo-polynomial when the distance of any job is bounded by a constant, where the distance of a job is the absolute difference of the two positions of this job in two WSPT-ordered job lists.

Keywords:

• Single-machine scheduling
• step-improving jobs
• weighted completion time
• dynamic programming

Acknowledgements

The authors are grateful to the anonymous reviewers for their constructive comments that help improve the quality and contribution of the paper. Kravchenko is grateful to The Hong Kong Polytechnic University for financing a visit to the Department of Logistics and Maritime Studies where this research was partially undertaken.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Lin was supported in part by the National Science and Technology Council of Taiwan under grant number MOST110-2410-H-A49-020-MY2.