Trade-off balancing between maximum and total completion times for no-wait flow shop production

Abstract

We propose a trade-off balancing (TOB) heuristic in a no-wait flow shop to minimise the weighted sum of maximum completion time ($C_{max}$) and total completion time (TCT) based on machine idle times. We introduce a factorisation scheme to construct the initial sequence based on current and future idle times at the operational level. In addition, we propose a novel estimation method to establish the mathematical relationship between the objectives min($C_{max}$) and min(TCT) at the production line level. To evaluate the performance of the TOB heuristic, computational experiments are conducted on the classic Taillard's benchmark and one-year historical data from University of Kentucky HealthCare (UKHC). The computational results show that minimisations of $C_{max}$ and TCT yield inconsistent scheduling sequences, and these two sequences are relatively uncorrelated. We also show that our TOB heuristic performs better than the best existing heuristics with the same computational complexity and generates stable performances in balancing trade-offs.

Keywords:

• scheduling
• no-wait flow shop
• trade-off balancing
• maximum completion time
• total completion time

Acknowledgments

We appreciate support from UK HeathCare, the Department of Mechanical Engineering at University of Kentucky, the Department of Industrial & Systems Engineering at University of Wisconsin-Madison, the Natural Sciences and Engineering Research Council of Canada, and the Haskayne School of Business at University of Calgary.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Wei Li  http://orcid.org/0000-0001-8524-8977

Additional information

Funding

This project was supported by grant number R03HS024633 from the Agency for Healthcare Research and Quality. The content is solely the responsibility of the authors and does not necessarily represent the official views of the Agency for Healthcare Research and Quality.