A note on scheduling on uniform parallel machines with unavailability constraints

Abstract

We show by counterexample that the binary integer quadratic programming model proposed by Kaabi and Harrath [2019. “Scheduling on Uniform Parallel Machines with Periodic Unavailability Constraints.” International Journal of Production Research 57: 216–227] is incorrect. We fix this model and propose two linear ones.

Keywords:

• Scheduling
• unavailability constraint
• uniform parallel machines
• linear programming
• unrelated parallel machines

Acknowledgments

We would like to express our warmest thanks to Professor Alexandre Dolgui (Editor-in-Chief of the journal) for communicating two earlier versions of this paper and his suggestion of preparing a short note. We would also like to express our warmest thanks to the two anonymous reviewers for their valuable comments, which prompt us to provide a counterexample that addresses all their concerns.

Disclosure statement

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

Additional information

Funding

This work was supported by the Qinglan Project of Universities in Jiangsu, the Science and Technology Project of Jiangxi Education Department [grant number GJJ170446], and the National Natural Science Foundation of China [grant number 71774080].