On exact algorithms for single-machine scheduling problems with a variable maintenance

•We point out that all models in a previous paper are incorrect.•Four improved mathematical programming models are presented.•Relationship among scheduling problems are analyzed.

The aim of this paper is to point out that all mathematical programming models proposed by Ying et al. (2016) are incorrect. We present four revised mathematical programming models and four improved mathematical programming models by adding and revising some constraints and decision variables. Moreover, we show that the first three scheduling problems considered in their paper are equivalent to the problems with the objective of minimizing the sum of completion times or minimizing the maximum lateness, which can be solved by algorithms proposed by Luo et al. (2015) in O(n2) time.