A note on “minimizing makespan in three machine flow shop with deteriorating jobs”

This paper is a note on “minimizing makespan in three machine flow shop with deteriorating jobs” [J.-B. Wang, M.-Z. Wang, minimizing makespan in three machine flow shop with deteriorating jobs, Computers & Operation Research 40 (2013) 547-557]. Wang and Wang presented a branch-and-bound algorithm with several dominance properties and a lower bound; however, we think that the dominance properties may not be true as they are neither necessary nor sufficient. We first show by means of a counter-example that the published dominance properties are incorrect, and then present a necessary and sufficient condition for them to be true. Moreover, a simplifying remark is provided for the above dominance properties.