On bottleneck assignment problems under categorization

In this note we consider two types of bottleneck assignment problems under categorization and show that the problems are strongly NP-hard. Further, it is observed that the algorithms developed in Agarwal and Tikekar for these problems are of pseudo-polynomial complexity. Thus contrary to what is reported in Agarwal and Tikekar, these algorithms do not guarantee exact optimality of the solutions produced, unless P = NP.