A note on a linear bilevel programming algorithm based on bicriteria programming

In this note the relationship between linear bilevel and bicriteria programming problems is clarified. This paper points out that the bicriteria programming algorithm is not suitable for all bilevel programming problems in searching for optimal solutions. A counterexample is given to demonstrate the shortcomings of the results by Ünlü and Bard. The authors also propose a sufficient condition to use the bicriteria programming algorithm for solving a bilevel programming problem.