Note on “Inverse minimum cost flow problems under the weighted Hamming distance”

•The inverse minimum cost flow problem under the Hamming distance is considered.•A counter example shows that algorithm proposed by Jiang et al. is not correct.•A strongly polynomial-time algorithm is proposed to solve the inverse problem.

Jiang et al. proposed an algorithm to solve the inverse minimum cost flow problems under the bottleneck-type weighted Hamming distance [Y. Jiang, L. Liu, B. Wuc, E. Yao, Inverse minimum cost flow problems under the weighted Hamming distance, European Journal of Operational Research 207 (2010) 50–54]. In this note, it is shown that their proposed algorithm does not solve correctly the inverse problem in the general case due to some incorrect results in that article. Then, a new algorithm is proposed to solve the inverse problem in strongly polynomial time. The algorithm uses the linear search technique and solves a shortest path problem in each iteration.