The 1-median and 1-highway problem

► We address the simultaneous location of a single service facility and a rapid transit line that minimizes the total cost. ► The same problem was considered in Computers and Operations Research 38 (2011) 525-538. ► We found that their algorithm is not correct and it may miss some highway locations. ► We provide one counterexample and an correct algorithm that solves the problem in O(n3) time. ► This paper states some interesting open questions by considering some variants of the studied problem.