An instance of a p-median problem gives n demand points. The objective is to locate p supply points in order to minimize the total distance of the demand points to their nearest supply point. p-median is polynomially solvable in one dimension but NP-hard in two or more dimensions, when either the Euclidean or the rectilinear distance measure is used. In this paper, we treat the p-median problem under a new distance measure, the directional rectilinear distance, which requires the assigned supply point for a given demand point to lie above and to the right of it. In a previous work, we showed that the directional p-median problem is polynomially solvable in one dimension; we give here an improved solution through reformulating the problem as a special case of the constrained shortest path problem.
