We consider a single facility location problem under the A-distance with respect to minisum criterion, study properties of the optimal solution for the problem, and propose ‘The Edge Tracing Algorithm’ to find all optimal solutions. In R2, we consider the problem minx∈R2 F(x) = ∑i=1n widA(x,yi), where dA is the A-distance. For each demand point and each given orientation, we draw an oriented line which passes the point. Then a plane is divided into regions. We call a point passing some lines an intersection point. It is shown that there exists an optimal solution in the set of intersection points. Let P be the smallest convex polygon including all demand points, in which all boundary lines are given oriented lines. It is shown that any optimal solution is in P. We propose ‘The Edge Tracing Algorithm’, where the solution in each step is an intersection point. This algorithm is as follows: We choose any demand point as an initial solution. The solution in the next step is determined as the adjacent intersection point in the steepest orientation among orientations according to lines which passes the present solution. We also propose the method to determine the adjacent intersection point easily by sorting lines.
