A Heuristic Algorithm for the Traveling Salesman Location Problem on Networks

In this paper, we present a heuristic for the traveling salesman location problem on a network. Each day the salesman (e.g., a repair vehicle) must visit all the calls that are registered in a service list. Each call is generated with a given probability and the service list contains at most n calls. The heuristic requires O(n³) time to find the location that “minimizes” the expected distance traveled. A worst case analysis of the heuristic indicates that it will produce a solution which is at most 50% worse than the optimal solution. The paper also contains several asymptotic results for the problem in the plane.