Optimal locations and districts of two traveling salesmen on a tree

Abstract

AbstractThis paper focuses on the problem of locating on a tree two service units that must service each working day all the customers that require service. The paper includes an O(n2) algorithm to find the optimal locations that minimize the expected distance traveled by the two service units. This algorithm also gives the optimal service territories of the two service units. The algorithm is based on an available O(n) algorithm to find the optimal location of a single service unit on a tree and on a new method to calculate the objective function value of a given location for the single server.