This paper deals with a heuristic algorithm for the vehicle routing-scheduling problem to minimize the total travel distance and the total cost. Because the aim of the Clarke-Wright method, one of famous heuristic methods, is to minimize the total travel distance of vehicles, it cannot consider the cost if the cost and the travel distance is not proportional. In the Clarke-Wright method, the route of each vehicle is found by using the saving matrix which is made by an assumption that the vehicle comes back to the starting point. The problem dealt with in the paper, however, does not need the vehicle to come back because each vehicle has its hoping-start-points and hoping-destination-points. Therefore we need a different saving matrix appropriate to this occasion. We propose a method to find an initial solution by applying network simplex method after transforming the vehicle routing-scheduling problem into the minimum cost problem. Moreover, we propose a method to minimize the total travel distance by using the modified saving matrix which is appropriate to no-return occasion and the method for the case of plural types of vehicles and freights.