The Single-Double Balanced Traveling Salesman Problem

In the Single-Double Balanced Traveling Salesman Problem (SDB-TSP), the customers must be visited over a period of two days: some must be visited daily, and the others on alternate days (even or odd days). The salesman’s objective is to minimize the total distance travelled over the two tours; moreover, the number of customers visited in every tour must be ‘balanced’, i.e the difference between the maximum and the minimum number of visited customers must be less than a given threshold. Although this problem may be viewed as a particular case of the Period Traveling Salesman Problem, in the SDB-TSP the assumptions allow for emphasising on routing aspects, more than on the best assignment of the customers to the various days of the period. The paper proposes a problem settlement and two (fast) heuristic algorithms. In order to enhance the properties of the proposed procedures, an application is also given.