A branch and bound algorithm for the travelling salesman and the transportation routing problems

In this paper, a branch and bound model with penalty tour building is developed for solving travelling salesman and transportation routing problems. The algorithm for determining the optimal solution of the problem is of the general form which can solve symmetric and asymmetric single and multiple travelling salesman problems (STS and MTS), and the transportation routing problems with capacity restrictions for the vehicles of same or of different capacities. The behavior of the developed algorithm is tested with randomly generated data. As an application, the routes for gas distribution is planned and carried out in several interior towns of a state, with the objective of making an efficient distribution in order to minimize the total cost of delivery with an optimal solution.