In today’s competitive transportation systems, passengers search to find traveling agencies that are able to serve them efficiently considering both traveling time and transportation costs. In this paper, we present a new model for the traveling SALESMAN PROBLEM with multiple transporters ((TSP)MT). In the proposed model, which is more applicable than the traditional versions, each city has different transporting vehicles and the cost of travel through each city is dependent on the transporting vehicles type. The aim is to determine an optimal sequence of visited cities with minimum traveling times by available transporting vehicles within a limited budget. First, the mathematical model of (TSP)MT is presented. Next, since the PROBLEM is NP-hard, a new hybrid parallel simulated annealing algorithm with a new coding scheme is proposed. To analyze the performance of the proposed algorithm, 50 numerical examples with different budget types are examined and solved using the algorithm. The computational results of these comparisons show that the algorithm is an excellent approach in speed and solution quality.

The TRAVELLING SALESMAN PROBLEM is one of the fundamental operational research PROBLEMs where the objective is to generate the cheapest route for a SALESMAN starting from a given city, visiting all the other cities only once and finally returning to the starting city. In this paper, we study the TRAVELLING SALESMAN PROBLEM in uncertain environment. Particularly, the single valued triangular neutrosophic environment is considered viewing that it is more realistic and general in real-world industrial PROBLEMs. Each element in the distance matrix of the TRAVELLING SALESMAN PROBLEM is presented as a single valued triangular neutrosophic number. To solve this PROBLEM, we enhance our novel column-row heuristic Dhouib-Matrix-(TSP)1 by the means of the center of gravity ranking function and the standard deviation metric. In fact, the center of gravity ranking function is applied for defuzzification in order to convert the single valued triangular neutrosophic number to crisp number.A stepwise application of several numerical TRAVELLING SALESMAN PROBLEMs on the single valued triangular neutrosophic environment shows that the optimal or a near optimal solution can be easily reached thanks to the Dhouib-Matrix-(TSP)1 heuristic enriched with the center of gravity ranking function and the standard deviation metric.