Parham Azimi - Assistant Professor, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Ramtin Rooeinfar - Msc, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Hani Pourvaziri - Msc, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

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 (TSPMT). 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 TSPMT 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

Traveling salesman problem; Transporter vehicles; Budget constraint; Mathematical programming;Simulated annealing algorithm