Maximizing the profit per unit time for the travelling salesman problem

This paper deals with a new extension of the Travelling Salesman Problem (TSP) in which the objective is to maximize the profit per unit time. A travelling salesman has to complete a tour comprised of n cities. The tour starts and ends at one of the cities and must pass through all n cities. There are several travelling options between every pair of cities which differ in their costs and durations. When completing the tour, the travelling salesman will receive a predefined known income. The salesman's profit per unit time is defined as the profit gained after completing the tour (calculated by subtracting the route's costs from the profit) divided by the total time required to complete the tour. This problem is a new practical and more complex extension of the well-studied TSP due to the multiple travelling options. The paper defines the problem and presents an iterative solution procedure, which converges after a limited number of iterations, while each iteration having the same time complexity of solving the classical TSP optimally or heuristically.