An efficient exact approach for the constrained shortest path tour problem

Given a directed graph with non-negative arc lengths, the Constrained Shortest Path Tour Problem (CSPTP) is aimed at finding a shortest path from a single-origin to a single-destination, such that a sequence of disjoint and possibly different-sized node subsets are crossed in a given fixed order. Moreover, the optimal path must not include repeated arcs. In this paper, for the (CSPTP)  we propose a new mathematical model and a new efficient Branch & Bound method. Extensive computational experiments have been carried out on a significant set of test problems in order to evaluate empirically the performance of the proposed approach.