The Traveling Salesman Problem with Precedence Constraints

The Traveling Salesman Problem with Precedence Constraints is to find an hamiltonian tour of minimum cost in a graph G=(X,A) of n vertices, starting from vertex 1, visiting every vertex that must precede i before i (i=2,3,...,n) and returning to vertex 1. In this paper we describe a new bounding procedure and a new optimal algorithm based on dynamic programming. Computational results are given for two classes of randomly generated test problems, including the Dial-A-Ride problem with the classical TSP objective function.