Hamiltonian paths in large clustered routing problems

When a company is faced with an extremely large vehicle routing problem, an interesting option is to divide the customers into zones and perform the routing using the zones rather than the individual customers. Although this greatly reduces the complexity of the original routing problem, customers within each zone still have to be scheduled. In this paper we discuss the shortest pre-Hamiltonian path problem, and argue that this problem provides a good basis to determine the order in which to visit all customers in a zone. We give a milp formulation for this problem and discuss its performance. In addition to the present work, we then discuss how this exact method will be embeded in a global metaheuristic framework that will solve the problem.