Exact algorithms for a selective Vehicle Routing Problem where the longest route is minimized

In this paper, we study a non-capacitated Vehicle Routing Problem (VRP) where not necessarily all clients need to be visited and the goal is to minimize the length of the longest vehicle route. An Integer Programming Formulation, a Branch-and-cut (BC) method and a Local Branching (LB) framework that uses BC as the inner solver are presented. Sharper upper bounds are obtained by LB, when the same time limit was imposed on the execution times of both approaches. Our results also suggest that the min-max nature of the objective function combined with the fact that not all vertices need to be visited make such problem very difficult to solve.