A joint routing and speed optimization problem

Vehicle speed plays a significant role on fuel consumption and greenhouse gas emissions in freight transportation. We study a general joint routing and speed optimization problem with the goal of minimizing the total fuel, emission, and labor costs; the fuel consumption and emission rate is allowed to be an arbitrary strictly convex function of vehicle speed. We propose a novel set partitioning formulation for this problem, in which each column represents a combination of a route and a subset of customers on the route whose time-window constraints are active, in contrast to the set partitioning formulation of the vehicle routing problem in which each column represents a route. This formulation facilitates the development of an efficient labeling algorithm for the pricing problem in a branch-cut-and-price framework. We test our formulation and branch-cut-and-price algorithm on a variety of instances on United Kingdom cities and modified Solomon instances. Our algorithm is capable of solving all the 25-customer instances including the most different UK-A family and several 50-customer instances; only 10-customer UK-A instances are solved to optimality to date by other published research.