Optimal Algorithms for the Vehicle Routing Problem with Heterogeneous Fleet, Flexible Time Windows and Stochastic Travel Times

Abstract

This project is associated with the doctoral thesis of Ramon Faganello Fachini initiated in 2015 under my supervision. It deals with a vehicle routing problem with flexible time windows, stochastic travel times, and a heterogeneous fleet with a limited or unlimited number of vehicles. We consider flexible time windows that allow limited early and late servicing at customers with respect to their time windows at the expense of penalty costs. The objective is to minimize the sum of the transportation costs and the service costs. The transportation cost comprises the total distance traveled, the number of vehicles used and the expected overtime of the drivers. Service costs correspond to the penalty costs for violating the customers' time windows. In order to solve this problem we exploit its structure in a mixed-integer stochastic programming formulation to design optimal and heuristic algorithms based on the Benders decomposition. We also exploit this methodology for solving the same problem with time windows that cannot be violated and deterministic travel times.