Algorithms for pickup and delivery problems with hours of service constraints

Abstract

We propose new exact and heuristic algorithms for solving an extension of the Pickup and Delivery problem with Time Windows that considers numerous constraints encountered in the real world. The problem involves optimally routing a fleet of identical vehicles to service a set of pickup and delivery pairs subject to capacity, time window, pairing, precedence, and last-in-first-out loading constraints as well as complex driver rules. We consider a set partitioning model based on routes, and also introduce a formulation based on fragments which are segments of routes with a particular structure. Computational results on randomly generated instances are used to compare the scalability of the two formulations with respect to the number of requests. A technique for reducing the number of routes or fragments is proposed which relies on a machine learning model to determine those that are likely to be in the optimal solution. When the number of routes or fragments is reduced using the machine learning model, high quality solutions are obtained on the instances solvable by the exact method. Solutions can also be obtained for instances where route or fragment generation is intractable.