Rich variants of the vehicle routing problem​​​​​​​

Abstract

The Vehicle Routing Problem (VRP) is one of the most important optimization problems in the field of Operations Research (OR) and it has been an interesting and challenging subject for OR researchers for more than fifty years. Moreover, routing problems are crucial in real life when people or goods are carried from one place to another. The solution of the VRP requires designing optimal routes from one or more depots to a number of customers. This will usually involve the minimization of some combination of the number of vehicles used and the total distance traveled. The term Rich Vehicle Routing Problems (RVRPs) arises when applying real-life extensions and when adding realistic constraints to the problem.The Pickup and Delivery Problem with Time Windows (PDPTW) is a generalization of the VRP. In the PDPTW vehicles with limited capacity must be routed to serve given requests each of which consists of a pickup and a corresponding delivery. For each request, the pickup must precede the delivery (precedence) and both must be performed by the same vehicle (pairing). Routes must respect precedence, pairing, vehicle-capacity, and time-window constraints, as well as constraints which apply to specific problem variants. Incorporating loading constraints to the routing will add more complexity to the problem and make it very challenging.Solution techniques for the PDPTW have focused on either heuristic approaches or increasingly complex exact algorithms based on branch-and-cut-and-price schemes. Very little work has been done on other possible exact solution techniques for variants of the PDPTW.This thesis proposes a novel exact method by introducing a new methodology and formulation for exactly solving the PDPTW and its variants. This method is based on fragments - a series of pickup and delivery requests starting and ending with an empty vehicle. Using fragments, we formulate a relaxed network flow model with side constraint and use lazy constraints to cut off any illegal solutions generated while solving the resultant integer program. This method is easy to implement and can be extended in a straightforward way to solve most variants of the PDPTW for problems where it is possible to generate all fragments. Computational results confirm that this method outperforms the current state-of-the-art algorithms for solving the Pickup and Delivery Problem with Time Windows and Last-in-First-Out Loading (PDPTWL) and the Pickup and Delivery Problem with Time Windows and Multiple Stacks (PDPTWMS). This thesis also introduces for the first time an algorithm for solving a real-life extension of the PDPTWMS. Moreover, new valid inequalities for solving the PDPTW and its variants are introduced.