A Geometrical Center based Two-way Search Heuristic Algorithm for Vehicle Routing Problem with Pickups and Deliveries

Abstract: The classical vehicle routing problem (VRP) can be extended by including customers who want to send goods to the depot. This type of VRP is called the vehicle routing problem with pickups and deliveries (VRPPD). This study proposes a novel way to solve VRPPD by introducing a two-phase heuristic routing algorithm which consists of a clustering phase and uses the geometrical center of a cluster and route establishment phase by applying a two-way search of each route after applying the TSP algorithm on each route. Experimental results show that the suggested algorithm can generate bet-ter initial solutions for more computer-intensive meta-heuristics than other existing methods such as the giant-tour-based partitioning method or the insertion-based method. Keywords: Vehicle Routing Problem, Heuristic Algorithm, Initial Solution 1. Introduction The vehicle routing problem (VRP) is a combinatorial optimization and nonlinear programming problem seeking to service a number of customers with a fleet of vehicles. VRP has been an important problem in the fields of trans-portation, distribution and logistics since Dantzig and Ramser [1] first proposed the problem. The vehicle routing problem with pickups and deliveries (VRPPD) is an exten-sion of the classical VRP. Recently, research on VRPPD has peaked essentially because pickup demands for pack-aging and used product returns from customer locations have increased substantially due to environmental and gov-ernment regulations, and the fact that integrating pickups with deliveries maximally utilizes vehicle capacity and saves money. So, VRPPD must take into account the goods that customers return to the delivery vehicle. This restric-tion makes the planning problem more difficult and in-creases travel distances or the number of vehicles. Re-stricted situations, in which there are no interchanges of goods between customers and all delivery demands start from the depot and all pickup demands are brought back to the depot, are usually considered in VRPPD. The VRPPD model can be classified into three: Deliv-ery-first and pickup-second; mixed pickups and deliveries; and simultaneous pickup and deliveries. The assumption of the delivery-first and pickup-second model is that all deliv-eries must be made before any pickups. This assumption was due to the fact that vehicles were rear-loaded and be-cause rearranging delivery loads onboard to accommodate new pickup loads was difficult. However, in recent days, most vehicles have side-loading as well as rear-loading functions. To accommodate new pickup loads, rearranging delivery loads onboard is no longer a requirement. Hence, the assumption that all deliveries must be made before any pickup can occur can be relaxed, allowing for the mixed pickups and deliveries model in which deliveries and pick-ups may occur in any sequence on a vehicle route. When customers can simultaneously receive and send goods, it is referred to as simultaneous pickup and delivery. A VRPPD solution is feasible only if the following three conditions are satisfied: delivery-feasibility, pickup-feasibility and load-feasibility. Delivery-feasibility and pickup-feasibility mean that both the total delivery and the total pickup de-mands on any vehicle route do not exceed the maximum capacity of the vehicle; and load-feasibility means that the maximum capacity of the vehicle is not exceeded at any point on the route. This study focuses on solving mixed pickups and deliv-eries by applying the two-phase heuristic algorithm. The first phase selects cluster seed as the farthest node (cus-tomers) among unclustered nodes and cluster nodes by using the notion of the geometrical center of a cluster. The result of the first phase satisfies the delivery-feasibility and pickup-feasibility since the total deliveries and pickups on any route is less than or equal to the maximum capacity of the vehicle. And the second phase of the algorithm applies the TSP algorithm on each cluster to find the shortest route regardless of load-feasibility and then finds routes that sat-DOI : 10.3745/JIPS.2009. 5.4. 237