Abstract
The pickup and delivery problem with time windows (PDPTW) is studied in this paper. It is referred to as the single-commodity capacitated vehicle routing problem with pickups and deliveries, in which a fleet of vehicles meet a group of customer demands. Each customer demand includes the usage of only one vehicle for both loading a specified quantity of one type of commodity at one place and delivering them to another place. All the demands of customers must be satisfied without exceeding the vehicle capacity and the pickup or delivery places time windows specified for each place. In this study, we introduce a novel Constraint Programming (CP) model for the PDPTW. CP is an exact solution approach that is popular for its performance to state complicated relationships and to achieve high-quality solutions within acceptable computational times for combinatorial optimization problems with complicated constraints such as the PDPTW. The performance of the proposed CP model is tested with well-known benchmark instances from literature. The results of computational analysis indicate that our CP model is very effective in finding high-quality solutions for even large size problems.
Highlights
Vehicle routing problem (VRP) is a very popular research area owing to its benefits for transportation and logistics applications
We develop a formulation in which all the constraints and the objective function are combined within the framework of Constraint Programming (CP), and we call this model as CP-pickup and delivery problem with time windows (PDPTW)
We developed a new CP model for the PDPTW and compared our model with a mixed integer programming (MIP) model adapted from the existing literature
Summary
Vehicle routing problem (VRP) is a very popular research area owing to its benefits for transportation and logistics applications. Numerous new constraints have been added to this problem to meet real-life demands. Some of these constraints are related with capacity, service times, time windows, loading, transshipment etc. One of the useful extensions of the VRP is the pickup and delivery problem which includes capacity and time windows constraints. The objective of the classic pickup and delivery problems with time windows (PDPTW) is to minimize the number of vehicles employed or to minimize the sum of travel distances of vehicles. Different variants of the PDPTW are studied in literature and classified according to their configurations, the pickup and delivery activities in the nodes, commodity types and the number of employed vehicles.
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