Vehicle routing problem with pickup and delivery

In Vehicle routing problem with pickup and delivery (VRPPD), each customer is associated with two quantities, dj and pi representing the demand of homogeneous commodities to be delivered and picked up at customer, respectively. The VRPPD consists of finding a collection of exactly K simple circuits or routes with minimum cost, such that ... 

The case of VRPPD in which time windows are present is called the Vehicle routing problem with Pickup and Deliveries and Time Windows (VRPPDTW) Summary of the common methods used to solve the Vehicle Routing Problem ... 

Sombuntham P (2010) PSO algorithms for generalized multi-depot vehicle routing problems with pickup and delivery requests. Master s Thesis No. ISE-10-07, Asian Institute of Technology, Thailand... 

The pickup-and-delivery problem can be modeled as a variation of the vehicle routing problem with time windows (VRPTW) and a single depot. Inputs for the VRPTW include matrices that specify the distance and travel time between every pair of customers (including the depot) service time and time window for each customer maximum (or specified) number of drivers starting time of the workday and maximum on-road time of the workday. The maximum on-road time of the workday can be implemented as a time window on the depot, so that the pickup and delivery problem described above can be considered as a traveling salesman problem with time windows and multiple routes (m-TSPTW). However, the term VRPTW will be used in this section for this uncapadtated pickup-and-delivery problem. 

Modified DE Algorithms for Solving Multi-depot Vehicle Routing Problem with Multiple Pickup and Delivery Requests... 

The vehicle routing problem (VRP) (Christofides 1985) is a capacitated version of the TSP. A fleet of vehicles is available at one or more terminals to serve a set of defined stops. A shipment size is associated with each stop, and a cost is associated with the movement between each peiir of stops (and between a stop and a terminal). The goal is to deliver the shipments to all the stops at minimum total cost in a set of cycles without violating vehicle capacity. The VRP formulation matches well local pickup and delivery problems where the pickup stops are known before the vehicle starts on the route. 

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