Vehicle routing problem with time windows

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. 

Kontoravdis, G., and Bard, J. (1995), A GRASP for the Vehicle Routing Problem with Time Windows, ORSA Journal on Computing, Vol. 7, pp. 10-23. 

Potvin, J., Kervahut, T, Garcia, B., and Rousseau, J. (1996), The Vehicle Routing Problem with Time Windows—Part 1 Tabu Search, INFORMS Journal on Computing, Vol. 8, pp. 158-164. 

Thangiah, S., Osman, I., and Sun, T. (1995), Metaheuristics for Vehicle Routing Problems with Time Windows, Technical Report, Computer Science Department, Shppery Rock University, Slippery Rock, PA. 

Vehicle-routing problem with time windows (VRPTW), 2061 Vehicles, off-highway, 1470 Velocity encoders, 1903 Vendor-managed inventory (VMI), 779 Ventilation ... 

Vehicle routing problem with time windows (VRPTW). The VRP with Time Windows is the extension of the CVRP in which capacity constraints are imposed and each customer is associated with a time interval [aj, bj, called a time window. The time instant in which the vehicles leave the depot, the travel time for each arc, and an additional service time Si for each customer should also be given. 

Sugarcane Harvester Planning Based on the Vehicle Routing Problem with Time Window (VRPTW) Approach... 

Tan KC, Lee LH, Zhu QL, Ou K (2001) Heuristic methods for vehicle routing problem with time windows. Artif Intell Eng 15(3) 281-295... 

Braysy, O., Gendreau, M. Vehicle routing problem with time windows, Part I Route construction and local search algorithms. Transportation Science 39(1), 104-118 (2005)... 

Potvin, J., and Rousseau, J. (1993), A Parallel Route Building Algorithm for the Vehicle Routing and Scheduling Problem with Time Windows, European Journal of Operational Research, Vol. 66, pp. 331-340. 

Solomon, M. (1987), Algorithms for the Vehicle Routing and Scheduhng Problems with Time Window Constraints, Operations Research, Vol. 35, pp. 254-265. 

Solomon, M., Baker, E., and Schaffer, J. (1988), Vehicle Routing and Scheduling Problems with Time Window Constraints Efficient Implementations of Solution Improvement Procedures, in Vehicle Routing Methods and Studies, B. Golden and A. Assad, Eds., North-Holland, Amsterdam, pp. 85-105. 

TaiUard, E., Badeau, P., Gendreau, M., Guertin, R, and Potvin, J. (1997), A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows, Transportation Science, Vol. 31, pp. 170-186. 

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 ... 

Thankfully, industrial engineers and software developers are aware of these real constraints, which are handled by various extensions of the TSP (Ball et rd. 1995 Golden and Assad 1988). For example, route capacities and times are considered by the vehicle routing problem (VRP), while time window constraints are included in the TSP with time windows (TSPTW) and the VRP with time windows (VRPTW). Advances in telecommunications make it now possible to implement models that take into account the dynamic aspects of vehicle routing, while time-dependent vehicle routing problems take into account time-dependent travel times and costs. The stochastic aspects of cost, time, demand... 

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