Fleet sizing problem

Gould (1969) brought a new view for the fleet size problem, as he considered the heterogeneous fleet for both fleet type and size. 

The fleet size and composition problem was first studied by Kirby (1959), and then by Wyatt (1961), and both of them, considered a homogenous fleet to be defined, taken into consideration seasonal demand, and the fact that deliveries should be done preferable by an internal fleet, but if the demand exceeds capacity, spot fleet could be hired to fulfill the demand. 

Zhang and Li (2007) presented an article that analyzes multi-periodic vehicle fleet size and routing problem, and dynamic vehicle fleet size. The authors decompose the model with Dantzig-Wolf decomposition method, and derive an exact algorithm for the model based on simplex method, dynamic programming method, and branch and bound method. 

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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