On fleet sizing and distribution policy of transportation equipments in pure hub-and-spoke networks: The case of compound Poisson process

Fleet sizing and empty equipment redistribution are two of the most critical problems in managing a fleet of equipment over a transportation network. Where the demand pattern followed the compound Poisson process (CPP) which can be generated one or more at a time under homogeneous Poisson process (HPP), this paper presented a mathematical model to determine control parameters of a decentralized distribution policy and fleet size in case of the pure hub-and-spoke system, a popular form of a logistics system, and validated this model by simulation. That is, where the number of demanded equipments followed geometric and binomial distributions, respectively, cost models on the pure hub-and-spoke logistics system with deterministic transportation times, which could be solved analytically, were established and analyzed. We also compared the deterministic case with the stochastic one that the transportation time follows some probability distributions.