• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.191-201
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• 2008

In this paper, we consider an insurance risk model governed by a compound Binomial arrival claim process and by a compound Binomial arrival premium process. Some formulas for the probabilities of ruin and the distribution of ruin time are given, we also prove the integral equation of the ultimate ruin probability and obtain the Lundberg inequality by the discrete martingale approach.

• Journal of the Korean Operations Research and Management Science Society
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• v.24 no.3
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• pp.109-123
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• 1999

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 trans-portation times, which could be solved analytically, were established and analyzed. We also compared the deterministic case with stochastic one that the transportation time follows some probability distributions.