An algorithm based on matrix analytic methods for the exact numerical performance evaluation of a two-echelon vendor-managed inventory system with lost sales is presented in this paper. Both supply and demand uncertainties are taken into consideration. Lead times are modeled using a phase-type (Coxian) distribution with two phases, while the stochastic nature of external demand is captured with a compound Poisson distribution comprised of a pure Poisson arrival process and a discrete empirical distribution for the demand of individual customers. A computer program based on the algorithm is developed and then it is used for an extensive numerical investigation with a view to obtain insights of possible managerial importance.
Varlas et al. (Fri,) studied this question.