An Evaluative Continuous Time Markov Chain Model for a Three Echelon Supply Chain with Stochastic Demand and Lead Time

In this paper, a three echelon supply chain model is explained, which considers supplier, manufacturer and distribution centers. Distribution centers face Poisson demand with the rate of Λd and manufacturer produces and ships their orders with stochastic lead time of the Exponential distribution with the rate of μd. A supplier, ships row materials to the manufacturer with stochastic lead time that follows the Exponential distribution with the rate of ys. Assuming lost sales at the distribution centers, an evaluative continuous time markov model is established to evaluate performance indexes of the model. Moreover, response surface methodology is used for optimizing the performance. Results show that the proposed model can evaluate performance indexes of the supply chain model accurately and determine optimum inventory policy. Moreover, the established response surface methodology can estimate net profit of the system as well.