Performance evaluation of a two-echelon supply chain with stochastic demand, lost sales, and Coxian-2 phase replenishment times

This paper deals with a two‐echelon supply chain comprising a retailer and manufacturer. The retailer faces Poisson demand and follows a (S, s) continuous review inventory policy. The manufacturer produces and ships the retailer's orders with random delay that follows the Coxian‐2 distribution. Assuming lost sales at the retailer and infinite capacity at the manufacturer, we try to explore the performance of the supply chain system. The system is modeled as a continuous‐time Markov process with discrete space. The structure of the transition matrices of these specific systems is categorized as block‐partitioned, and a computational algorithm generates the matrices for different values of system characteristics. The proposed algorithm allows the calculation of performance measures–fill rate, cycle times, average inventory (work in progress [WIP])–from the derivation of the steady‐state probabilities. Moreover, expressions for the holding costs and shortage costs are derived.