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.