Analysis of a multi-echelon supply chain network with Erlang replenishments, (s, S) inventory policies, lost sales and Poisson external demand

Abstract

This manuscript examines a serial multi-echelon inventory system with N, N ≥ 2 stages. The last stage satisfies Poisson external demand that is equal to one product unit. Each stage of the system places orders to its immediate upstream stage based on a reorder point-order quantity inventory control policy (s, S). The replenishment rate of every stage to its immediate downstream stage follows the Erlang distribution with K phases. A continuous time Markov process with discrete states is used to analyze the examined system and an algorithm that creates the transition probabilities matrix is also presented. Using the stationary probabilities of the Markov chain, important performance measures of the system such as the fill rate and the average inventory, among others can be evaluated. Additionally, the best configuration of the system to minimise a total cost function that considers holding, transit and stockout costs is also explored. © 2022 Inderscience Enterprises Ltd.. All rights reserved.