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

Authors: Despoina D. Ntio; Michael I. Vidalis; Stylianos I. Koukoumialos; Alexandros C. Diamantidis

Addresses: Department of Business Administration, University of Applied Sciences, Western Macedonia, Greece ' Department of Business Administration, University of the Aegean, Chios Island, Greece ' General Department, University of Thessaly, Larisa, Greece ' Department of Economics, Aristotle University of Thessaloniki, Thessaloniki, Greece

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.

Keywords: continuous review inventory policy; supply chain management; Markov processes; performance evaluation.

DOI: 10.1504/IJSOM.2022.123066

International Journal of Services and Operations Management, 2022 Vol.42 No.1, pp.75 - 102

Received: 12 Jun 2019
Accepted: 21 Dec 2019
Published online: 26 May 2022 *

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