Analysis of a Three-Echelon Supply Chain System with Multiple Retailers, Stochastic Demand and Transportation Times

Georgios Varlas, Stelios Koukoumialos, Alexandros Diamantidis and Evangelos Ioannidis ()
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Georgios Varlas: Department of Business Administration, University of the Aegean, 82100 Chios, Greece
Stelios Koukoumialos: Department of Business Administration, University of Thessaly, 41500 Larissa, Greece
Alexandros Diamantidis: Department of Economics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Evangelos Ioannidis: Department of Economics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

Mathematics, 2025, vol. 13, issue 19, 1-28

Abstract: In this paper we present an exact numerical model for the evaluation of a three-echelon supply chain with multiple retailers. Poisson demand, exponentially distributed transportation times and lost sales at the retailers are assumed. The system is modeled as a continuous time Markov chain, and the analysis is based on matrix analytic methods. We analyze the infinitesimal generator matrix of the process and develop an algorithm for its construction. Performance measures for the system are calculated algorithmically from the stationary probabilities vector. The algorithm is used for an extensive numerical investigation of the system so that conclusions of managerial importance may be drawn.

Keywords: Markov chain processes; supply chain systems; performance evaluation; stochastic demand; lost sales (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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