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Exact analysis of a push–pull system with multiple non identical retailers, a distribution center and multiple non identical unreliable suppliers with supply disruptions

Author

Listed:
  • Angelos Kourepis

    (Aristotle University of Thessaloniki)

  • Alexandros Diamantidis

    (Aristotle University of Thessaloniki)

  • Stylianos Koukoumialos

    (University of Thessaly)

Abstract

In this paper, a push–pull system with K ( $$K \ge 1$$ K ≥ 1 ) non identical suppliers with disruptions that send products to an intermediate distribution center which in turn serves M ( $$M \ge 1$$ M ≥ 1 ) non identical retailers is analyzed. Each retailer satisfies a Poisson distributed external demand of one product unit.The flow of material at the upstream stages (suppliers) is push type. The flow of material at the downstream stages (retailers) is driven by a continuous review inventory control policy (s, S). The replenishment rate of suppliers and retailers is exponentially distributed. More over it is assumed that the suppliers may not be always operational. This is modelled using exponentially distributed failure and repair rates of the suppliers. The considered system is modelled as a continuous time Markov process with discrete states. The derivation of the transition probabilities among the various states of the system is given. Solving the corresponding transition equations system, the stationary probabilities of the system's states are computed and therefore using the stationary probabilities, performance measures of the considered system such as the Fill Rate and WIP are evaluated. Moreover the effect of the system parameters on its performance measures is thoroughly explored. Finally the proposed model is examined from an economic point of view, where the optimal parameter values for the (s, S) type policy are detected to minimize a total inventory cost function.

Suggested Citation

  • Angelos Kourepis & Alexandros Diamantidis & Stylianos Koukoumialos, 2022. "Exact analysis of a push–pull system with multiple non identical retailers, a distribution center and multiple non identical unreliable suppliers with supply disruptions," Operational Research, Springer, vol. 22(5), pages 4801-4827, November.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:5:d:10.1007_s12351-022-00722-0
    DOI: 10.1007/s12351-022-00722-0
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    References listed on IDEAS

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    1. Alexandros Diamantidis & Stylianos Koukoumialos & Michael Vidalis, 2017. "Markovian Analysis of a Push-Pull Merge System with Two Suppliers, An Intermediate Buffer, and Two Retailers," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 8(2), pages 1-35, April.
    2. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
    3. A.C. Diamantidis & S.I. Koukoumialos & M.I. Vidalis, 2016. "Performance evaluation of a push--pull merge system with multiple suppliers, an intermediate buffer and a distribution centre with parallel machines/channels," International Journal of Production Research, Taylor & Francis Journals, vol. 54(9), pages 2628-2652, May.
    4. Rafael Diaz & Barry Charles Ezell, 2012. "A Simulation-Based Optimization Approach to a Lost Sale Stochastic Inventory Model," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 3(2), pages 46-63, April.
    5. Yonit Barron & Opher Baron, 2020. "QMCD approach for perishability models: The (S, s) control policy with lead time," IISE Transactions, Taylor & Francis Journals, vol. 52(2), pages 133-150, February.
    6. Visentin, Andrea & Prestwich, Steven & Rossi, Roberto & Tarim, S. Armagan, 2021. "Computing optimal (R,s,S) policy parameters by a hybrid of branch-and-bound and stochastic dynamic programming," European Journal of Operational Research, Elsevier, vol. 294(1), pages 91-99.
    7. Sandun Perera & Ganesh Janakiraman & Shun†Chen Niu, 2018. "Optimality of (s, S) Inventory Policies under Renewal Demand and General Cost Structures," Production and Operations Management, Production and Operations Management Society, vol. 27(2), pages 368-383, February.
    8. Nazanin Esmaili & Bryan A. Norman & Jayant Rajgopal, 2019. "Exact analysis of (R, s, S) inventory control systems with lost sales and zero lead time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(2), pages 123-132, March.
    9. Diomidis Spinellis & Michael J. Vidalis & Michael E. J. O'Kelly & Chrissoleon T. Papadopoulos, 2009. "Analysis and Design of Discrete Part Production Lines," Springer Optimization and Its Applications, Springer, number 978-0-387-89494-2, June.
    10. Nasr, Walid W. & Maddah, Bacel, 2015. "Continuous (s, S) policy with MMPP correlated demand," European Journal of Operational Research, Elsevier, vol. 246(3), pages 874-885.
    11. Noblesse, Ann M. & Boute, Robert N. & Lambrecht, Marc R. & Van Houdt, Benny, 2014. "Characterizing order processes of continuous review (s,S) and (r,nQ) policies," European Journal of Operational Research, Elsevier, vol. 236(2), pages 534-547.
    12. Kamran Karimi Movahed & Zhi-Hai Zhang, 2015. "Robust design of (, ) inventory policy parameters in supply chains with demand and lead time uncertainties," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2258-2268, September.
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