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Continuous (s, S) policy with MMPP correlated demand

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  • Nasr, Walid W.
  • Maddah, Bacel

Abstract

This work considers a continuous inventory replenishment system where demand is stochastic and dependent on the state of the environment. A Markov Modulated Poisson Process (MMPP) is utilized to model the demand process where the corresponding embedded Markov Chain represents the state of the environment. The equations to calculate the system inventory measures and the number of orders per unit time are obtained for a continuous, infinite horizon and dynamically changing (s, S) policy. An efficient optimization heuristic is presented and compared to the commonly used approach of approximating the demand-count process over the lead time with a Normal distribution. An investigation of the MMPP demand process is considered where we quantify the impact of variability in the demand-count process which is due to auto-correlation. Our findings indicate that when demand correlation is high, a dynamic control, where the (s, S) policy changes with state of the environment governing the MMPP, is highly superior to the commonly used “static” heuristics. We propose two dynamic policies of varying computational complexity, and cost efficiency, depending on the class of the product (one for class A, and one for classes B and C), to handle such high-correlation situations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:246:y:2015:i:3:p:874-885
    DOI: 10.1016/j.ejor.2015.05.029
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    Cited by:

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    2. 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.
    3. Jorge A. Sefair & Oscar Guaje & Andrés L. Medaglia, 2021. "A column-oriented optimization approach for the generation of correlated random vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 777-808, September.
    4. Nasr, Walid W. & Elshar, Ibrahim J., 2018. "Continuous inventory control with stochastic and non-stationary Markovian demand," European Journal of Operational Research, Elsevier, vol. 270(1), pages 198-217.
    5. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.
    6. Manafzadeh Dizbin, Nima & Tan, Barış, 2020. "Optimal control of production-inventory systems with correlated demand inter-arrival and processing times," International Journal of Production Economics, Elsevier, vol. 228(C).
    7. Benjamin Avanzi & Greg Taylor & Bernard Wong & Alan Xian, 2020. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," Papers 2003.13888, arXiv.org, revised May 2020.
    8. Walid W. Nasr, 2022. "Inventory systems with stochastic and batch demand: computational approaches," Annals of Operations Research, Springer, vol. 309(1), pages 163-187, February.
    9. Ehsan Ahmadi & Dale T. Masel & Seth Hostetler & Reza Maihami & Iman Ghalehkhondabi, 2020. "A centralized stochastic inventory control model for perishable products considering age-dependent purchase price and lead time," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 231-269, April.

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