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Repairable Stocking and Expediting in a Fluctuating Demand Environment: Optimal Policy and Heuristics

Author

Listed:
  • Joachim Arts

    (School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands, PO Box 513, 5600MB)

  • Rob Basten

    (School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands, PO Box 513, 5600MB)

  • Geert-Jan Van Houtum

    (School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands, PO Box 513, 5600MB)

Abstract

We consider a single stock-point for a repairable item facing Markov modulated Poisson demand. Repair of failed parts may be expedited at an additional cost to receive a shorter lead time. Demand that cannot be filled immediately is backordered and penalized. The manager decides on the number of spare repairables to purchase and on the expediting policy. We characterize the optimal expediting policy using a Markov decision process formulation and provide closed-form necessary and sufficient conditions that determine whether the optimal policy is a type of threshold policy or a no-expediting policy. We derive further asymptotic results as demand fluctuates arbitrarily slowly. In this regime, the cost of this system can be written as a weighted average of costs for systems facing Poisson demand. These asymptotics are leveraged to show that approximating Markov modulated Poisson demand by stationary Poisson demand can lead to arbitrarily poor results. We propose two heuristics based on our analytical results, and numerical tests show good performance with average optimality gaps of 0.11% and 0.33% respectively. Naive heuristics that ignore demand fluctuations have average optimality gaps of more than 11%. This shows that there is great value in leveraging knowledge about demand fluctuations in making repairable expediting and stocking decisions.

Suggested Citation

  • Joachim Arts & Rob Basten & Geert-Jan Van Houtum, 2016. "Repairable Stocking and Expediting in a Fluctuating Demand Environment: Optimal Policy and Heuristics," Operations Research, INFORMS, vol. 64(6), pages 1285-1301, December.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:6:p:1285-1301
    DOI: 10.1287/opre.2016.1498
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    References listed on IDEAS

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    Cited by:

    1. Arts, Joachim, 2017. "A multi-item approach to repairable stocking and expediting in a fluctuating demand environment," European Journal of Operational Research, Elsevier, vol. 256(1), pages 102-115.
    2. 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.
    3. Jing-Sheng Song & Li Xiao & Hanqin Zhang & Paul Zipkin, 2017. "Optimal Policies for a Dual-Sourcing Inventory Problem with Endogenous Stochastic Lead Times," Operations Research, INFORMS, vol. 65(2), pages 379-395, April.
    4. Bram Westerweel & Rob Basten & Jelmar den Boer & Geert‐Jan van Houtum, 2021. "Printing Spare Parts at Remote Locations: Fulfilling the Promise of Additive Manufacturing," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1615-1632, June.
    5. 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.
    6. Topan, E. & van der Heijden, M.C., 2020. "Operational level planning of a multi-item two-echelon spare parts inventory system with reactive and proactive interventions," European Journal of Operational Research, Elsevier, vol. 284(1), pages 164-175.
    7. Topan, E. & Eruguz, A.S. & Ma, W. & van der Heijden, M.C. & Dekker, R., 2020. "A review of operational spare parts service logistics in service control towers," European Journal of Operational Research, Elsevier, vol. 282(2), pages 401-414.
    8. Gerrits, B. & Topan, E. & van der Heijden, M.C., 2022. "Operational planning in service control towers – heuristics and case study," European Journal of Operational Research, Elsevier, vol. 302(3), pages 983-998.
    9. 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.

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