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Efficient optimization of the dual-index policy using Markov chains

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  • Joachim Arts
  • Marcel van Vuuren
  • Gudrun Kiesmüller

Abstract

This article considers the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster “emergency” supply source. Unsatisfied demand is backordered and ordering decisions are made periodically. The optimal control policy for this system is known to be complex. For this reason a type of base-stock policy known as the Dual-Index Policy (DIP) is used as the as control mechanism for this inventory system. Under this policy ordering decisions are based on a regular and an emergency inventory position and their corresponding order-up-to levels. Previous work on this policy assumes deterministic lead times and uses simulation to find the optimal order-up-to levels. This article provides an alternate proof for the result that separates the optimization of the DIP in two one-dimensional problems. An insight from this proof allows the model to be generalized to accommodate stochastic regular lead times and provide an approximate evaluation method based on limiting results so that optimization can be done without simulation. An extensive numerical study shows that this approach yields excellent results for deterministic lead times and good results for stochastic lead times.

Suggested Citation

  • Joachim Arts & Marcel van Vuuren & Gudrun Kiesmüller, 2011. "Efficient optimization of the dual-index policy using Markov chains," IISE Transactions, Taylor & Francis Journals, vol. 43(8), pages 604-620.
    • Handle: RePEc:taf:uiiexx:v:43:y:2011:i:8:p:604-620
    DOI: 10.1080/0740817X.2010.550908
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    Citations

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    Cited by:

    1. Chaolin Yang & Diyuan Huang & Chenyang Xu, 2022. "Multi-index base-stock policy for inventory systems with multiple capacitated suppliers," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 155-177, March.
    2. Ju, Wanrong & Gabor, Adriana F. & van Ommeren, J.C.W., 2015. "An approximate policy for a dual-sourcing inventory model with positive lead times and binomial yield," European Journal of Operational Research, Elsevier, vol. 244(2), pages 490-497.
    3. Younes Hamdouch & Youssef Boulaksil & Kilani Ghoudi, 2023. "Dual sourcing inventory management with nonconsecutive lead times from a supply chain perspective: a numerical study," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 1013-1041, September.
    4. Jakšič, M. & Fransoo, J.C., 2018. "Dual sourcing in the age of near-shoring: Trading off stochastic capacity limitations and long lead times," European Journal of Operational Research, Elsevier, vol. 267(1), pages 150-161.
    5. Chand, Suresh & Li, Jian & Xu, Yanyi, 2016. "A periodic review inventory model with two delivery modes, fractional lead-times, and age-and-period-dependent backlogging costs," International Journal of Production Economics, Elsevier, vol. 173(C), pages 199-206.
    6. Cheaitou, Ali & van Delft, Christian, 2013. "Finite horizon stochastic inventory problem with dual sourcing: Near myopic and heuristics bounds," International Journal of Production Economics, Elsevier, vol. 143(2), pages 371-378.
    7. Svoboda, Josef & Minner, Stefan & Yao, Man, 2021. "Typology and literature review on multiple supplier inventory control models," European Journal of Operational Research, Elsevier, vol. 293(1), pages 1-23.
    8. Barron, Yonit, 2022. "The continuous (S,s,Se) inventory model with dual sourcing and emergency orders," European Journal of Operational Research, Elsevier, vol. 301(1), pages 18-38.
    9. Boulaksil, Youssef & Hamdouch, Younes & Ghoudi, Kilani & Fransoo, Jan C., 2021. "Comparing policies for the stochastic multi-period dual sourcing problem from a supply chain perspective," Other publications TiSEM 242598b9-99de-4a3c-a1a9-4, Tilburg University, School of Economics and Management.
    10. Boulaksil, Youssef & Hamdouch, Younes & Ghoudi, Kilani & Fransoo, Jan C., 2021. "Comparing policies for the stochastic multi-period dual sourcing problem from a supply chain perspective," International Journal of Production Economics, Elsevier, vol. 232(C).
    11. Ahiska, S. Sebnem & Appaji, Samyuktha R. & King, Russell E. & Warsing, Donald P., 2013. "A Markov decision process-based policy characterization approach for a stochastic inventory control problem with unreliable sourcing," International Journal of Production Economics, Elsevier, vol. 144(2), pages 485-496.
    12. Arts, Joachim & Kiesmüller, Gudrun P., 2013. "Analysis of a two-echelon inventory system with two supply modes," European Journal of Operational Research, Elsevier, vol. 225(2), pages 263-272.
    13. Tamás Bányai & Christian Landschützer & Ágota Bányai, 2018. "Markov-Chain Simulation-Based Analysis of Human Resource Structure: How Staff Deployment and Staffing Affect Sustainable Human Resource Strategy," Sustainability, MDPI, vol. 10(10), pages 1-21, October.
    14. Dong, Chuanwen & Transchel, Sandra & Hoberg, Kai, 2018. "An inventory control model for modal split transport: A tailored base-surge approach," European Journal of Operational Research, Elsevier, vol. 264(1), pages 89-105.
    15. Steffen T. Klosterhalfen & Stefan Minner & Sean P. Willems, 2014. "Strategic Safety Stock Placement in Supply Networks with Static Dual Supply," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 204-219, May.
    16. Johansen, Søren Glud, 2019. "Emergency orders in the periodic-review inventory system with fixed ordering costs and stochastic lead times for normal orders," International Journal of Production Economics, Elsevier, vol. 209(C), pages 205-214.
    17. Sean X. Zhou & Chaolin Yang, 2016. "Continuous-Review ( R, nQ ) Policies for Inventory Systems with Dual Delivery Modes," Operations Research, INFORMS, vol. 64(6), pages 1302-1319, December.
    18. N. Knofius & M. C. Heijden & A. Sleptchenko & W. H. M. Zijm, 2021. "Improving effectiveness of spare parts supply by additive manufacturing as dual sourcing option," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(1), pages 189-221, March.
    19. Drent, Melvin & Moradi, Poulad & Arts, Joachim, 2023. "Efficient emission reduction through dynamic supply mode selection," European Journal of Operational Research, Elsevier, vol. 311(3), pages 925-941.
    20. 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.
    21. Roni, Mohammad S. & Jin, Mingzhou & Eksioglu, Sandra D., 2015. "A hybrid inventory management system responding to regular demand and surge demand," Omega, Elsevier, vol. 52(C), pages 190-200.

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