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Inventory Control for Supply Chains with Service Level Constraints: A Synergy between Large Deviations and Perturbation Analysis

Author

Listed:
  • Ioannis Paschalidis
  • Yong Liu
  • Christos Cassandras
  • Christos Panayiotou

Abstract

We consider a model of a supply chain consisting of n production facilities in tandem and producing a single product class. External demand is met from the finished goods inventory maintained in front of the most downstream facility (stage 1); unsatisfied demand is backlogged. We adopt a base-stock production policy at each stage of the supply chain, according to which the facility at stage i produces if inventory falls below a certain level w i and idles otherwise. We seek to optimize the hedging vector w=(w 1 ,...,w n ) to minimize expected inventory costs at all stages subject to maintaining the stockout probability at stage 1 below a prescribed level (service level constraint). We make rather general modeling assumptions on demand and production processes that include autocorrelated stochastic processes. We solve this stochastic optimization problem by combining analytical (large deviations) and sample path-based (perturbation analysis) techniques. We demonstrate that there is a natural synergy between these two approaches. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Ioannis Paschalidis & Yong Liu & Christos Cassandras & Christos Panayiotou, 2004. "Inventory Control for Supply Chains with Service Level Constraints: A Synergy between Large Deviations and Perturbation Analysis," Annals of Operations Research, Springer, vol. 126(1), pages 231-258, February.
    • Handle: RePEc:spr:annopr:v:126:y:2004:i:1:p:231-258:10.1023/b:anor.0000012283.36012.e8
    DOI: 10.1023/B:ANOR.0000012283.36012.e8
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    Citations

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    Cited by:

    1. Miguel A. Lejeune & Andrzej Ruszczyński, 2007. "An Efficient Trajectory Method for Probabilistic Production-Inventory-Distribution Problems," Operations Research, INFORMS, vol. 55(2), pages 378-394, April.
    2. Yao Zhao & Benjamin Melamed, 2006. "IPA Derivatives for Make-to-Stock Production-Inventory Systems with Backorders," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 191-222, June.
    3. Seong-Cheol Kang & Theodora Brisimi & Ioannis Paschalidis, 2015. "Distribution-dependent robust linear optimization with applications to inventory control," Annals of Operations Research, Springer, vol. 231(1), pages 229-263, August.
    4. Xiangling Hu & Charles Munson & Stergios Fotopoulos, 2012. "Purchasing decisions under stochastic prices: Approximate solutions for order time, order quantity and supplier selection," Annals of Operations Research, Springer, vol. 201(1), pages 287-305, December.
    5. Yihong Fan & Benjamin Melamed & Yao Zhao & Yorai Wardi, 2009. "IPA Derivatives for Make-to-Stock Production-Inventory Systems With Backorders Under the (R,r) Policy," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 159-179, June.
    6. Souheil Ayed & Zied Hajej & Sadok Turki & Nidhal Rezg, 2017. "FPA method for optimal production planning under availability/degradation machine and subcontracting constraint," International Journal of Production Research, Taylor & Francis Journals, vol. 55(8), pages 2135-2148, April.
    7. Lejeune, Miguel A., 2013. "Probabilistic modeling of multiperiod service levels," European Journal of Operational Research, Elsevier, vol. 230(2), pages 299-312.
    8. Benjamin Melamed & Yihong Fan & Yao Zhao & Yorai Wardi, 2010. "IPA derivatives for a discrete model of make-to-stock production-inventory systems with backorders," Annals of Operations Research, Springer, vol. 181(1), pages 1-19, December.

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