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Reliability and Inventory in a Production-Storage System

Author

Listed:
  • Robert R. Meyer

    (University of Wisconsin-Madison)

  • Michael H. Rothkopf
  • Stephen A. Smith

    (Xerox Palo Alto Research Center)

Abstract

The reliability of a single stage production-storage system in meeting a constant known demand is analyzed. This system consists of a production facility subject to stochastic failure and repair processes and a storage facility of fixed capacity. When operable, the production facility is assumed to produce at a rate greater than the demand until the storage capacity is exhausted and then at the demand rate. Expressions are developed for the fraction of time demand is met and the average inventory level in the storage facility. Two variants of this problem are also solved.

Suggested Citation

  • Robert R. Meyer & Michael H. Rothkopf & Stephen A. Smith, 1979. "Reliability and Inventory in a Production-Storage System," Management Science, INFORMS, vol. 25(8), pages 799-807, August.
    • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:8:p:799-807
    DOI: 10.1287/mnsc.25.8.799
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    Cited by:

    1. Brian Tomlin, 2006. "On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks," Management Science, INFORMS, vol. 52(5), pages 639-657, May.
    2. Mahmut Parlar & David Perry, 1996. "Inventory models of future supply uncertainty with single and multiple suppliers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 191-210, March.
    3. Jiaping Xie & Lihong Wei & Weisi Zhang & Yu Xia & Jing Li, 2019. "A Responsive Pricing Grid Operator Sourcing from Competing Generators under Uncertain Supply and Demand," Sustainability, MDPI, vol. 11(15), pages 1-30, July.
    4. Silbermayr, Lena & Minner, Stefan, 2014. "A multiple sourcing inventory model under disruption risk," International Journal of Production Economics, Elsevier, vol. 149(C), pages 37-46.
    5. Sarah Yini Gao & David Simchi-Levi & Chung-Piaw Teo & Zhenzhen Yan, 2019. "Disruption Risk Mitigation in Supply Chains: The Risk Exposure Index Revisited," Operations Research, INFORMS, vol. 67(3), pages 831-852, May.
    6. Moshe Dror & Kenneth R. Smith & Candace Arai Yano, 2009. "Deux Chemicals Inc. Goes Just-in-Time," Interfaces, INFORMS, vol. 39(6), pages 503-515, December.
    7. Israel David & Eitan Greenshtein & Avraham Mehrez, 1997. "A dynamic‐programming approach to continuous‐review obsolescent inventory problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(8), pages 757-774, December.
    8. Süleyman Demirel & Roman Kapuscinski & Man Yu, 2018. "Strategic Behavior of Suppliers in the Face of Production Disruptions," Management Science, INFORMS, vol. 64(2), pages 533-551, February.
    9. Parlar, Mahmut & Perry, David, 1995. "Analysis of a (Q, r, T) inventory policy with deterministic and random yields when future supply is uncertain," European Journal of Operational Research, Elsevier, vol. 84(2), pages 431-443, July.
    10. Snyder, Lawrence V., 2014. "A tight approximation for an EOQ model with supply disruptions," International Journal of Production Economics, Elsevier, vol. 155(C), pages 91-108.
    11. Harun Öztürk, 2019. "Modeling an inventory problem with random supply, inspection and machine breakdown," OPSEARCH, Springer;Operational Research Society of India, vol. 56(2), pages 497-527, June.
    12. B. Khoury, 2009. "A discrete approach to designing optimal hedging-point control policies for production-inventory systems with general stochastic behavior," Computational Management Science, Springer, vol. 6(4), pages 399-409, October.
    13. Yimin Wang & Brian Tomlin, 2009. "To wait or not to wait: Optimal ordering under lead time uncertainty and forecast updating," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 766-779, December.
    14. Antonio Arreola‐Risa & Gregory A. DeCroix, 1998. "Inventory management under random supply disruptions and partial backorders," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(7), pages 687-703, October.
    15. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2022. "Minimizing mission cost for production system with unreliable storage," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    16. Fang, Yaner & Shou, Biying, 2015. "Managing supply uncertainty under supply chain Cournot competition," European Journal of Operational Research, Elsevier, vol. 243(1), pages 156-176.
    17. Luangkesorn, K.L. & Klein, G. & Bidanda, B., 2016. "Analysis of production systems with potential for severe disruptions," International Journal of Production Economics, Elsevier, vol. 171(P4), pages 478-486.
    18. Jingfu Huang & Gaoke Wu & Yiju Wang, 2021. "Retailer’s Emergency Ordering Policy When Facing an Impending Supply Disruption," Sustainability, MDPI, vol. 13(13), pages 1-21, June.
    19. Mohebbi, Esmail, 2004. "A replenishment model for the supply-uncertainty problem," International Journal of Production Economics, Elsevier, vol. 87(1), pages 25-37, January.
    20. Gregory A. DeCroix, 2013. "Inventory Management for an Assembly System Subject to Supply Disruptions," Management Science, INFORMS, vol. 59(9), pages 2079-2092, September.
    21. Seyed M.R. Iravani & Izak Duenyas & Tava Lennon Olsen, 2000. "A Production/Inventory System Subject to Failure with Limited Repair Capacity," Operations Research, INFORMS, vol. 48(6), pages 951-964, December.
    22. Boxma, O. J. & Perry, D., 2001. "A queueing model with dependence between service and interarrival times," European Journal of Operational Research, Elsevier, vol. 128(3), pages 611-624, February.
    23. Mahmut Parlar & Defne Berkin, 1991. "Future supply uncertainty in EOQ models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 107-121, February.
    24. E J Lodree Jr & S Taskin, 2008. "An insurance risk management framework for disaster relief and supply chain disruption inventory planning," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 674-684, May.

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