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An Inventory Model with Order Crossover

Author

Listed:
  • Xin X. He

    (South Carolina State University, Orangeburg, South Carolina)

  • Susan H. Xu

    (Penn State University, University Park, Pennsylvania)

  • J. Keith Ord

    (Penn State University, University Park, Pennsylvania)

  • Jack C. Hayya

    (Penn State University, University Park, Pennsylvania)

Abstract

In inventory systems with stochastic lead times, it is possible that more than a single order will be outstanding. In that case, orders may cross; that is, they may not be received in the same sequence in which they are placed. In this paper we develop a multicycle analysis for the case when lead times are independently and identically distributed. When contrasted with the conventional single cycle analysis, the multicycle approach provides a more accurate assessment of the overall inventory cost and leads to a superior inventory policy.

Suggested Citation

  • Xin X. He & Susan H. Xu & J. Keith Ord & Jack C. Hayya, 1998. "An Inventory Model with Order Crossover," Operations Research, INFORMS, vol. 46(3-supplem), pages 112-119, June.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:3-supplement-3:p:s112-s119
    DOI: 10.1287/opre.46.3.S112
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    References listed on IDEAS

    as
    1. Robert S. Kaplan, 1970. "A Dynamic Inventory Model with Stochastic Lead Times," Management Science, INFORMS, vol. 16(7), pages 491-507, March.
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    3. Ranga V. Ramasesh & J. Keith Ord & Jack C. Hayya & Andrew Pan, 1991. "Sole Versus Dual Sourcing in Stochastic Lead-Time (s, Q) Inventory Models," Management Science, INFORMS, vol. 37(4), pages 428-443, April.
    4. Georghios P. Sphicas, 1982. "Technical Note—On the Solution of an Inventory Model with Variable Lead Times," Operations Research, INFORMS, vol. 30(2), pages 404-410, April.
    5. Matthew J. Liberatore, 1979. "Technical Note—The EOQ Model under Stochastic Lead Time," Operations Research, INFORMS, vol. 27(2), pages 391-396, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Kim, Taebok & Glock, Christoph H. & Kwon, Yongjang, 2014. "A closed-loop supply chain for deteriorating products under stochastic container return times," Omega, Elsevier, vol. 43(C), pages 30-40.
    2. Faicel Hnaien & Alexandre Dolgui & Desheng Dash Wu, 2016. "Single-period inventory model for one-level assembly system with stochastic lead times and demand," International Journal of Production Research, Taylor & Francis Journals, vol. 54(1), pages 186-203, January.
    3. Achin Srivastav & Sunil Agrawal, 2020. "On a single item single stage mixture inventory models with independent stochastic lead times," Operational Research, Springer, vol. 20(4), pages 2189-2227, December.
    4. Louly, Mohamed-Aly & Dolgui, Alexandre, 2011. "Optimal time phasing and periodicity for MRP with POQ policy," International Journal of Production Economics, Elsevier, vol. 131(1), pages 76-86, May.
    5. Hum, Sin-Hoon & Parlar, Mahmut & Zhou, Yun, 2018. "Measurement and optimization of responsiveness in supply chain networks with queueing structures," European Journal of Operational Research, Elsevier, vol. 264(1), pages 106-118.
    6. Achin Srivastav & Sunil Agrawal, 2020. "Multi-objective optimization of mixture inventory system experiencing order crossover," Annals of Operations Research, Springer, vol. 290(1), pages 943-960, July.
    7. He, Xin James & Kim, Jeon G. & Hayya, Jack C., 2005. "The cost of lead-time variability: The case of the exponential distribution," International Journal of Production Economics, Elsevier, vol. 97(2), pages 130-142, August.
    8. Hayya, Jack C. & Harrison, Terry P. & He, X. James, 2011. "The impact of stochastic lead time reduction on inventory cost under order crossover," European Journal of Operational Research, Elsevier, vol. 211(2), pages 274-281, June.
    9. Chatfield, Dean C. & Pritchard, Alan M., 2018. "Crossover aware base stock decisions for service-driven systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 312-330.
    10. Lawrence W. Robinson & James R. Bradley & L. Joseph Thomas, 2001. "Consequences of Order Crossover Under Order-Up-To Inventory Policies," Manufacturing & Service Operations Management, INFORMS, vol. 3(3), pages 175-188, September.
    11. Andreas Thorsen & Tao Yao, 2017. "Robust inventory control under demand and lead time uncertainty," Annals of Operations Research, Springer, vol. 257(1), pages 207-236, October.
    12. Louly, Mohamed-Aly Ould & Dolgui, Alexandre, 2009. "Calculating safety stocks for assembly systems with random component procurement lead times: A branch and bound algorithm," European Journal of Operational Research, Elsevier, vol. 199(3), pages 723-731, December.
    13. Hellemans, Tim & Boute, Robert N. & Van Houdt, Benny, 2019. "Analysis of lead time correlation under a base-stock policy," European Journal of Operational Research, Elsevier, vol. 276(2), pages 519-535.
    14. Thomas Wensing & Heinrich Kuhn, 2015. "Analysis of production and inventory systems when orders may cross over," Annals of Operations Research, Springer, vol. 231(1), pages 265-281, August.
    15. Louly, Mohamed-Aly & Dolgui, Alexandre & Hnaien, Faicel, 2008. "Supply planning for single-level assembly system with stochastic component delivery times and service-level constraint," International Journal of Production Economics, Elsevier, vol. 115(1), pages 236-247, September.
    16. James R. Bradley & Lawrence W. Robinson, 2005. "Improved Base-Stock Approximations for Independent Stochastic Lead Times with Order Crossover," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 319-329, November.
    17. Riezebos, Jan, 2006. "Inventory order crossovers," International Journal of Production Economics, Elsevier, vol. 104(2), pages 666-675, December.
    18. Hayya, Jack C. & Bagchi, Uttarayan & Kim, Jeon G. & Sun, Daewon, 2008. "On static stochastic order crossover," International Journal of Production Economics, Elsevier, vol. 114(1), pages 404-413, July.
    19. Ould-Louly, Mohamed-Aly & Dolgui, Alexandre, 2004. "The MPS parameterization under lead time uncertainty," International Journal of Production Economics, Elsevier, vol. 90(3), pages 369-376, August.
    20. Jeon G. Kim & Daewon Sun & Xin James He & Jack C. Hayya, 2004. "The (s, Q) inventory model with Erlang lead time and deterministic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 906-923, September.

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