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A single-item inventory model for expected inventory order crossovers

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  • Riezebos, J.
  • Gaalman, G.J.C.

Abstract

Expected inventory order crossovers occur if at the moment of ordering it is expected that orders will not arrive in the sequence they are ordered. Recent research has shown that (a) expected inventory order crossovers will be encountered more frequently in future, and that (b) use of a myopic order-up-to policy based on a stochastic dynamic programming approach leads to improved performance compared to the classical approach. In this paper, we show that the improved policy is still heuristic in nature, as it neglects several control options that are available on the various ordering moments and makes some restrictive assumptions with respect to the separability (i.e., decomposability) of the stochastic dynamic programming problem. We propose further improvements in the policy for situations where a quadratic cost function is appropriate.

Suggested Citation

  • Riezebos, J. & Gaalman, G.J.C., 2009. "A single-item inventory model for expected inventory order crossovers," International Journal of Production Economics, Elsevier, vol. 121(2), pages 601-609, October.
    • Handle: RePEc:eee:proeco:v:121:y:2009:i:2:p:601-609
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    References listed on IDEAS

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    1. Yossi Aviv, 2003. "A Time-Series Framework for Supply-Chain Inventory Management," Operations Research, INFORMS, vol. 51(2), pages 210-227, April.
    2. Stephen C. Graves, 1999. "Addendum to "A Single-Item Inventory Model for a Nonstationary Demand Process"," Manufacturing & Service Operations Management, INFORMS, vol. 1(2), pages 174-174.
    3. 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.
    4. Arthur F. Veinott, Jr., 1965. "Optimal Policy for a Multi-Product, Dynamic, Nonstationary Inventory Problem," Management Science, INFORMS, vol. 12(3), pages 206-222, November.
    5. G. D. Johnson & H. E. Thompson, 1975. "Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes," Management Science, INFORMS, vol. 21(11), pages 1303-1307, July.
    6. 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.
    7. R. Bellman & I. Glicksberg & O. Gross, 1955. "On the Optimal Inventory Equation," Management Science, INFORMS, vol. 2(1), pages 83-104, October.
    8. Riezebos, Jan, 2006. "Inventory order crossovers," International Journal of Production Economics, Elsevier, vol. 104(2), pages 666-675, December.
    9. Stephen C. Graves, 1999. "A Single-Item Inventory Model for a Nonstationary Demand Process," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 50-61.
    10. Urban, Timothy L., 2005. "A periodic-review model with serially-correlated, inventory-level-dependent demand," International Journal of Production Economics, Elsevier, vol. 95(3), pages 287-295, March.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Hayya, Jack C. & Bagchi, Uttarayan & Ramasesh, Ranga, 2011. "Cost relationships in stochastic inventory systems: A simulation study of the (S, S-1, t=1) model," International Journal of Production Economics, Elsevier, vol. 130(2), pages 196-202, April.

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