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The impact of stochastic lead time reduction on inventory cost under order crossover

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  • Hayya, Jack C.
  • Harrison, Terry P.
  • He, X. James

Abstract

We use exponential lead times to demonstrate that reducing mean lead time has a secondary reduction of the variance due to order crossover. The net effect is that of reducing the inventory cost, and if the reduction in inventory cost overrides the investment in lead time reduction, then the lead time reduction strategy would be tenable. We define lead time reduction as the process of decreasing lead time at an increased cost. To date, decreasing lead times has been confined to deterministic instances. We examine the case where lead times are exponential, for when lead times are stochastic, deliveries are subject to order crossover, so that we must consider effective lead times rather than the actual lead times. The result is that the variance of these lead times is less than the variance of the original replenishment lead times. Here we present a two-stage procedure for reducing the mean and variance for exponentially distributed lead times. We assume that the lead time is made of one or several components and is the time between when the need of a replenishment order is determined to the time of receipt.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:211:y:2011:i:2:p:274-281
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    References listed on IDEAS

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    Cited by:

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    3. Hansen, Ole & Transchel, Sandra & Friedrich, Hanno, 2023. "Replenishment strategies for lost sales inventory systems of perishables under demand and lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 308(2), pages 661-675.
    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.
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    6. Hsien-Jen Lin, 2015. "A stochastic periodic review inventory model with back-order discounts and ordering cost dependent on lead time for the mixtures of distributions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 386-400, July.
    7. Riezebos, Jan & Zhu, Stuart X., 2020. "Inventory control with seasonality of lead times," Omega, Elsevier, vol. 92(C).
    8. Dominguez, Roberto & Cannella, Salvatore & Ponte, Borja & Framinan, Jose M., 2020. "On the dynamics of closed-loop supply chains under remanufacturing lead time variability," Omega, Elsevier, vol. 97(C).
    9. Wang, Xun & Disney, Stephen M., 2017. "Mitigating variance amplification under stochastic lead-time: The proportional control approach," European Journal of Operational Research, Elsevier, vol. 256(1), pages 151-162.
    10. Rabin Kumar Mallick & Kartik Patra & Shyamal Kumar Mondal, 2020. "Mixture inventory model of lost sale and back-order with stochastic lead time demand on permissible delay in payments," Annals of Operations Research, Springer, vol. 292(1), pages 341-369, September.
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    12. Disney, Stephen M. & Maltz, Arnold & Wang, Xun & Warburton, Roger D.H., 2016. "Inventory management for stochastic lead times with order crossovers," European Journal of Operational Research, Elsevier, vol. 248(2), pages 473-486.
    13. Dipak Barman & Gour Chandra Mahata, 2022. "Two-echelon production inventory model with imperfect quality items with ordering cost reduction depending on controllable lead time," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(5), pages 2656-2671, October.
    14. 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.
    15. Jian, Ming & Fang, Xin & Jin, Liu-qian & Rajapov, Azamat, 2015. "The impact of lead time compression on demand forecasting risk and production cost: A newsvendor model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 84(C), pages 61-72.
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    18. Fang, Xin & Zhang, Cheng & Robb, David J. & Blackburn, Joseph D., 2013. "Decision support for lead time and demand variability reduction," Omega, Elsevier, vol. 41(2), pages 390-396.

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