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A solution for the intractable inventory model when both demand and lead time are stochastic

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  • Hayya, Jack C.
  • Harrison, Terry P.
  • Chatfield, Dean C.

Abstract

We consider the reorder point, order quantity inventory model where the demand, D, and the lead time, L, are independently and identically distributed (iid) random variables. This model is analytically intractable because of order crossover. However, we show how to resolve the intractability by empirical means, for example, by regression relationships produced by simulation and factorial experiments. Using a normal approximation, we show how to obtain regression equations for the optimal cost and the optimal policy parameters (here the order quantity and the safety stock factor) in terms of the problem parameters (ordering cost per order, holding cost per unit per unit time, shortage cost per unit, the standard deviation of demand, and the standard deviation of lead time).

Suggested Citation

  • Hayya, Jack C. & Harrison, Terry P. & Chatfield, Dean C., 2009. "A solution for the intractable inventory model when both demand and lead time are stochastic," International Journal of Production Economics, Elsevier, vol. 122(2), pages 595-605, December.
    • Handle: RePEc:eee:proeco:v:122:y:2009:i:2:p:595-605
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    References listed on IDEAS

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    1. 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.
    2. Lawrence W. Robinson & James R. Bradley, 2008. "Note--Further Improvements on Base-Stock Approximations for Independent Stochastic Lead Times with Order Crossover," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 325-327, December.
    3. 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.
    4. 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.
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    Cited by:

    1. Daniela Favaretto & Alessandro Marin & Marco Tolotti, 2023. "A theoretical validation of the DDMRP reorder policy," Computational Management Science, Springer, vol. 20(1), pages 1-28, December.
    2. 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.
    3. Barros, Júlio & Cortez, Paulo & Carvalho, M. Sameiro, 2021. "A systematic literature review about dimensioning safety stock under uncertainties and risks in the procurement process," Operations Research Perspectives, Elsevier, vol. 8(C).
    4. 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.
    5. 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.
    6. Muriana, Cinzia, 2016. "An EOQ model for perishable products with fixed shelf life under stochastic demand conditions," European Journal of Operational Research, Elsevier, vol. 255(2), pages 388-396.
    7. Taleizadeh, Ata Allah & Zarei, Hamid Reza & Sarker, Bhaba R., 2017. "An optimal control of inventory under probablistic replenishment intervals and known price increase," European Journal of Operational Research, Elsevier, vol. 257(3), pages 777-791.
    8. Osman, Hany & Demirli, Kudret, 2012. "Integrated safety stock optimization for multiple sourced stockpoints facing variable demand and lead time," International Journal of Production Economics, Elsevier, vol. 135(1), pages 299-307.
    9. 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.
    10. Mekhtiev, Mirza Arif, 2013. "Analytical evaluation of lead-time demand in polytree supply chains with uncertain demand, lead-time and inter-demand time," International Journal of Production Economics, Elsevier, vol. 145(1), pages 304-317.
    11. Gonçalves, João N.C. & Sameiro Carvalho, M. & Cortez, Paulo, 2020. "Operations research models and methods for safety stock determination: A review," Operations Research Perspectives, Elsevier, vol. 7(C).

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