IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v248y2016i2p473-486.html
   My bibliography  Save this article

Inventory management for stochastic lead times with order crossovers

Author

Listed:
  • Disney, Stephen M.
  • Maltz, Arnold
  • Wang, Xun
  • Warburton, Roger D.H.

Abstract

We study the impact of stochastic lead times with order crossover on inventory costs and safety stocks in the order-up-to (OUT) policy. To motivate our research we present global logistics data which violates the traditional assumption that lead time demand is normally distributed. We also observe that order crossover is a common and important phenomenon in real supply chains. We present a new method for determining the distribution of the number of open orders. Using this method we identify the distribution of inventory levels when orders and the work-in-process are correlated. This correlation is present when demand is auto-correlated, demand forecasts are generated with non-optimal methods, or when certain ordering policies are present. Our method allows us to obtain exact safety stock requirements for the so-called proportional order-up-to (POUT) policy, a popular, implementable, linear generalization of the OUT policy. We highlight that the OUT replenishment policy is not cost optimal in global supply chains, as we are able to demonstrate the POUT policy always outperforms it under order cross-over. We show that unlike the constant lead-time case, minimum safety stocks and minimal inventory variance do not always lead to minimum costs under stochastic lead-times with order crossover. We also highlight an interesting side effect of minimizing inventory costs under stochastic lead times with order crossover with the POUT policy—an often significant reduction in the order variance.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:248:y:2016:i:2:p:473-486
    DOI: 10.1016/j.ejor.2015.07.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715006815
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Disney, Stephen M. & Lambrecht, Marc R., 2008. "On Replenishment Rules, Forecasting, and the Bullwhip Effect in Supply Chains," Foundations and Trends(R) in Technology, Information and Operations Management, now publishers, vol. 2(1), pages 1-80, April.
    2. Christoph A. Schneeweiss, 1974. "Optimal Production Smoothing and Safety Inventory," Management Science, INFORMS, vol. 20(7), pages 1122-1130, March.
    3. So, Kut C. & Zheng, Xiaona, 2003. "Impact of supplier's lead time and forecast demand updating on retailer's order quantity variability in a two-level supply chain," International Journal of Production Economics, Elsevier, vol. 86(2), pages 169-179, November.
    4. Dejonckheere, J. & Disney, S. M. & Lambrecht, M. R. & Towill, D. R., 2003. "Measuring and avoiding the bullwhip effect: A control theoretic approach," European Journal of Operational Research, Elsevier, vol. 147(3), pages 567-590, June.
    5. Hau L. Lee & Kut C. So & Christopher S. Tang, 2000. "The Value of Information Sharing in a Two-Level Supply Chain," Management Science, INFORMS, vol. 46(5), pages 626-643, May.
    6. Kim, Jeon G. & Chatfield, Dean & Harrison, Terry P. & Hayya, Jack C., 2006. "Quantifying the bullwhip effect in a supply chain with stochastic lead time," European Journal of Operational Research, Elsevier, vol. 173(2), pages 617-636, September.
    7. Robert S. Kaplan, 1970. "A Dynamic Inventory Model with Stochastic Lead Times," Management Science, INFORMS, vol. 16(7), pages 491-507, March.
    8. Gary D. Eppen & R. Kipp Martin, 1988. "Determining Safety Stock in the Presence of Stochastic Lead Time and Demand," Management Science, INFORMS, vol. 34(11), pages 1380-1390, November.
    9. Disney, S. M. & Towill, D. R. & van de Velde, W., 2004. "Variance amplification and the golden ratio in production and inventory control," International Journal of Production Economics, Elsevier, vol. 90(3), pages 295-309, August.
    10. Disney, Stephen M. & Gaalman, Gerard J.C. & Hedenstierna, Carl Philip T. & Hosoda, Takamichi, 2015. "Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 501-512.
    11. Matthew J. Sobel, 2004. "Fill Rates of Single-Stage and Multistage Supply Systems," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 41-52, June.
    12. Jula, Payman & Leachman, Robert C., 2011. "Long- and Short-Run supply-chain optimization models for the allocation and congestion management of containerized imports from Asia to the United States," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(5), pages 593-608, September.
    13. 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.
    14. Boute, Robert N. & Disney, Stephen M. & Lambrecht, Marc R. & Houdt, Benny Van, 2014. "Coordinating lead times and safety stocks under autocorrelated demand," European Journal of Operational Research, Elsevier, vol. 232(1), pages 52-63.
    15. 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.
    16. Disney, S. M. & Towill, D. R., 2003. "On the bullwhip and inventory variance produced by an ordering policy," Omega, Elsevier, vol. 31(3), pages 157-167, June.
    17. Leachman, Robert C. & Jula, Payman, 2012. "Estimating flow times for containerized imports from Asia to the United States through the Western rail network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 296-309.
    18. 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.
    19. 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.
    20. Anantaram Balakrishnan & Joseph Geunes & Michael S. Pangburn, 2004. "Coordinating Supply Chains by Controlling Upstream Variability Propagation," Manufacturing & Service Operations Management, INFORMS, vol. 6(2), pages 163-183, July.
    21. David Zalkind, 1978. "Order-Level Inventory Systems with Independent Stochastic Leadtimes," Management Science, INFORMS, vol. 24(13), pages 1384-1392, September.
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Nagaraja, Chaitra H. & McElroy, Tucker, 2018. "The multivariate bullwhip effect," European Journal of Operational Research, Elsevier, vol. 267(1), pages 96-106.
    3. Zhuoqun Li & Weiwei Fei & Ermin Zhou & Yuvraj Gajpal & Xiding Chen, 2019. "The Impact of Lead Time Uncertainty on Supply Chain Performance Considering Carbon Cost," Sustainability, MDPI, Open Access Journal, vol. 11(22), pages 1-1, November.
    4. Ben-Ammar, Oussama & Bettayeb, Belgacem & Dolgui, Alexandre, 2019. "Optimization of multi-period supply planning under stochastic lead times and a dynamic demand," International Journal of Production Economics, Elsevier, vol. 218(C), pages 106-117.
    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. Michna, Zbigniew & Disney, Stephen M. & Nielsen, Peter, 2020. "The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts," Omega, Elsevier, vol. 93(C).
    8. 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.
    9. Qiu, Ruozhen & Sun, Minghe & Lim, Yun Fong, 2017. "Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches," European Journal of Operational Research, Elsevier, vol. 261(3), pages 880-892.
    10. Riezebos, Jan & Zhu, Stuart X., 2020. "Inventory control with seasonality of lead times," Omega, Elsevier, vol. 92(C).
    11. 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.
    12. 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).
    13. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2019. "Solution procedures for lost sales base-stock inventory systems with compound Poisson demand," International Journal of Production Economics, Elsevier, vol. 209(C), pages 172-182.
    14. Qinyun Li & Stephen M. Disney, 2017. "Revisiting rescheduling: MRP nervousness and the bullwhip effect," International Journal of Production Research, Taylor & Francis Journals, vol. 55(7), pages 1992-2012, April.
    15. Ponte, Borja & Puche, Julio & Rosillo, Rafael & de la Fuente, David, 2020. "The effects of quantity discounts on supply chain performance: Looking through the Bullwhip lens," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    16. Ponte, Borja & Costas, José & Puche, Julio & Pino, Raúl & de la Fuente, David, 2018. "The value of lead time reduction and stabilization: A comparison between traditional and collaborative supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 165-185.
    17. Metin Çakanyildirim & Sirong Luo, 2017. "Stochastic inventory system with lead time flexibility: offered by a manufacturer/transporter," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1533-1552, December.
    18. Dominguez, Roberto & Cannella, Salvatore & Barbosa-Póvoa, Ana P. & Framinan, Jose M., 2018. "OVAP: A strategy to implement partial information sharing among supply chain retailers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 110(C), pages 122-136.
    19. Dominguez, Roberto & Cannella, Salvatore & Barbosa-Póvoa, Ana P. & Framinan, Jose M., 2018. "Information sharing in supply chains with heterogeneous retailers," Omega, Elsevier, vol. 79(C), pages 116-132.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:248:y:2016:i:2:p:473-486. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Haili He). General contact details of provider: http://www.elsevier.com/locate/eor .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.