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The Joint Effect of Leadtime Variance and Lot Size in a Parallel Processing Environment

Author

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  • Jing-Sheng Song

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Paul H. Zipkin

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27708-0120)

Abstract

We study a basic (r, q) system, in which the demand is a Poisson process and the leadtimes are independent, identically-distributed random variables. The key issue is the joint effect of the leadtime variance and the lot size q on performance. We know that, under a simple base-stock policy (with q = 1), the leadtime variance has no effect at all. We find here that, for larger q, the leadtime variance can have a significant adverse impact on performance. To explore this effect, we test two simple approximations. The simplest ignores the leadtime variance. The second approach is only a bit more complex; it captures the variance effect through a hybrid of two limiting approximations. Both methods provide useful information, but the second is more robust.

Suggested Citation

  • Jing-Sheng Song & Paul H. Zipkin, 1996. "The Joint Effect of Leadtime Variance and Lot Size in a Parallel Processing Environment," Management Science, INFORMS, vol. 42(9), pages 1352-1363, September.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:9:p:1352-1363
    DOI: 10.1287/mnsc.42.9.1352
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    Citations

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    Cited by:

    1. Boute, Robert N. & Disney, Stephen M. & Lambrecht, Marc R. & Van Houdt, Benny, 2007. "An integrated production and inventory model to dampen upstream demand variability in the supply chain," European Journal of Operational Research, Elsevier, vol. 178(1), pages 121-142, April.
    2. 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.
    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. Van Nieuwenhuyse, Inneke & Vandaele, Nico & Rajaram, Kumar & Karmarkar, Uday S., 2007. "Buffer sizing in multi-product multi-reactor batch processes: Impact of allocation and campaign sizing policies," European Journal of Operational Research, Elsevier, vol. 179(2), pages 424-443, June.
    5. Jing-Sheng Song & Hanqin Zhang & Yumei Hou & Mingzheng Wang, 2010. "The Effect of Lead Time and Demand Uncertainties in ( r, q ) Inventory Systems," Operations Research, INFORMS, vol. 58(1), pages 68-80, February.
    6. Hernan Caceres & Dongchen Yu & Alexander Nikolaev, 2018. "Evaluating shortfall distributions in periodic inventory systems with stochastic endogenous demands and lead-times," Annals of Operations Research, Springer, vol. 271(2), pages 405-427, December.
    7. Awi Federgruen & Min Wang, 2013. "Monotonicity properties of a class of stochastic inventory systems," Annals of Operations Research, Springer, vol. 208(1), pages 155-186, September.
    8. Alp Muharremoglu & Nan Yang, 2010. "Inventory Management with an Exogenous Supply Process," Operations Research, INFORMS, vol. 58(1), pages 111-129, February.
    9. 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.
    10. Robert N. Boute & Marc R. Lambrecht & Benny Van Houdt, 2007. "Performance evaluation of a production/inventory system with periodic review and endogenous lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 462-473, June.
    11. Dimitrova, Dimitrina S. & Ignatov, Zvetan G. & Kaishev, Vladimir K. & Tan, Senren, 2020. "On double-boundary non-crossing probability for a class of compound processes with applications," European Journal of Operational Research, Elsevier, vol. 282(2), pages 602-613.
    12. 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.
    13. Saibal Ray & Shanling Li & Yuyue Song, 2005. "Tailored Supply Chain Decision Making Under Price-Sensitive Stochastic Demand and Delivery Uncertainty," Management Science, INFORMS, vol. 51(12), pages 1873-1891, December.
    14. 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.
    15. Qi Feng & J. George Shanthikumar, 2022. "Applications of Stochastic Orders and Stochastic Functions in Inventory and Pricing Problems," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1433-1453, April.
    16. Marcus Ang & Karl Sigman & Jing-Sheng Song & Hanqin Zhang, 2017. "Closed-Form Approximations for Optimal ( r , q ) and ( S , T ) Policies in a Parallel Processing Environment," Operations Research, INFORMS, vol. 65(5), pages 1414-1428, October.

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