IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v112y2008i1p354-366.html
   My bibliography  Save this article

Some insights regarding the optimal reorder period in periodic review inventory systems

Author

Listed:
  • Silver, Edward A.
  • Robb, David J.

Abstract

The periodic review inventory system is not only pervasive, but also has an extensive literature dealing with various aspects, from its theoretical underpinnings through to its performance. However, the selection of the best review period and its behaviour with respect to basic inventory parameters such as demand and supply variability appears to be poorly understood. In this paper we treat the normal and gamma distributions which are probably the two most commonly used distributions of demand over the key (protection) time interval in a periodic review system. We show that the total cost function is not necessarily well behaved as a function of the review period; in particular, it can be non-convex, which complicates the determination of the best value of the review interval. Also we demonstrate and explain how the best review period changes as the values of various parameters are modified. Some of these changes are initially counterintuitive in nature. Managerially oriented interpretations should also be helpful to organisations seeking improvement in inventory system performance.

Suggested Citation

  • Silver, Edward A. & Robb, David J., 2008. "Some insights regarding the optimal reorder period in periodic review inventory systems," International Journal of Production Economics, Elsevier, vol. 112(1), pages 354-366, March.
    • Handle: RePEc:eee:proeco:v:112:y:2008:i:1:p:354-366
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(07)00172-7
    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. H Shore, 2004. "A general solution for the newsboy model with random order size and possibly a cutoff transaction size," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(11), pages 1218-1228, November.
    2. Eynan, Amit & Kropp, Dean H., 2007. "Effective and simple EOQ-like solutions for stochastic demand periodic review systems," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1135-1143, August.
    3. Chiang, Chi, 2006. "Optimal ordering policies for periodic-review systems with replenishment cycles," European Journal of Operational Research, Elsevier, vol. 170(1), pages 44-56, April.
    4. Ganesh Janakiraman & Robin O. Roundy, 2004. "Lost-Sales Problems with Stochastic Lead Times: Convexity Results for Base-Stock Policies," Operations Research, INFORMS, vol. 52(5), pages 795-803, October.
    5. D J Robb & E A Silver, 2006. "Erratum: Inventory management under date-terms supplier trade credit with stochastic demand and leadtime," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 755-755, June.
    6. Tang, Ou & W. Grubbstrom, Robert, 2006. "On using higher-order moments for stochastic inventory systems," International Journal of Production Economics, Elsevier, vol. 104(2), pages 454-461, December.
    7. D J Robb & E A Silver, 2006. "Inventory management under date-terms supplier trade credit with stochastic demand and leadtime," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 692-702, June.
    8. Steven Nahmias & Stephen A. Smith, 1994. "Optimizing Inventory Levels in a Two-Echelon Retailer System with Partial Lost Sales," Management Science, INFORMS, vol. 40(5), pages 582-596, May.
    9. 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.
    10. Uday S. Rao, 2003. "Properties of the Periodic Review (R, T) Inventory Control Policy for Stationary, Stochastic Demand," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 37-53, February.
    11. 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.
    12. Bylka, Stanislaw, 2005. "Turnpike policies for periodic review inventory model with emergency orders," International Journal of Production Economics, Elsevier, vol. 93(1), pages 357-373, January.
    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. Nenes, George & Panagiotidou, Sofia & Tagaras, George, 2010. "Inventory management of multiple items with irregular demand: A case study," European Journal of Operational Research, Elsevier, vol. 205(2), pages 313-324, September.
    2. Petropoulos, Fotios & Wang, Xun & Disney, Stephen M., 2019. "The inventory performance of forecasting methods: Evidence from the M3 competition data," International Journal of Forecasting, Elsevier, vol. 35(1), pages 251-265.
    3. Dreyfuss, Michael & Giat, Yahel, 2019. "Allocating spares to maximize the window fill rate in a periodic review inventory system," International Journal of Production Economics, Elsevier, vol. 214(C), pages 151-162.
    4. Tyworth, John E., 2018. "A note on lead-time paradoxes and a tale of competing prescriptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 139-150.
    5. Hedenstierna, Carl Philip T. & Disney, Stephen M., 2016. "Inventory performance under staggered deliveries and autocorrelated demand," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1082-1091.
    6. Ray, Saibal & Song, Yuyue & Verma, Manish, 2010. "Comparison of two periodic review models for stochastic and price-sensitive demand environment," International Journal of Production Economics, Elsevier, vol. 128(1), pages 209-222, November.
    7. Tang, Shaolong & Wang, Wenjie & Yan, Hong & Hao, Gang, 2015. "Low carbon logistics: Reducing shipment frequency to cut carbon emissions," International Journal of Production Economics, Elsevier, vol. 164(C), pages 339-350.
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    2. Jianxin Chen & Yong-Wu Zhou, 2017. "A Risk-Averse Newsvendor Model Under Trade Credit Contract with CVaR," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(03), pages 1-20, June.
    3. Bougheas, Spiros & Mateut, Simona & Mizen, Paul, 2009. "Corporate trade credit and inventories: New evidence of a trade-off from accounts payable and receivable," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 300-307, February.
    4. Bijvank, Marco & Vis, Iris F.A., 2012. "Lost-sales inventory systems with a service level criterion," European Journal of Operational Research, Elsevier, vol. 220(3), pages 610-618.
    5. Dey, Oshmita & Chakraborty, Debjani, 2009. "Fuzzy periodic review system with fuzzy random variable demand," European Journal of Operational Research, Elsevier, vol. 198(1), pages 113-120, October.
    6. Shih-Hsien Tseng & Jia-Chen Yu, 2019. "Data-Driven Iron and Steel Inventory Control Policies," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
    7. Shi, Xiaojun & Zhang, Shunming, 2010. "An incentive-compatible solution for trade credit term incorporating default risk," European Journal of Operational Research, Elsevier, vol. 206(1), pages 178-196, October.
    8. 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.
    9. Ali, Mohammad M. & Boylan, John E. & Syntetos, Aris A., 2012. "Forecast errors and inventory performance under forecast information sharing," International Journal of Forecasting, Elsevier, vol. 28(4), pages 830-841.
    10. Nita Shah, 2015. "Retailer’s replenishment and credit policies for deteriorating inventory under credit period-dependent demand and bad-debt loss," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 298-312, April.
    11. Lagodimos, A.G. & Skouri, K. & Christou, I.T. & Chountalas, P.T., 2018. "The discrete-time EOQ model: Solution and implications," European Journal of Operational Research, Elsevier, vol. 266(1), pages 112-121.
    12. Ji Seong Noh & Jong Soo Kim & Biswajit Sarkar, 2019. "Stochastic joint replenishment problem with quantity discounts and minimum order constraints," Operational Research, Springer, vol. 19(1), pages 151-178, March.
    13. 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.
    14. Ray, Saibal & Song, Yuyue & Verma, Manish, 2010. "Comparison of two periodic review models for stochastic and price-sensitive demand environment," International Journal of Production Economics, Elsevier, vol. 128(1), pages 209-222, November.
    15. Xu, Xinhan & Chen, Xiangfeng & Jia, Fu & Brown, Steve & Gong, Yu & Xu, Yifan, 2018. "Supply chain finance: A systematic literature review and bibliometric analysis," International Journal of Production Economics, Elsevier, vol. 204(C), pages 160-173.
    16. Seifert, Daniel & Seifert, Ralf W. & Protopappa-Sieke, Margarita, 2013. "A review of trade credit literature: Opportunities for research in operations," European Journal of Operational Research, Elsevier, vol. 231(2), pages 245-256.
    17. Yan, Jinjiang & Wang, Xianyu & Cheng, Hong & Huang, Lu, 2016. "Study on the coordination contract in supply chain under trade credit based on risk compensation," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 533-538.
    18. D J Robb & E A Silver, 2006. "Inventory management under date-terms supplier trade credit with stochastic demand and leadtime," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 692-702, June.
    19. Whybark, D. Clay & Yang, Shitao, 1996. "Positioning inventory in distribution systems," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 271-278, August.
    20. Hill, R.M. & Seifbarghy, M. & Smith, D.K., 2007. "A two-echelon inventory model with lost sales," European Journal of Operational Research, Elsevier, vol. 181(2), pages 753-766, September.

    More about this item

    Statistics

    Access and download statistics

    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:proeco:v:112:y:2008:i:1:p:354-366. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijpe .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.