IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v266y2018i1p112-121.html
   My bibliography  Save this article

The discrete-time EOQ model: Solution and implications

Author

Listed:
  • Lagodimos, A.G.
  • Skouri, K.
  • Christou, I.T.
  • Chountalas, P.T.

Abstract

Consideration is given to the classical EOQ (with backorders) model, where one of its original assumptions is modified. Instead of being continuous, time forms a sequence of indivisible quanta (unit periods). The implications of this assumption, common in the analysis of periodic review policies, are explored for deterministic demand. Modeled as an inventory system under the (S, T) policy, long-run average cost is derived, and it is shown that optimal control involves the solution of a two-dimensional non-convex integer optimization problem. Properties are established, leading to a solution algorithm which guarantees optimal S and T determination with (at most) three cost-function evaluations. It is shown that, contrary to intuition, the classical EOQ optimal cost is not a lower bound for the system studied. This is exploited to develop distribution-free lower bounds for stochastic periodic review systems together with properties rendering them useful in inventory optimization.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:1:p:112-121
    DOI: 10.1016/j.ejor.2017.09.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717308391
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.09.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Nils Rudi & Harry Groenevelt & Taylor R. Randall, 2009. "End-of-Period vs. Continuous Accounting of Inventory-Related Costs," Operations Research, INFORMS, vol. 57(6), pages 1360-1366, December.
    2. Kevin H. Shang & Sean X. Zhou, 2010. "Optimal and Heuristic Echelon ( r, nQ, T ) Policies in Serial Inventory Systems with Fixed Costs," Operations Research, INFORMS, vol. 58(2), pages 414-427, April.
    3. Fang Liu & Jing-Sheng Song, 2012. "Good and Bad News About the ( S , T ) Policy," Manufacturing & Service Operations Management, INFORMS, vol. 14(1), pages 42-49, January.
    4. Guillermo Gallego, 1998. "New Bounds and Heuristics for (Q, r) Policies," Management Science, INFORMS, vol. 44(2), pages 219-233, February.
    5. Avinadav, Tal & Henig, Mordecai I., 2015. "Exact accounting of inventory costs in stochastic periodic-review models," International Journal of Production Economics, Elsevier, vol. 169(C), pages 89-98.
    6. Ang, Marcus & Song, Jing-Sheng & Wang, Mingzheng & Zhang, Hanqin, 2013. "On properties of discrete (r, q) and (s, T) inventory systems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 95-105.
    7. 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.
    8. Yu-Sheng Zheng & A. Federgruen, 1991. "Finding Optimal (s, S) Policies Is About As Simple As Evaluating a Single Policy," Operations Research, INFORMS, vol. 39(4), pages 654-665, August.
    9. 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.
    10. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, January.
    11. Lagodimos, A.G. & Christou, I.T. & Skouri, K., 2012. "Computing globally optimal (s,S,T) inventory policies," Omega, Elsevier, vol. 40(5), pages 660-671.
    12. Sven Axsäter, 1996. "Using the Deterministic EOQ Formula in Stochastic Inventory Control," Management Science, INFORMS, vol. 42(6), pages 830-834, June.
    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. Li, Ruihai & Yang, Hui-Ling & Shi, Yan & Teng, Jinn-Tsair & Lai, Kuei-Kuei, 2021. "EOQ-based pricing and customer credit decisions under general supplier payments," European Journal of Operational Research, Elsevier, vol. 289(2), pages 652-665.
    2. Konstantaras, I. & Skouri, K. & Lagodimos, A.G., 2019. "EOQ with independent endogenous supply disruptions," Omega, Elsevier, vol. 83(C), pages 96-106.
    3. Debopriya Dey & Samarjit Kar & Dilip Kumar Bhattacharya, 2024. "Periodic review policy in the production management of a single-item inventory with deterioration," Operational Research, Springer, vol. 24(2), pages 1-25, June.

    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. Konstantaras, I. & Skouri, K. & Lagodimos, A.G., 2019. "EOQ with independent endogenous supply disruptions," Omega, Elsevier, vol. 83(C), pages 96-106.
    2. Avinadav, Tal & Henig, Mordecai I., 2015. "Exact accounting of inventory costs in stochastic periodic-review models," International Journal of Production Economics, Elsevier, vol. 169(C), pages 89-98.
    3. Tal Avinadav, 2016. "Stochastic Periodic-Review Models with Duration- and Quantity-Dependent Inventory Costs: Properties and Approximations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-25, August.
    4. 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.
    5. Ang, Marcus & Song, Jing-Sheng & Wang, Mingzheng & Zhang, Hanqin, 2013. "On properties of discrete (r, q) and (s, T) inventory systems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 95-105.
    6. Lagodimos, A.G. & Christou, I.T. & Skouri, K., 2012. "Computing globally optimal (s,S,T) inventory policies," Omega, Elsevier, vol. 40(5), pages 660-671.
    7. Tal Avinadav, 2015. "Continuous accounting of inventory costs with Brownian-motion and Poisson demand processes," Annals of Operations Research, Springer, vol. 229(1), pages 85-102, June.
    8. 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.
    9. Qinan Wang & Sven Axsäter, 2013. "Fixed‐interval joint‐replenishment policies for distribution systems with multiple retailers and stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 637-651, December.
    10. Tamer Boyacı & Guillermo Gallego, 2002. "Managing waiting times of backordered demands in single‐stage (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 557-573, September.
    11. 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.
    12. Vipul Agrawal & Sridhar Seshadri, 2000. "Distribution free bounds for service constrained (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 635-656, December.
    13. Kilic, Onur A. & Tarim, S. Armagan, 2024. "A simple heuristic for computing non-stationary inventory policies based on function approximation," European Journal of Operational Research, Elsevier, vol. 316(3), pages 899-905.
    14. Gérard P. Cachon & A. Gürhan Kök, 2007. "Implementation of the Newsvendor Model with Clearance Pricing: How to (and How Not to) Estimate a Salvage Value," Manufacturing & Service Operations Management, INFORMS, vol. 9(3), pages 276-290, October.
    15. Taleizadeh, Ata Allah & Tafakkori, Keivan & Thaichon, Park, 2021. "Resilience toward supply disruptions: A stochastic inventory control model with partial backordering under the base stock policy," Journal of Retailing and Consumer Services, Elsevier, vol. 58(C).
    16. Wang, Qinan, 2013. "A periodic-review inventory control policy for a two-level supply chain with multiple retailers and stochastic demand," European Journal of Operational Research, Elsevier, vol. 230(1), pages 53-62.
    17. Avinadav, Tal & Levy, Priel, 2022. "Value of information in a mobile app supply chain under hidden or known information superiority," International Journal of Production Economics, Elsevier, vol. 248(C).
    18. Kevin H. Shang & Zhijie Tao & Sean X. Zhou, 2015. "Optimizing Reorder Intervals for Two-Echelon Distribution Systems with Stochastic Demand," Operations Research, INFORMS, vol. 63(2), pages 458-475, April.
    19. Zhu, Han & Liu, Xing & Chen, Youhua (Frank), 2015. "Effective inventory control policies with a minimum order quantity and batch ordering," International Journal of Production Economics, Elsevier, vol. 168(C), pages 21-30.
    20. Tamjidzad, Shahrzad & Mirmohammadi, S. Hamid, 2015. "An optimal (r, Q) policy in a stochastic inventory system with all-units quantity discount and limited sharable resource," European Journal of Operational Research, Elsevier, vol. 247(1), pages 93-100.

    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:266:y:2018:i:1:p:112-121. 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/eor .

    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.