IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/533.html

Optimal continuous order quantity (s,S) policies - the 45-degrees algorithm

Author

Listed:
  • Bazsa-Oldenkamp, E.M.
  • den Iseger, P.

Abstract

The most recent optimization algorithm for (s,S) order policies with continuous demand was developed by Federgruen and Zipkin (1985). This was also the first efficient algorithm, which uses policy iteration instead of discretization. Zheng and Federgruen (1991) developed an even more efficient algorithm for computing discrete order quantity (s,S) inventory policies. Since the continuous case prohibits enumeration, this algorithm does not apply to continuous order quantity systems. In this paper an efficient algorithm for continuous order quantity (s,S) policies is developed. A marginal cost approach is used for determining the optimal s. Furthermore, we construct two aid functions (generated by the optimality conditions for s and S), and exploiting their special properties a simple and efficient algorithm is obtained. The algorithm converges monotonically, such that at every iteration a policy improvement is obtained. Since every iteration finds a local minimum of the expected average cost, the number of iterations is at most N, where N

Suggested Citation

  • Bazsa-Oldenkamp, E.M. & den Iseger, P., 2003. "Optimal continuous order quantity (s,S) policies - the 45-degrees algorithm," Econometric Institute Research Papers EI 2002-47, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:533
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/533/feweco20021219120649.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    2. 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.
    3. Arthur F. Veinott, Jr. & Harvey M. Wagner, 1965. "Computing Optimal (s, S) Inventory Policies," Management Science, INFORMS, vol. 11(5), pages 525-552, March.
    4. Kaj Rosling, 1989. "Optimal Inventory Policies for Assembly Systems Under Random Demands," Operations Research, INFORMS, vol. 37(4), pages 565-579, August.
    5. Bazsa-Oldenkamp, E.M. & den Iseger, P., 2002. "Single item inventory models; time- and event-averages approach," Econometric Institute Research Papers EI 2002-46, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    Full references (including those not matched with items on IDEAS)

    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. Bazsa-Oldenkamp, E.M. & den Iseger, P., 2002. "Optimal continuous order quantity (s,S) policies; the 45-degrees algorithm," Econometric Institute Research Papers EI 2002-47, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Emöke Bázsa & Peter den Iseger, 2001. "Optimal Continuous Order Quantity (s,s) Policies," Tinbergen Institute Discussion Papers 01-102/4, Tinbergen Institute.
    3. Tong Wang & Beril L. Toktay, 2008. "Inventory Management with Advance Demand Information and Flexible Delivery," Management Science, INFORMS, vol. 54(4), pages 716-732, April.
    4. Li, Xiaoming, 2010. "Optimal inventory policies in decentralized supply chains," International Journal of Production Economics, Elsevier, vol. 128(1), pages 303-309, November.
    5. Matthew J. Sobel & Volodymyr Babich, 2012. "Optimality of Myopic Policies for Dynamic Lot-Sizing Problems in Serial Production Lines with Random Yields and Autoregressive Demand," Operations Research, INFORMS, vol. 60(6), pages 1520-1536, December.
    6. Fangruo Chen & Rungson Samroengraja, 2000. "A Staggered Ordering Policy for One-Warehouse, Multiretailer Systems," Operations Research, INFORMS, vol. 48(2), pages 281-293, April.
    7. Tan Wang & L. Jeff Hong, 2023. "Large-Scale Inventory Optimization: A Recurrent Neural Networks–Inspired Simulation Approach," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 196-215, January.
    8. Tovey C. Bachman & Pamela J. Williams & Kristen M. Cheman & Jeffrey Curtis & Robert Carroll, 2016. "PNG: Effective Inventory Control for Items with Highly Variable Demand," Interfaces, INFORMS, vol. 46(1), pages 18-32, February.
    9. Song, Yuyue & Wang, Yunzeng, 2017. "Periodic review inventory systems with fixed order cost and uniform random yield," European Journal of Operational Research, Elsevier, vol. 257(1), pages 106-117.
    10. Diwakar Gupta & N. Selvaraju, 2006. "Performance Evaluation and Stock Allocation in Capacitated Serial Supply Systems," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 169-191, July.
    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. Chiang, Chi, 2007. "Optimal ordering policies for periodic-review systems with a refined intra-cycle time scale," European Journal of Operational Research, Elsevier, vol. 177(2), pages 872-881, March.
    13. Zümbül Atan & Ton de Kok & Nico P. Dellaert & Richard van Boxel & Fred Janssen, 2016. "Setting Planned Leadtimes in Customer-Order-Driven Assembly Systems," Manufacturing & Service Operations Management, INFORMS, vol. 18(1), pages 122-140, February.
    14. Guillermo Gallego & Paul Zipkin, 1999. "Stock Positioning and Performance Estimation in Serial Production-Transportation Systems," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 77-88.
    15. Karaarslan, A.G. & Kiesmüller, G.P. & de Kok, A.G., 2013. "Analysis of an assemble-to-order system with different review periods," International Journal of Production Economics, Elsevier, vol. 143(2), pages 335-341.
    16. Alexandar Angelus & Evan L. Porteus, 2008. "An Asset Assembly Problem," Operations Research, INFORMS, vol. 56(3), pages 665-680, June.
    17. Huang, Boray & Wu, Andy, 2017. "Reduce shortage with self-reservation policy for a manufacturer paying both fixed and variable stockout expenditure," European Journal of Operational Research, Elsevier, vol. 262(3), pages 944-953.
    18. Awi Federgruen & Min Wang, 2015. "Inventory Models with Shelf-Age and Delay-Dependent Inventory Costs," Operations Research, INFORMS, vol. 63(3), pages 701-715, June.
    19. Van Foreest, Nicky D. & Teunter, Ruud H. & Syntetos, Aris A., 2018. "Base-stock policies with reservations," Omega, Elsevier, vol. 81(C), pages 48-56.
    20. Inderfurth, Karl & Minner, Stefan, 1998. "Safety stocks in multi-stage inventory systems under different service measures," European Journal of Operational Research, Elsevier, vol. 106(1), pages 57-73, April.

    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:ems:eureir:533. 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: RePub The email address of this maintainer does not seem to be valid anymore. Please ask RePub to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

    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.