IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v49y2001i1p157-162.html
   My bibliography  Save this article

Inventory Policies for Systems with Stochastic and Deterministic Demand

Author

Listed:
  • Matthew J. Sobel

    (Weatherhead School of Management, Case Western Reserve University, Cleveland, Ohio 44106)

  • Rachel Q. Zhang

    (Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853)

Abstract

We consider a periodic review inventory system with demand arriving simultaneously from a deterministic source and a random source. The deterministic demand has to be satisfied immediately and the stochastic demand can be backordered. Assuming that the stochastic demand is never backlogged if there is stock in the system, we prove that a modified ( s, S ) policy is optimal under general conditions if there is a setup cost. If there is a smoothing cost instead of the setup cost, we observe that the problem corresponds to a standard model with one source of demand.

Suggested Citation

  • Matthew J. Sobel & Rachel Q. Zhang, 2001. "Inventory Policies for Systems with Stochastic and Deterministic Demand," Operations Research, INFORMS, vol. 49(1), pages 157-162, February.
  • Handle: RePEc:inm:oropre:v:49:y:2001:i:1:p:157-162
    DOI: 10.1287/opre.49.1.157.11197
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.49.1.157.11197
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.49.1.157.11197?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
    ---><---

    References listed on IDEAS

    as
    1. Morris A. Cohen & Paul R. Kleindorfer & Hau L. Lee, 1988. "Service Constrained (s, S) Inventory Systems with Priority Demand Classes and Lost Sales," Management Science, INFORMS, vol. 34(4), pages 482-499, April.
    2. S. Christian Albright, 1976. "Optimal Stock Depletion Policies with Stochastic Lives," Management Science, INFORMS, vol. 22(8), pages 852-857, April.
    3. Donald M. Topkis, 1968. "Optimal Ordering and Rationing Policies in a Nonstationary Dynamic Inventory Model with n Demand Classes," Management Science, INFORMS, vol. 15(3), pages 160-176, November.
    4. Arthur F. Veinott, Jr. & Harvey M. Wagner, 1965. "Computing Optimal (s, S) Inventory Policies," Management Science, INFORMS, vol. 11(5), pages 525-552, March.
    5. Steven Nahmias & W. Steven Demmy, 1981. "Operating Characteristics of an Inventory System with Rationing," Management Science, INFORMS, vol. 27(11), pages 1236-1245, November.
    6. Albert Y. Ha, 1997. "Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales," Management Science, INFORMS, vol. 43(8), pages 1093-1103, August.
    7. Martin J. Beckmann, 1961. "Production Smoothing and Inventory Control," Operations Research, INFORMS, vol. 9(4), pages 456-467, August.
    8. Matthew J. Sobel, 1969. "Production Smoothing with Stochastic Demand I: Finite Horizon Case," Management Science, INFORMS, vol. 16(3), pages 195-207, November.
    9. Arthur F. Veinott, Jr., 1965. "Optimal Policy for a Multi-Product, Dynamic, Nonstationary Inventory Problem," Management Science, INFORMS, vol. 12(3), pages 206-222, November.
    10. Steven Nahmias, 1974. "Inventory Depletion Management When the Field Life is Random," Management Science, INFORMS, vol. 20(9), pages 1276-1283, May.
    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. Saif Benjaafar & Mohsen ElHafsi & Tingliang Huang, 2010. "Optimal control of a production‐inventory system with both backorders and lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(3), pages 252-265, April.
    2. Barut, M. & Sridharan, V, 2004. "Design and evaluation of a dynamic capacity apportionment procedure," European Journal of Operational Research, Elsevier, vol. 155(1), pages 112-133, May.
    3. Bing Lin & Shaoxiang Chen & Yi Feng & Jianjun Xu, 2018. "The Joint Stock and Capacity Rationings of a Make-To-Stock System with Flexible Demand," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-27, February.
    4. ElHafsi, Mohsen & Camus, Herve & Craye, Etienne, 2010. "Managing an integrated production inventory system with information on the production and demand status and multiple non-unitary demand classes," European Journal of Operational Research, Elsevier, vol. 207(2), pages 986-1001, December.
    5. Ayanso, Anteneh & Diaby, Moustapha & Nair, Suresh K., 2006. "Inventory rationing via drop-shipping in Internet retailing: A sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 171(1), pages 135-152, May.
    6. Chen-Ritzo, Ching-Hua & Ervolina, Tom & Harrison, Terry P. & Gupta, Barun, 2011. "Component rationing for available-to-promise scheduling in configure-to-order systems," European Journal of Operational Research, Elsevier, vol. 211(1), pages 57-65, May.
    7. ElHafsi, Mohsen & Fang, Jianxin & Hamouda, Essia, 2021. "Optimal production and inventory control of multi-class mixed backorder and lost sales demand class models," European Journal of Operational Research, Elsevier, vol. 291(1), pages 147-161.
    8. Xu, Jianjun & Serrano, Alejandro & Lin, Bing, 2017. "Optimal production and rationing policy of two-stage tandem production system," International Journal of Production Economics, Elsevier, vol. 185(C), pages 100-112.
    9. Albert Y. Ha, 2000. "Stock Rationing in an M/E k /1 Make-to-Stock Queue," Management Science, INFORMS, vol. 46(1), pages 77-87, January.
    10. Alfieri, Arianna & Pastore, Erica & Zotteri, Giulio, 2017. "Dynamic inventory rationing: How to allocate stock according to managerial priorities. An empirical study," International Journal of Production Economics, Elsevier, vol. 189(C), pages 14-29.
    11. Elhafsi, Mohsen & Hamouda, Essia, 2018. "Managing an integrated production and inventory system selling to a dual market: Long-term and walk-in," European Journal of Operational Research, Elsevier, vol. 268(1), pages 215-230.
    12. Karin T. Möllering & Ulrich W. Thonemann, 2008. "An optimal critical level policy for inventory systems with two demand classes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 632-642, October.
    13. Francis de Véricourt & Fikri Karaesmen & Yves Dallery, 2002. "Optimal Stock Allocation for a Capacitated Supply System," Management Science, INFORMS, vol. 48(11), pages 1486-1501, November.
    14. R. Dekker & R.M. Hill & M.J. Kleijn & R.H. Teunter, 2002. "On the (S − 1, S) lost sales inventory model with priority demand classes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 593-610, September.
    15. Liu, Shudong & Song, Miao & Tan, Kok Choon & Zhang, Changyong, 2015. "Multi-class dynamic inventory rationing with stochastic demands and backordering," European Journal of Operational Research, Elsevier, vol. 244(1), pages 153-163.
    16. Vinayak Deshpande & Morris A. Cohen & Karen Donohue, 2003. "A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes," Management Science, INFORMS, vol. 49(6), pages 683-703, June.
    17. Teunter, Ruud H. & Klein Haneveld, Willem K., 2008. "Dynamic inventory rationing strategies for inventory systems with two demand classes, Poisson demand and backordering," European Journal of Operational Research, Elsevier, vol. 190(1), pages 156-178, October.
    18. P Melchiors & R Dekker & M J Kleijn, 2000. "Inventory rationing in an (s, Q) inventory model with lost sales and two demand classes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(1), pages 111-122, January.
    19. Mohammad Najjartabar Bisheh & G. Reza Nasiri & Esmaeil Esmaeili & Hamid Davoudpour & Shing I. Chang, 2022. "A new supply chain distribution network design for two classes of customers using transfer recurrent neural network," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(5), pages 2604-2618, October.
    20. Lee, Jeong Eun & Hong, Yushin, 2003. "A stock rationing policy in a (s,S)-controlled stochastic production system with 2-phase Coxian processing times and lost sales," International Journal of Production Economics, Elsevier, vol. 83(3), pages 299-307, March.

    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:inm:oropre:v:49:y:2001:i:1:p:157-162. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.