IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v244y2015i1p153-163.html
   My bibliography  Save this article

Multi-class dynamic inventory rationing with stochastic demands and backordering

Author

Listed:
  • Liu, Shudong
  • Song, Miao
  • Tan, Kok Choon
  • Zhang, Changyong

Abstract

Dynamic inventory rationing is considered for systems with multiple demand classes, stationary stochastic demands, and backordering. In the literature, dynamic programming has been often applied to address this type of problems. However, due to the curse of dimensionality, computation is a critical challenge for dynamic programming. In this paper, an innovative two-step approach is proposed based on an idea similar to the certainty equivalence principle. First the deterministic inventory rationing problem is studied, where the future demands are set to be the expectation of the stochastic demand processes. The important properties obtained from solving the problem with the KKT conditions are then used to develop effective dynamic rationing policies for stochastic demands, which gives closed-form expressions for dynamic rationing thresholds. These expressions are easy to calculate and are applicable to any number of demand classes. Numerical results show that the expressions are close to and provide a lower bound for the optimal dynamic thresholds. They also shed light on important managerial insights, for example, the relation between different parameters and the rationing thresholds.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:244:y:2015:i:1:p:153-163
    DOI: 10.1016/j.ejor.2015.01.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715000429
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.01.022?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. 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. Melchiors, Philip, 2003. "Restricted time-remembering policies for the inventory rationing problem," International Journal of Production Economics, Elsevier, vol. 81(1), pages 461-468, January.
    3. Hasan Arslan & Stephen C. Graves & Thomas A. Roemer, 2007. "A Single-Product Inventory Model for Multiple Demand Classes," Management Science, INFORMS, vol. 53(9), pages 1486-1500, September.
    4. 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.
    5. 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.
    6. 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.
    7. Dekker, R. & Kleijn, M. J. & de Rooij, P. J., 1998. "A spare parts stocking policy based on equipment criticality," International Journal of Production Economics, Elsevier, vol. 56(1), pages 69-77, September.
    8. Steven Nahmias & W. Steven Demmy, 1981. "Operating Characteristics of an Inventory System with Rationing," Management Science, INFORMS, vol. 27(11), pages 1236-1245, November.
    9. Alan Kaplan, 1969. "Stock Rationing," Management Science, INFORMS, vol. 15(5), pages 260-267, January.
    10. FadIloglu, Mehmet Murat & Bulut, Önder, 2010. "A dynamic rationing policy for continuous-review inventory systems," European Journal of Operational Research, Elsevier, vol. 202(3), pages 675-685, May.
    11. Richard V. Evans, 1968. "Sales and Restocking Policies in a Single Item Inventory System," Management Science, INFORMS, vol. 14(7), pages 463-472, March.
    12. Rajesh Piplani & Shudong Liu, 2014. "Comparison of capacity rationing policies for a make-to-order production system with two customer classes," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 16(2), pages 223-237.
    13. 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.
    14. 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.
    15. 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.
    16. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, 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. Xiaoqing Liu & Felix T. S. Chan & Xinsheng Xu, 2019. "Hedging Risks in the Loss-Averse Newsvendor Problem with Backlogging," Mathematics, MDPI, vol. 7(5), pages 1-23, May.
    2. Ma, Weina & Hekimoğlu, Mustafa & Dekker, Rommert, 2023. "Admission control for a capacitated supply system with real-time replenishment information," International Journal of Production Economics, Elsevier, vol. 266(C).
    3. Wang, Yi & Zhang, Sheng Hao, 2021. "Optimal production and inventory rationing policies with selective-information sharing and two demand classes," European Journal of Operational Research, Elsevier, vol. 288(2), pages 394-407.
    4. 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.
    5. Seitz, Alexander & Grunow, Martin & Akkerman, Renzo, 2020. "Data driven supply allocation to individual customers considering forecast bias," International Journal of Production Economics, Elsevier, vol. 227(C).
    6. Wang, Daqin & Tang, Ou & Zhang, Lihua, 2015. "A note on the rationing policies of multiple demand classes with lost sales," International Journal of Production Economics, Elsevier, vol. 165(C), pages 145-154.
    7. Xufeng Yang & Juliang Zhang & Wen Jiao & Hong Yan, 2023. "Optimal Capacity Rationing Policy for a Container Leasing System with Multiple Kinds of Customers and Substitutable Containers," Management Science, INFORMS, vol. 69(3), pages 1468-1485, March.
    8. Sagawa, Juliana Keiko & Nagano, Marcelo Seido & Speranza Neto, Mauro, 2017. "A closed-loop model of a multi-station and multi-product manufacturing system using bond graphs and hybrid controllers," European Journal of Operational Research, Elsevier, vol. 258(2), pages 677-691.
    9. Zümbül Atan & Lawrence V. Snyder & George R. Wilson, 2018. "Transshipment policies for systems with multiple retailers and two demand classes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 159-186, January.

    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. 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.
    2. P. Escalona & F. Ordóñez & I. Kauak, 2017. "Critical level rationing in inventory systems with continuously distributed demand," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 273-301, January.
    3. 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.
    4. 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.
    5. FadIloglu, Mehmet Murat & Bulut, Önder, 2010. "A dynamic rationing policy for continuous-review inventory systems," European Journal of Operational Research, Elsevier, vol. 202(3), pages 675-685, May.
    6. 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.
    7. 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.
    8. Quan-Lin Li & Yi-Meng Li & Jing-Yu Ma & Heng-Li Liu, 2023. "A complete algebraic solution to the optimal dynamic rationing policy in the stock-rationing queue with two demand classes," Journal of Combinatorial Optimization, Springer, vol. 45(3), pages 1-54, April.
    9. 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.
    10. Samii, Amir-Behzad, 2016. "Impact of nested inventory allocation policies in a newsvendor setting," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 247-256.
    11. Samii, Amir-Behzad & Pibernik, Richard & Yadav, Prashant & Vereecke, Ann, 2012. "Reservation and allocation policies for influenza vaccines," European Journal of Operational Research, Elsevier, vol. 222(3), pages 495-507.
    12. Du, Bisheng & Larsen, Christian, 2017. "Reservation policies of advance orders in the presence of multiple demand classes," European Journal of Operational Research, Elsevier, vol. 256(2), pages 430-438.
    13. Samii, Amir-Behzad & Pibernik, Richard & Yadav, Prashant, 2011. "An inventory reservation problem with nesting and fill rate-based performance measures," International Journal of Production Economics, Elsevier, vol. 133(1), pages 393-402, September.
    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. Tan, Tarkan & Güllü, Refik & Erkip, Nesim, 2009. "Using imperfect advance demand information in ordering and rationing decisions," International Journal of Production Economics, Elsevier, vol. 121(2), pages 665-677, October.
    16. Hasan Arslan & Stephen C. Graves & Thomas A. Roemer, 2007. "A Single-Product Inventory Model for Multiple Demand Classes," Management Science, INFORMS, vol. 53(9), pages 1486-1500, September.
    17. 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.
    18. Zümbül Atan & Lawrence V. Snyder & George R. Wilson, 2018. "Transshipment policies for systems with multiple retailers and two demand classes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 159-186, January.
    19. Berling, Peter & Johansson, Lina & Marklund, Johan, 2023. "Controlling inventories in omni/multi-channel distribution systems with variable customer order-sizes," Omega, Elsevier, vol. 114(C).
    20. Pinto, Roberto, 2012. "Stock rationing under service level constraints in a vertically integrated distribution system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 231-240.

    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:244:y:2015:i:1:p:153-163. 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.