IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v54y2008i8p1441-1452.html
   My bibliography  Save this article

Managing the Inventory of an Item with a Replacement Warranty

Author

Listed:
  • Wei Huang

    (Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599)

  • Vidyadhar Kulkarni

    (Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599)

  • Jayashankar M. Swaminathan

    (The Kenan-Flagler Business School, University of North Carolina, Chapel Hill, North Carolina 27599)

Abstract

In this paper, we study a firm that faces demand from two sources: demand for new items and demand to replace failed items under warranty. We model this setting as a multiperiod single-product inventory problem where the demands for new items in different periods are independent and the demands for replacing failed items depend on the number and ages of the items under warranty. We consider backlogging and emergency supply cases, and study both discounted cost and average cost criteria. We prove the optimality of the w-dependent base-stock ordering policy where the base-stock level is a function of w, the vector representing the number of items at different ages currently under warranty. For the special case where the demand for new products is identically distributed, we prove the optimality of a stationary w-dependent base stock policy for the finite-horizon discounted and the infinite-horizon discounted and average cost cases. In our computational study, we find that an optimal w-dependent policy can lead to 69% average improvement in expected costs when compared to a policy that neglects demands from items under warranty.

Suggested Citation

  • Wei Huang & Vidyadhar Kulkarni & Jayashankar M. Swaminathan, 2008. "Managing the Inventory of an Item with a Replacement Warranty," Management Science, INFORMS, vol. 54(8), pages 1441-1452, August.
    • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:8:p:1441-1452
    DOI: 10.1287/mnsc.1080.0863
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1080.0863
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1080.0863?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. Wang, Chih-Hsiung & Sheu, Shey-Heui, 2003. "Optimal lot sizing for products sold under free-repair warranty," European Journal of Operational Research, Elsevier, vol. 149(1), pages 131-141, August.
    2. Gregory A. DeCroix, 2006. "Optimal Policy for a Multiechelon Inventory System with Remanufacturing," Operations Research, INFORMS, vol. 54(3), pages 532-543, June.
    3. 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.
    4. Djamaludin, I. & Murthy, D. N. P. & Wilson, R. J., 1994. "Quality control through lot sizing for items sold with warranty," International Journal of Production Economics, Elsevier, vol. 33(1-3), pages 97-107, January.
    5. Gregory DeCroix & Jing-Sheng Song & Paul Zipkin, 2005. "A Series System with Returns: Stationary Analysis," Operations Research, INFORMS, vol. 53(2), pages 350-362, April.
    6. Vincent P. Simpson, 1978. "Optimum Solution Structure for a Repairable Inventory Problem," Operations Research, INFORMS, vol. 26(2), pages 270-281, April.
    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. Shi, Zhenyang & Liu, Shaoxuan, 2020. "Optimal inventory control and design refresh selection in managing part obsolescence," European Journal of Operational Research, Elsevier, vol. 287(1), pages 133-144.
    2. Meng Li & Yunchuan Liu, 2021. "Beneficial Product Returns in Supply Chains," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 3849-3855, November.
    3. Kunpeng Li & Suman Mallik & Dilip Chhajed, 2012. "Design of Extended Warranties in Supply Chains under Additive Demand," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 730-746, July.
    4. Lin, Yizhong & Leung, Janny M.Y. & Zhang, Lianmin & Gu, Jia-Wen, 2020. "Single-item repairable inventory system with stochastic new and warranty demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    5. Barιş Ata & Deishin Lee & Erkut Sönmez, 2019. "Dynamic Volunteer Staffing in Multicrop Gleaning Operations," Operations Research, INFORMS, vol. 67(2), pages 295-314, March.
    6. Tomoaki Yamazaki & Keisuke Shida & Takashi Kanazawa, 2016. "An approach to establishing a method for calculating inventory," International Journal of Production Research, Taylor & Francis Journals, vol. 54(8), pages 2320-2331, April.
    7. Andre P. Calmon & Stephen C. Graves, 2017. "Inventory Management in a Consumer Electronics Closed-Loop Supply Chain," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 568-585, October.
    8. Nabajyoti Bhattacharjee & Nabendu Sen & Sanjukta Malakar, 2022. "A sustainable retailer’s inventory model to study the partial replacement for deteriorating items with variable shelf-life," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1502-1521, December.
    9. Afsahi, Mohsen & Shafiee, Mahmood, 2020. "A stochastic simulation-optimization model for base-warranty and extended-warranty decision-making of under- and out-of-warranty products," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    10. Yang, Rui & Feng, Lin & Zhang, Jianxiong & Li, Xiangqian, 2024. "Co-creation in a duopoly considering the effect of product return," Omega, Elsevier, vol. 129(C).
    11. Çerağ Pinçe & Mark Ferguson & Beril Toktay, 2016. "Extracting Maximum Value from Consumer Returns: Allocating Between Remarketing and Refurbishing for Warranty Claims," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 475-492, October.
    12. Vinayak Deshpande & Jayashankar M. Swaminathan, 2020. "Introduction to the Special Issue on Responsible Operations and Supply Chain Management," Manufacturing & Service Operations Management, INFORMS, vol. 22(6), pages 1107-1111, November.

    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. Alexandar Angelus, 2011. "A Multiechelon Inventory Problem with Secondary Market Sales," Management Science, INFORMS, vol. 57(12), pages 2145-2162, December.
    2. Lin, Yizhong & Leung, Janny M.Y. & Zhang, Lianmin & Gu, Jia-Wen, 2020. "Single-item repairable inventory system with stochastic new and warranty demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    3. Xuanming Su, 2009. "Consumer Returns Policies and Supply Chain Performance," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 595-612, March.
    4. K-L Hou, 2005. "Optimal production run length for deteriorating production system with a two-state continuous-time Markovian processes under allowable shortages," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 346-350, March.
    5. Gregory A. DeCroix & Jing-Sheng Song & Paul H. Zipkin, 2009. "Managing an Assemble-to-Order System with Returns," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 144-159, October.
    6. Cai, Xiaoqiang & Lai, Minghui & Li, Xiang & Li, Yongjian & Wu, Xianyi, 2014. "Optimal acquisition and production policy in a hybrid manufacturing/remanufacturing system with core acquisition at different quality levels," European Journal of Operational Research, Elsevier, vol. 233(2), pages 374-382.
    7. Feng, Yan & Viswanathan, S., 2014. "Heuristics with guaranteed performance bounds for a manufacturing system with product recovery," European Journal of Operational Research, Elsevier, vol. 232(2), pages 322-329.
    8. Vercraene, Samuel & Gayon, Jean-Philippe & Flapper, Simme Douwe, 2014. "Coordination of manufacturing, remanufacturing and returns acceptance in hybrid manufacturing/remanufacturing systems," International Journal of Production Economics, Elsevier, vol. 148(C), pages 62-70.
    9. Gregory A. DeCroix, 2006. "Optimal Policy for a Multiechelon Inventory System with Remanufacturing," Operations Research, INFORMS, vol. 54(3), pages 532-543, June.
    10. Wang, Chih-Hsiung, 2009. "Determining the optimal probing lot size for the wafer probe operation in semiconductor manufacturing," European Journal of Operational Research, Elsevier, vol. 197(1), pages 126-133, August.
    11. Gregory A. DeCroix & Paul H. Zipkin, 2005. "Inventory Management for an Assembly System with Product or Component Returns," Management Science, INFORMS, vol. 51(8), pages 1250-1265, August.
    12. Zerhouni, Hichem & Gayon, Jean-Philippe & Frein, Yannick, 2013. "Influence of dependency between demands and returns in a reverse logistics system," International Journal of Production Economics, Elsevier, vol. 143(1), pages 62-71.
    13. Xiting Gong & Xiuli Chao, 2013. "Technical Note---Optimal Control Policy for Capacitated Inventory Systems with Remanufacturing," Operations Research, INFORMS, vol. 61(3), pages 603-611, June.
    14. Vercraene, Samuel & Gayon, Jean-Philippe, 2013. "Optimal control of a production-inventory system with productreturns," International Journal of Production Economics, Elsevier, vol. 142(2), pages 302-310.
    15. Gayon, Jean-Philippe & Vercraene, Samuel & Flapper, Simme Douwe P., 2017. "Optimal control of a production-inventory system with product returns and two disposal options," European Journal of Operational Research, Elsevier, vol. 262(2), pages 499-508.
    16. Wei, Cansheng & Li, Yongjian & Cai, Xiaoqiang, 2011. "Robust optimal policies of production and inventory with uncertain returns and demand," International Journal of Production Economics, Elsevier, vol. 134(2), pages 357-367, December.
    17. Sean X. Zhou & Yikun Yu, 2011. "TECHNICAL NOTE---Optimal Product Acquisition, Pricing, and Inventory Management for Systems with Remanufacturing," Operations Research, INFORMS, vol. 59(2), pages 514-521, April.
    18. Perez Becker, Nicole & Arts, Joachim & Reichardt, Sven & Lange, Anne, 2024. "Managing inventories of reusable containers for food take-away at a restaurant," International Journal of Production Economics, Elsevier, vol. 267(C).
    19. Gökbayrak, Esra & Kayış, Enis, 2023. "Single item periodic review inventory control with sales dependent stochastic return flows," International Journal of Production Economics, Elsevier, vol. 255(C).
    20. John Khawam & Warren H. Hausman & Dinah W. Cheng, 2007. "Warranty Inventory Optimization for Hitachi Global Storage Technologies, Inc," Interfaces, INFORMS, vol. 37(5), pages 455-471, October.

    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:ormnsc:v:54:y:2008:i:8:p:1441-1452. 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.