IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v284y2020i2p538-549.html
   My bibliography  Save this article

Optimal ordering policy for complementary components with partial backordering and emergency replenishment under spectral risk measure

Author

Listed:
  • Li, Yanhai
  • Ou, Jinwen

Abstract

A firm (assembler) faces random demand for a final product which is made up of multiple complementary components. Before demand is realized, the firm purchases the components via a regular channel. After demand realization, unsatisfied demand is allowed to be partially backordered in case of component shortages, where the firm is assumed to have an option to purchase the components via an emergency channel with a relatively higher unit cost. The firm needs to adopt an appropriate ordering policy to maximize the spectral risk measure of its profit. We formulate and transform the newsvendor problem into a concise optimization problem which can be further decomposed into two sub-problems. We provide optimality properties and show that the objective function of each sub-problem is separable, which enables us to determine the optimal order quantity of each component independently. We show that the optimal order quantity of each component decreases in the firm's level of risk-aversion. Numerical experiments are conducted to illustrate the effectiveness of our solution method and examine the impacts of lost sales and risk attitude on the optimal solutions.

Suggested Citation

  • Li, Yanhai & Ou, Jinwen, 2020. "Optimal ordering policy for complementary components with partial backordering and emergency replenishment under spectral risk measure," European Journal of Operational Research, Elsevier, vol. 284(2), pages 538-549.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:2:p:538-549
    DOI: 10.1016/j.ejor.2020.01.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221720300230
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2020.01.006?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. Lee, Hwansik & Lodree Jr., Emmett J., 2010. "Modeling customer impatience in a newsboy problem with time-sensitive shortages," European Journal of Operational Research, Elsevier, vol. 205(3), pages 595-603, September.
    2. Liao, Yi & Shen, Wenjing & Hu, Xinxin & Yang, Shilei, 2014. "Optimal responses to stockouts: Lateral transshipment versus emergency order policies," Omega, Elsevier, vol. 49(C), pages 79-92.
    3. Kevin Dowd & John Cotter & Ghulam Sorwar, 2008. "Spectral Risk Measures: Properties and Limitations," Journal of Financial Services Research, Springer;Western Finance Association, vol. 34(1), pages 61-75, August.
    4. Taleizadeh, Ata Allah & Pentico, David W., 2014. "An Economic Order Quantity model with partial backordering and all-units discount," International Journal of Production Economics, Elsevier, vol. 155(C), pages 172-184.
    5. San José, L.A. & Sicilia, J. & Garcia-Laguna, J., 2006. "Analysis of an inventory system with exponential partial backordering," International Journal of Production Economics, Elsevier, vol. 100(1), pages 76-86, March.
    6. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    7. Pando, Valentín & San-José, Luis A. & García-Laguna, Juan & Sicilia, Joaquín, 2013. "A newsboy problem with an emergency order under a general backorder rate function," Omega, Elsevier, vol. 41(6), pages 1020-1028.
    8. Pentico, David W. & Drake, Matthew J. & Toews, Carl, 2009. "The deterministic EPQ with partial backordering: A new approach," Omega, Elsevier, vol. 37(3), pages 624-636, June.
    9. Zhishuang Yao & Loo Lee & Ek Chew & Vernon Hsu & Wikrom Jaruphongsa, 2013. "Dual-channel component replenishment problem in an assemble-to-order system," IISE Transactions, Taylor & Francis Journals, vol. 45(3), pages 229-243.
    10. Alexandre Adam & Mohamed Houkari & Jean-Paul Laurent, 2008. "Spectral risk measures and portfolio selection," Post-Print hal-03676385, HAL.
    11. Youhua (Frank) Chen & Minghui Xu & Zhe George Zhang, 2009. "Technical Note---A Risk-Averse Newsvendor Model Under the CVaR Criterion," Operations Research, INFORMS, vol. 57(4), pages 1040-1044, August.
    12. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    13. Xiao, Yongbo & Chen, Jian & Lee, Chung-Yee, 2010. "Optimal decisions for assemble-to-order systems with uncertain assembly capacity," International Journal of Production Economics, Elsevier, vol. 123(1), pages 155-165, January.
    14. Douglas C. Montgomery & M. S. Bazaraa & Ajit K. Keswani, 1973. "Inventory models with a mixture of backorders and lost sales," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 255-263, June.
    15. Abad, P. L., 2003. "Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale," European Journal of Operational Research, Elsevier, vol. 144(3), pages 677-685, February.
    16. Pentico, David W. & Drake, Matthew J., 2009. "The deterministic EOQ with partial backordering: A new approach," European Journal of Operational Research, Elsevier, vol. 194(1), pages 102-113, April.
    17. Lodree, Emmett Jr., 2007. "Advanced supply chain planning with mixtures of backorders, lost sales, and lost contract," European Journal of Operational Research, Elsevier, vol. 181(1), pages 168-183, August.
    18. Hossein Salehi & Ata Allah Taleizadeh & Reza Tavakkoli-Moghaddam, 2016. "An EOQ model with random disruption and partial backordering," International Journal of Production Research, Taylor & Francis Journals, vol. 54(9), pages 2600-2609, May.
    19. Xu, Xinsheng & Wang, Hongwei & Dang, Chuangyin & Ji, Ping, 2017. "The loss-averse newsvendor model with backordering," International Journal of Production Economics, Elsevier, vol. 188(C), pages 1-10.
    20. Gotoh, Jun-ya & Takano, Yuichi, 2007. "Newsvendor solutions via conditional value-at-risk minimization," European Journal of Operational Research, Elsevier, vol. 179(1), pages 80-96, May.
    21. Abad, Prakash L., 2008. "Optimal price and order size under partial backordering incorporating shortage, backorder and lost sale costs," International Journal of Production Economics, Elsevier, vol. 114(1), pages 179-186, July.
    22. Ke Fu & Vernon N. Hsu & Chung-Yee Lee, 2009. "Note--Optimal Component Acquisition for a Single-Product, Single-Demand Assemble-to-Order Problem with Expediting," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 229-236, December.
    23. P. L. Abad, 1996. "Optimal Pricing and Lot-Sizing Under Conditions of Perishability and Partial Backordering," Management Science, INFORMS, vol. 42(8), pages 1093-1104, August.
    24. Atan, Zümbül & Ahmadi, Taher & Stegehuis, Clara & Kok, Ton de & Adan, Ivo, 2017. "Assemble-to-order systems: A review," European Journal of Operational Research, Elsevier, vol. 261(3), pages 866-879.
    25. Brandtner, Mario & Kürsten, Wolfgang, 2015. "Decision making with Expected Shortfall and spectral risk measures: The problem of comparative risk aversion," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 268-280.
    26. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    27. Fu, Ke & Xu, Jiayan & Miao, Zhaowei, 2013. "Newsvendor with multiple options of expediting," European Journal of Operational Research, Elsevier, vol. 226(1), pages 94-99.
    28. Jian Li & Suresh Chand & Maqbool Dada & Shailendra Mehta, 2009. "Managing Inventory Over a Short Season: Models with Two Procurement Opportunities," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 174-184, April.
    29. Arıkan, Emel & Fichtinger, Johannes, 2017. "The risk-averse newsvendor problem under spectral risk measures: A classification with extensions," European Journal of Operational Research, Elsevier, vol. 256(1), pages 116-125.
    30. Yunzeng Wang & Yigal Gerchak, 2003. "Capacity Games in Assembly Systems with Uncertain Demand," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 252-267, January.
    31. San-José, L.A. & Sicilia, J. & García-Laguna, J., 2015. "Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost," Omega, Elsevier, vol. 54(C), pages 147-157.
    32. Brito, Anderson J. & de Almeida, Adiel T., 2012. "Modeling a multi-attribute utility newsvendor with partial backlogging," European Journal of Operational Research, Elsevier, vol. 220(3), pages 820-830.
    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, Yanhai & Ou, Jinwen, 2022. "Replenishment decisions for complementary components with supply capacity uncertainty under the CVaR criterion," European Journal of Operational Research, Elsevier, vol. 297(3), pages 904-916.
    2. Zhou, Haijie & Chen, Kebing & Wang, Shengbin, 2023. "Two-period pricing and inventory decisions of perishable products with partial lost sales," European Journal of Operational Research, Elsevier, vol. 310(2), pages 611-626.
    3. Svoboda, Josef & Minner, Stefan & Yao, Man, 2021. "Typology and literature review on multiple supplier inventory control models," European Journal of Operational Research, Elsevier, vol. 293(1), pages 1-23.
    4. Hu, Man & Liu, Xue-Xin & Jia, Fu, 2024. "Optimal Emergency Order Policy for Supply Disruptions in the Semiconductor Industry," International Journal of Production Economics, Elsevier, vol. 272(C).

    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. Joaquín Sicilia & Luis San-José & Juan García-Laguna, 2012. "An inventory model where backordered demand ratio is exponentially decreasing with the waiting time," Annals of Operations Research, Springer, vol. 199(1), pages 137-155, October.
    2. Wee, Hui-Ming & Huang, Yen-Deng & Wang, Wan-Tsu & Cheng, Yung-Lung, 2014. "An EPQ model with partial backorders considering two backordering costs," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 898-907.
    3. Pentico, David W. & Drake, Matthew J. & Toews, Carl, 2011. "The EPQ with partial backordering and phase-dependent backordering rate," Omega, Elsevier, vol. 39(5), pages 574-577, October.
    4. 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.
    5. Pentico, David W. & Drake, Matthew J., 2011. "A survey of deterministic models for the EOQ and EPQ with partial backordering," European Journal of Operational Research, Elsevier, vol. 214(2), pages 179-198, October.
    6. Pando, Valentín & San-José, Luis A. & García-Laguna, Juan & Sicilia, Joaquín, 2013. "A newsboy problem with an emergency order under a general backorder rate function," Omega, Elsevier, vol. 41(6), pages 1020-1028.
    7. Pentico, David W. & Toews, Carl & Drake, Matthew J., 2015. "Approximating the EOQ with partial backordering at an exponential or rational rate by a constant or linearly changing rate," International Journal of Production Economics, Elsevier, vol. 162(C), pages 151-159.
    8. Toews, Carl & Pentico, David W. & Drake, Matthew J., 2011. "The deterministic EOQ and EPQ with partial backordering at a rate that is linearly dependent on the time to delivery," International Journal of Production Economics, Elsevier, vol. 131(2), pages 643-649, June.
    9. Mario Brandtner, 2016. "Spektrale Risikomaße: Konzeption, betriebswirtschaftliche Anwendungen und Fallstricke," Management Review Quarterly, Springer, vol. 66(2), pages 75-115, April.
    10. Li, Yanhai & Gu, Chaocheng & Ou, Jinwen, 2020. "Supporting a financially constrained supplier under spectral risk measures: The efficiency of buyer lending," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 136(C).
    11. Xu, Xinsheng & Wang, Hongwei & Dang, Chuangyin & Ji, Ping, 2017. "The loss-averse newsvendor model with backordering," International Journal of Production Economics, Elsevier, vol. 188(C), pages 1-10.
    12. Omid Momen & Akbar Esfahanipour & Abbas Seifi, 2020. "A robust behavioral portfolio selection: model with investor attitudes and biases," Operational Research, Springer, vol. 20(1), pages 427-446, March.
    13. Brandtner, Mario, 2018. "Expected Shortfall, spectral risk measures, and the aggravating effect of background risk, or: risk vulnerability and the problem of subadditivity," Journal of Banking & Finance, Elsevier, vol. 89(C), pages 138-149.
    14. V. Pando & L. San-José & J. García-Laguna & J. Sicilia, 2014. "Some general properties for the newsboy problem with an extraordinary order," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 674-693, July.
    15. Brandtner, Mario & Kürsten, Wolfgang, 2017. "Consistent modeling of risk averse behavior with spectral risk measures: Wächter/Mazzoni revisited," European Journal of Operational Research, Elsevier, vol. 259(1), pages 394-399.
    16. Brito, Anderson J. & de Almeida, Adiel T., 2012. "Modeling a multi-attribute utility newsvendor with partial backlogging," European Journal of Operational Research, Elsevier, vol. 220(3), pages 820-830.
    17. Irfanullah Khan & Biswajit Sarkar, 2021. "Transfer of Risk in Supply Chain Management with Joint Pricing and Inventory Decision Considering Shortages," Mathematics, MDPI, vol. 9(6), pages 1-20, March.
    18. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    19. Brandtner, Mario & Kürsten, Wolfgang, 2015. "Decision making with Expected Shortfall and spectral risk measures: The problem of comparative risk aversion," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 268-280.
    20. Matyska, Branka, 2021. "Salience, systemic risk and spectral risk measures as capital requirements," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).

    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:284:y:2020:i:2:p:538-549. 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.