IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v169y2020icp133-148.html
   My bibliography  Save this article

Dynamics of a risk-averse newsvendor model with continuous-time delay in supply chain financing

Author

Listed:
  • Chen, Jianxin
  • Zhang, Tonghua
  • Zhou, Yongwu

Abstract

In this paper, delay differential equations are adopted to describe the ordering performance of the risk-averse newsvendor with supply chain financing. Firstly, authors theoretically explore the local asymptotical stability for equilibrium point, and also the conditions and directions for Hopf bifurcation of the ordering quantity for risk-averse retailer. Secondly, they investigate the influence of important parameters on the bifurcation, and find that the initial capital, risk aversion and friction coefficient can make the Hopf bifurcation undergo a long time, but the adjustment speed induces the inverse effect. Then phase diagram, stable region, bifurcation to chaos, time series and CVaR profit are illustrated by means of numerical simulation. It is found that the upstream supplier can share the risk from market uncertain with stochastic demand under supply chain financing. The results also indicate that the optimal ordering quantity placed by risk-averse newsvendor is smaller than the risk-neutral ordering quantity. Furthermore, the less initial capital may cause the CVaR profit to increase steadily or drop sharply, which exhibits complex dynamical behaviour in the presence of the time delay. Finally, the stability and bifurcation analysis of a fractional delay ordering model has also been proposed and studied. It is worth pointing out that in this study authors assume there is only one retailer who is risk-averse. Therefore, it will be more interesting and meaningful to consider the scenario having multiple retailers and to incorporate the upstream supplier’s optimal decision into the dynamical decision model.

Suggested Citation

  • Chen, Jianxin & Zhang, Tonghua & Zhou, Yongwu, 2020. "Dynamics of a risk-averse newsvendor model with continuous-time delay in supply chain financing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 133-148.
    • Handle: RePEc:eee:matcom:v:169:y:2020:i:c:p:133-148
    DOI: 10.1016/j.matcom.2019.09.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475419302630
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2019.09.009?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. Tang, Xiaosong & Song, Yongli, 2015. "Stability, Hopf bifurcations and spatial patterns in a delayed diffusive predator–prey model with herd behavior," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 375-391.
    2. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 166-177.
    3. Jianxin Chen & Yong-Wu Zhou & Yuanguang Zhong, 2017. "A pricing/ordering model for a dyadic supply chain with buyback guarantee financing and fairness concerns," International Journal of Production Research, Taylor & Francis Journals, vol. 55(18), pages 5287-5304, September.
    4. Cerboni Baiardi, Lorenzo & Naimzada, Ahmad K., 2019. "An oligopoly model with rational and imitation rules," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 254-278.
    5. Luca Gori & Luca Guerrini & Mauro Sodini, 2017. "A characterisation of duopoly dynamics with frictions in production adjustments," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 963-988, November.
    6. John Conlisk, 1996. "Why Bounded Rationality?," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 669-700, June.
    7. Bonanno, Giacomo & Christopher Zeeman, E., 1985. "Limited knowledge of demand and oligopoly equilibria," Journal of Economic Theory, Elsevier, vol. 35(2), pages 276-283, August.
    8. Mackey, Michael C., 1989. "Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors," Journal of Economic Theory, Elsevier, vol. 48(2), pages 497-509, August.
    9. Monika Joanna Piotrowska & Urszula Foryś, 2014. "Delay Differential Equations in Bio-Populations," Mathematical Population Studies, Taylor & Francis Journals, vol. 21(3), pages 125-126, September.
    10. Bonanno, Giacomo, 1988. "Oligopoly Equilibria When Firms Have Local Knowledge of Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 45-55, February.
    11. Bischi, Gian Italo & Lamantia, Fabio & Radi, Davide, 2015. "An evolutionary Cournot model with limited market knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 219-238.
    12. Matsumoto, Akio & Szidarovszky, Ferenc, 2012. "Nonlinear delay monopoly with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 507-519.
    13. Zhou, Yong-Wu & Li, Jicai & Zhong, Yuanguang, 2018. "Cooperative advertising and ordering policies in a two-echelon supply chain with risk-averse agents," Omega, Elsevier, vol. 75(C), pages 97-117.
    14. Maurice E. Schweitzer & Gérard P. Cachon, 2000. "Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence," Management Science, INFORMS, vol. 46(3), pages 404-420, March.
    15. Vipul Agrawal & Sridhar Seshadri, 2000. "Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem," Manufacturing & Service Operations Management, INFORMS, vol. 2(4), pages 410-423, July.
    16. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    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. Chen, Jianxin & Zhang, Tonghua & Zhou, Yong-wu, 2021. "Stochastic sensitivity and dynamical complexity of newsvendor models subject to trade credit," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 471-486.
    2. Xu, Xinsheng & Ji, Ping & Sang, Shuming, 2023. "Supply option purchasing decisions via mismatch cost minimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 260-280.
    3. Xu, Xinsheng & Ji, Ping & Chan, Felix T.S., 2022. "On maximizing a loss-averse buyer’s expected utility in a multi-sourcing problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 388-404.
    4. Wu, Chengfeng & Liu, Xin & Li, Annan, 2021. "A loss-averse retailer–supplier supply chain model under trade credit in a supplier-Stackelberg game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 353-365.
    5. Zhang, Wen & Yan, Shaoshan & Li, Jian & Tian, Xin & Yoshida, Taketoshi, 2022. "Credit risk prediction of SMEs in supply chain finance by fusing demographic and behavioral data," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    6. Shujian Ma & Jilong Cai & Gang Wang & Xiangxiang Ge & Ying Teng & Hua Jiang, 2024. "Research on Decision Analysis with CVaR for Supply Chain Finance Based on Blockchain Technology," Mathematics, MDPI, vol. 12(3), pages 1-25, 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. Serena Brianzoni & Giovanni Campisi & Luca Guerrini, 2018. "A continuous-time heterogeneous duopoly model with delays," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 259-275, November.
    2. Wang, Daao & Dimitrov, Stanko & Jian, Lirong, 2020. "Optimal inventory decisions for a risk-averse retailer when offering layaway," European Journal of Operational Research, Elsevier, vol. 284(1), pages 108-120.
    3. Kopányi, Dávid, 2017. "The coexistence of stable equilibria under least squares learning," Journal of Economic Behavior & Organization, Elsevier, vol. 141(C), pages 277-300.
    4. Jia Liu & Cuixia Li, 2023. "Dynamic Game Analysis on Cooperative Advertising Strategy in a Manufacturer-Led Supply Chain with Risk Aversion," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    5. Brian Tomlin & Yimin Wang, 2005. "On the Value of Mix Flexibility and Dual Sourcing in Unreliable Newsvendor Networks," Manufacturing & Service Operations Management, INFORMS, vol. 7(1), pages 37-57, June.
    6. Felix T. S. Chan & Xinsheng Xu, 2019. "The Loss-Averse Retailer’s Order Decisions Under Risk Management," Mathematics, MDPI, vol. 7(7), pages 1-16, July.
    7. Wu, Meng & Zhu, Stuart X. & Teunter, Ruud H., 2013. "The risk-averse newsvendor problem with random capacity," European Journal of Operational Research, Elsevier, vol. 231(2), pages 328-336.
    8. Xia Yan & Shaofu Du & Li Hu, 2020. "Supply chain performance for a risk inequity averse newsvendor," Annals of Operations Research, Springer, vol. 290(1), pages 897-921, July.
    9. Wu, Meng & Zhu, Stuart X. & Teunter, Ruud H., 2014. "A risk-averse competitive newsvendor problem under the CVaR criterion," International Journal of Production Economics, Elsevier, vol. 156(C), pages 13-23.
    10. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    11. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    12. Wu, Meng & Zhu, Stuart X. & Teunter, Ruud H., 2013. "Newsvendor problem with random shortage cost under a risk criterion," International Journal of Production Economics, Elsevier, vol. 145(2), pages 790-798.
    13. Xinsheng, Xu & Zhiqing, Meng & Rui, Shen & Min, Jiang & Ping, Ji, 2015. "Optimal decisions for the loss-averse newsvendor problem under CVaR," International Journal of Production Economics, Elsevier, vol. 164(C), pages 146-159.
    14. Zhou, Yong-Wu & Li, Jicai & Zhong, Yuanguang, 2018. "Cooperative advertising and ordering policies in a two-echelon supply chain with risk-averse agents," Omega, Elsevier, vol. 75(C), pages 97-117.
    15. Chahar, Kiran & Taaffe, Kevin, 2009. "Risk averse demand selection with all-or-nothing orders," Omega, Elsevier, vol. 37(5), pages 996-1006, October.
    16. Chen, Jianxin & Zhang, Tonghua & Zhou, Yong-wu, 2021. "Stochastic sensitivity and dynamical complexity of newsvendor models subject to trade credit," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 471-486.
    17. Wu, Jun & Wang, Shouyang & Chao, Xiuli & Ng, C.T. & Cheng, T.C.E., 2010. "Impact of risk aversion on optimal decisions in supply contracts," International Journal of Production Economics, Elsevier, vol. 128(2), pages 569-576, December.
    18. Qin, Yan & Wang, Ruoxuan & Vakharia, Asoo J. & Chen, Yuwen & Seref, Michelle M.H., 2011. "The newsvendor problem: Review and directions for future research," European Journal of Operational Research, Elsevier, vol. 213(2), pages 361-374, September.
    19. Poormoaied, Saeed & Atan, Zümbül, 2020. "A multi-attribute utility theory approach to ordering policy for perishable items," International Journal of Production Economics, Elsevier, vol. 225(C).
    20. He, Haonan & Wang, Shanyong, 2019. "Cost-benefit associations in consumer inventory problem with uncertain benefit," Journal of Retailing and Consumer Services, Elsevier, vol. 51(C), pages 271-284.

    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:matcom:v:169:y:2020:i:c:p:133-148. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.