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Bullwhip effect and complexity analysis in a multi-channel supply chain considering price game with discount sensitivity

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  • Junhai Ma
  • Wandong Lou
  • Yi Tian

Abstract

This paper constructs a multi-channel supply chain that includes a manufacturer, a dual-channel retailer and an online retailer. The dual-channel retailer has a traditional channel and an online channel, while the manufacturer cooperates with the retailers and opens a direct channel simultaneously. The horizontal and historical price discount sensitivities are taken into account to establish the price-sensitive demand functions. A price game model with the heterogeneous expectations is proposed and analysed with the methods of the stability domain, the bifurcation diagram and the maximum Lyapunov exponent. The complexity and bullwhip effect of each channel are investigated with respect to the price adjustment speed and historical price discount sensitivity. The results show that a moderate or low price discount sensitivity keeps the system stable and a high price discount sensitivity brings the system into the twofold cycle state or chaotic state. It is interesting that if both online channels increase the adjustment speeds with similar strategy the system will enter chaos through the Neimark–Sacker bifurcation. The bullwhip effect is affected by the price adjustment speed and the price discount sensitivity, especially in the double-period or chaotic state, where the bullwhip of the overall supply chain is increased significantly. The results show that controlling price discount sensitivity is useful for supply chain node companies.

Suggested Citation

  • Junhai Ma & Wandong Lou & Yi Tian, 2019. "Bullwhip effect and complexity analysis in a multi-channel supply chain considering price game with discount sensitivity," International Journal of Production Research, Taylor & Francis Journals, vol. 57(17), pages 5432-5452, September.
    • Handle: RePEc:taf:tprsxx:v:57:y:2019:i:17:p:5432-5452
    DOI: 10.1080/00207543.2018.1526420
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    Citations

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    Cited by:

    1. Yingxiao Li & Jianheng Zhou, 2022. "Sustainable Supplier’s Equilibrium Discount Strategy under Random Demand," Sustainability, MDPI, vol. 14(8), pages 1-12, April.
    2. Jin Sha & Sisi Zheng, 2023. "Analysis of Sub-Optimization Impact on Partner Selection in VMI," Sustainability, MDPI, vol. 15(3), pages 1-11, February.
    3. Yuan, Xuchuan & Brian Hwarng, H., 2023. "Examining the dynamics of reactive capacity allocation through a chaos lens," European Journal of Operational Research, Elsevier, vol. 308(2), pages 912-928.
    4. Davide Settembre-Blundo & Rocío González-Sánchez & Sonia Medina-Salgado & Fernando E. García-Muiña, 2021. "Flexibility and Resilience in Corporate Decision Making: A New Sustainability-Based Risk Management System in Uncertain Times," Global Journal of Flexible Systems Management, Springer;Global Institute of Flexible Systems Management, vol. 22(2), pages 107-132, December.
    5. Xi, Xuan & Zhang, Jixiang, 2020. "Complexity analysis of a decision-making game concerning governments and heterogeneous agricultural enterprises with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. Erkan Bayraktar & Kazim Sari & Ekrem Tatoglu & Selim Zaim & Dursun Delen, 2020. "Assessing the supply chain performance: a causal analysis," Annals of Operations Research, Springer, vol. 287(1), pages 37-60, April.
    7. Germán Herrera Vidal & Jairo R. Coronado-Hernández & Claudia Minnaard, 2023. "Measuring manufacturing system complexity: a literature review," Journal of Intelligent Manufacturing, Springer, vol. 34(7), pages 2865-2888, October.
    8. Li-Ling Liu, 2021. "Control model for cosmetic service: risk and price sensitivity," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 20(5), pages 580-587, October.
    9. Syed Asif Raza, 2022. "A bibliometric analysis of pricing models in supply chain," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(2), pages 228-251, April.
    10. Junhai Ma & Lijiao Gong & Jie Fan, 2022. "Pricing strategy and coordination of small‐ to medium‐sized enterprises based on bank‐insurance cooperative financing," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(8), pages 3915-3930, December.

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