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A Closed-Loop Supply Chain Equilibrium Model with Random and Price-Sensitive Demand and Return

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  • Younes Hamdouch

    (United Arab Emirates University)

  • Qiang Patrick Qiang

    (The Pennsylvania State University)

  • Kilani Ghoudi

    (United Arab Emirates University)

Abstract

This paper proposes a decentralized closed-loop supply chain network model consisting of raw material suppliers, manufacturers, retailers, and recovery centers. We assume that the demands for the product and the corresponding returns are random and price-sensitive. Retailers and recovery centers face penalties associated with shortage demand and supply, respectively. We derive the optimality conditions of the various decision-makers, and establish that the governing equilibrium conditions can be formulated as a finite-dimensional variational inequality problem. The qualitative properties of the solution to the variational inequality are discussed. Numerical examples are provided to illustrate the effects of demand and return uncertainties on quantity shipments and prices.

Suggested Citation

  • Younes Hamdouch & Qiang Patrick Qiang & Kilani Ghoudi, 2017. "A Closed-Loop Supply Chain Equilibrium Model with Random and Price-Sensitive Demand and Return," Networks and Spatial Economics, Springer, vol. 17(2), pages 459-503, June.
    • Handle: RePEc:kap:netspa:v:17:y:2017:i:2:d:10.1007_s11067-016-9333-y
    DOI: 10.1007/s11067-016-9333-y
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    Cited by:

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    2. Boulaksil, Youssef & Hamdouch, Younes & Ghoudi, Kilani & Fransoo, Jan C., 2021. "Comparing policies for the stochastic multi-period dual sourcing problem from a supply chain perspective," Other publications TiSEM 242598b9-99de-4a3c-a1a9-4, Tilburg University, School of Economics and Management.
    3. Boulaksil, Youssef & Hamdouch, Younes & Ghoudi, Kilani & Fransoo, Jan C., 2021. "Comparing policies for the stochastic multi-period dual sourcing problem from a supply chain perspective," International Journal of Production Economics, Elsevier, vol. 232(C).
    4. Hamdouch, Younes & Ghoudi, Kilani, 2020. "A Supply Chain Equilibrium Model with General Price-Dependent Demand," Operations Research Perspectives, Elsevier, vol. 7(C).
    5. Luttiely Santos Oliveira & Ricardo Luiz Machado, 2021. "Application of optimization methods in the closed-loop supply chain: a literature review," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 357-400, February.
    6. Guitao Zhang & Xiao Zhang & Hao Sun & Xinyu Zhao, 2021. "Three-Echelon Closed-Loop Supply Chain Network Equilibrium under Cap-and-Trade Regulation," Sustainability, MDPI, vol. 13(11), pages 1-26, June.
    7. Behnam Vahdani & Elham Ahmadzadeh, 2021. "Incorporating Price-Dependent Demands into a Multi-Echelon Closed-Loop Network Considering the Lost Sales and Backorders: a Case Study of Wireless Network," Networks and Spatial Economics, Springer, vol. 21(3), pages 639-680, September.
    8. Jingfeng Dong & Shufa Sun & Guichen Gao & Ruoyi Yang, 2021. "Pricing and strategy selection in a closed-loop supply chain under demand and return rate uncertainty," 4OR, Springer, vol. 19(4), pages 501-530, December.

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