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A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

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  • Toyasaki, Fuminori
  • Daniele, Patrizia
  • Wakolbinger, Tina

Abstract

Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints; in this case the equivalence between equilibrium problems and variational inequality problems is achieved with a standard procedure because of the linearity of the constraints. However, in reality, often nonlinear constraints can be observed in the context of economic networks. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions, including a constraint qualification and convexity of the feasible set, which allow us to characterize the economic problem by using a variational inequality formulation. Then, we provide numerical examples that highlight the applicability of the model to real-world problems. The numerical examples provide specific insights related to the role of collection targets in achieving sustainability goals.

Suggested Citation

  • Toyasaki, Fuminori & Daniele, Patrizia & Wakolbinger, Tina, 2014. "A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints," European Journal of Operational Research, Elsevier, vol. 236(1), pages 340-350.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:340-350
    DOI: 10.1016/j.ejor.2013.12.006
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    References listed on IDEAS

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    1. Tina Wakolbinger & Anna Nagurney, 2004. "Dynamic supernetworks for the integration of social networks and supply chains with electronic commerce: modeling and analysis of buyer–seller relationships with computations," Netnomics, Springer, vol. 6(2), pages 153-185, October.
    2. Giancarlo Bigi & Mauro Passacantando, 2012. "Gap functions and penalization for solving equilibrium problems with nonlinear constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 323-346, October.
    3. Qiang, Qiang & Ke, Ke & Anderson, Trisha & Dong, June, 2013. "The closed-loop supply chain network with competition, distribution channel investment, and uncertainties," Omega, Elsevier, vol. 41(2), pages 186-194.
    4. Nagurney, Anna & Toyasaki, Fuminori, 2005. "Reverse supply chain management and electronic waste recycling: a multitiered network equilibrium framework for e-cycling," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 41(1), pages 1-28, January.
    5. Anna Nagurney, 2000. "Sustainable Transportation Networks," Books, Edward Elgar Publishing, number 2069.
    6. P. Daniele & A. Maugeri & W. Oettli, 1999. "Time-Dependent Traffic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 543-555, December.
    7. Hammond, David & Beullens, Patrick, 2007. "Closed-loop supply chain network equilibrium under legislation," European Journal of Operational Research, Elsevier, vol. 183(2), pages 895-908, December.
    8. Yu, Min & Nagurney, Anna, 2013. "Competitive food supply chain networks with application to fresh produce," European Journal of Operational Research, Elsevier, vol. 224(2), pages 273-282.
    9. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    10. Nagurney, Anna & Liu, Zugang & Cojocaru, Monica-Gabriela & Daniele, Patrizia, 2007. "Dynamic electric power supply chains and transportation networks: An evolutionary variational inequality formulation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(5), pages 624-646, September.
    11. Anna Nagurney & David Parkes & Patrizia Daniele, 2007. "The Internet, evolutionary variational inequalities, and the time-dependent Braess paradox," Computational Management Science, Springer, vol. 4(4), pages 355-375, October.
    12. Patrizia Daniele, 2006. "Dynamic Networks and Evolutionary Variational Inequalities," Books, Edward Elgar Publishing, number 3516.
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    Cited by:

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    3. Chan, Chi Kin & Zhou, Yan & Wong, Kar Hung, 2019. "An equilibrium model of the supply chain network under multi-attribute behaviors analysis," European Journal of Operational Research, Elsevier, vol. 275(2), pages 514-535.
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    5. Nagurney, Anna & Salarpour, Mojtaba & Daniele, Patrizia, 2019. "An integrated financial and logistical game theory model for humanitarian organizations with purchasing costs, multiple freight service providers, and budget, capacity, and demand constraints," International Journal of Production Economics, Elsevier, vol. 212(C), pages 212-226.
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    7. Anna Nagurney, 2022. "Supply chain networks, wages, and labor productivity: insights from Lagrange. analysis and computations," Journal of Global Optimization, Springer, vol. 83(3), pages 615-638, July.
    8. Gossler, Timo & Wakolbinger, Tina & Nagurney, Anna & Daniele, Patrizia, 2019. "How to increase the impact of disaster relief: A study of transportation rates, framework agreements and product distribution," European Journal of Operational Research, Elsevier, vol. 274(1), pages 126-141.
    9. E. Allevi & A. Gnudi & I. V. Konnov & G. Oggioni, 2018. "Evaluating the effects of environmental regulations on a closed-loop supply chain network: a variational inequality approach," Annals of Operations Research, Springer, vol. 261(1), pages 1-43, February.
    10. Nagurney, Anna & Flores, Emilio Alvarez & Soylu, Ceren, 2016. "A Generalized Nash Equilibrium network model for post-disaster humanitarian relief," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 1-18.
    11. Anna Nagurney & Patrizia Daniele & Shivani Shukla, 2017. "A supply chain network game theory model of cybersecurity investments with nonlinear budget constraints," Annals of Operations Research, Springer, vol. 248(1), pages 405-427, January.
    12. Zhou, Yan & Chan, Chi Kin & Wong, Kar Hung, 2018. "A multi-period supply chain network equilibrium model considering retailers’ uncertain demands and dynamic loss-averse behaviors," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 51-76.
    13. Caruso, Valeria & Daniele, Patrizia, 2018. "A network model for minimizing the total organ transplant costs," European Journal of Operational Research, Elsevier, vol. 266(2), pages 652-662.
    14. Anna Nagurney & Patrizia Daniele & Ladimer S. Nagurney, 2020. "Refugee migration networks and regulations: a multiclass, multipath variational inequality framework," Journal of Global Optimization, Springer, vol. 78(3), pages 627-649, November.
    15. Ciarcià, Carla & Daniele, Patrizia, 2016. "New existence theorems for quasi-variational inequalities and applications to financial models," European Journal of Operational Research, Elsevier, vol. 251(1), pages 288-299.
    16. Yu, Min & Cruz, Jose M. & Li, Dong Michelle, 2019. "The sustainable supply chain network competition with environmental tax policies," International Journal of Production Economics, Elsevier, vol. 217(C), pages 218-231.
    17. Nagurney, Anna, 2021. "Supply chain game theory network modeling under labor constraints: Applications to the Covid-19 pandemic," European Journal of Operational Research, Elsevier, vol. 293(3), pages 880-891.
    18. Nagurney, Anna, 2022. "Attracting international migrant labor: Investment optimization to alleviate supply chain labor shortages," Operations Research Perspectives, Elsevier, vol. 9(C).
    19. Andreani, R. & Júdice, J.J. & Martínez, J.M. & Martini, T., 2016. "Feasibility problems with complementarity constraints," European Journal of Operational Research, Elsevier, vol. 249(1), pages 41-54.
    20. Xiao Liao & Guangyu Ye & Juan Yu & Yunjiang Xi, 2021. "Identifying lead users in online user innovation communities based on supernetwork," Annals of Operations Research, Springer, vol. 300(2), pages 515-543, May.
    21. Saberi, Sara & Cruz, Jose M. & Sarkis, Joseph & Nagurney, Anna, 2018. "A competitive multiperiod supply chain network model with freight carriers and green technology investment option," European Journal of Operational Research, Elsevier, vol. 266(3), pages 934-949.
    22. Chao Min & Feifei Fan & Zhaozhong Yang & Xiaogang Li, 2019. "An Iterative Algorithm for the Nonlinear MC 2 Model with Variational Inequality Method," Mathematics, MDPI, vol. 7(6), pages 1-13, June.
    23. Dong Li & Anna Nagurney, 2017. "Supply chain performance assessment and supplier and component importance identification in a general competitive multitiered supply chain network model," Journal of Global Optimization, Springer, vol. 67(1), pages 223-250, January.

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