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A Variational Equilibrium Network Framework for Humanitarian Organizations in Disaster Relief: Effective Product Delivery Under Competition for Financial Funds

In: Dynamics of Disasters

Author

Listed:
  • Anna Nagurney

    (University of Massachusetts)

  • Patrizia Daniele

    (University of Catania)

  • Emilio Alvarez Flores

    (Cisco Services)

  • Valeria Caruso

    (University of Catania)

Abstract

In this paper, we present a new Generalized Nash Equilibrium (GNE) model for post-disaster humanitarian relief by introducing novel financial funding functions and altruism functions, and by also capturing competition on the logistics side among humanitarian organizations. The common, that is, the shared, constraints associated with the relief item deliveries at points of need are imposed by an upper level humanitarian organization or regulatory body and consist of lower and upper bounds to ensure the effective delivery of the estimated volumes of supplies to the victims of the disaster. We identify the network structure of the problem, with logistical and financial flows, and propose a variational equilibrium framework, which allows us to then formulate, analyze, and solve the model using the theory of variational inequalities (rather than quasivariational inequality theory). We then utilize Lagrange analysis and investigate qualitatively the humanitarian organizations’ marginal utilities if and when the equilibrium relief item flows are (or are not) at the imposed demand point bounds. We illustrate the game theory model through a case study focused on tornadoes hitting western Massachusetts, a highly unusual event that occurred in 2011. This work significantly extends the original model of Nagurney (Dynamics of Disasters: Key Concepts, Models, Algorithms, and Insights. Springer International Publishing, Switzerland, 2016), which, under the imposed assumptions therein, allowed for an optimization formulation, and adds to the literature of game theory and disaster relief, which is nascent.

Suggested Citation

  • Anna Nagurney & Patrizia Daniele & Emilio Alvarez Flores & Valeria Caruso, 2018. "A Variational Equilibrium Network Framework for Humanitarian Organizations in Disaster Relief: Effective Product Delivery Under Competition for Financial Funds," Springer Optimization and Its Applications, in: Ilias S. Kotsireas & Anna Nagurney & Panos M. Pardalos (ed.), Dynamics of Disasters, pages 109-133, Springer.
  • Handle: RePEc:spr:spochp:978-3-319-97442-2_6
    DOI: 10.1007/978-3-319-97442-2_6
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    Cited by:

    1. Salarpour, Mojtaba & Nagurney, Anna, 2021. "A multicountry, multicommodity stochastic game theory network model of competition for medical supplies inspired by the Covid-19 pandemic," International Journal of Production Economics, Elsevier, vol. 236(C).
    2. 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.
    3. 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.
    4. Anna Nagurney & Mojtaba Salarpour & June Dong & Ladimer S. Nagurney, 2020. "A Stochastic Disaster Relief Game Theory Network Model," SN Operations Research Forum, Springer, vol. 1(2), pages 1-33, June.
    5. 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.

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