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Evolutionary variational inequalities and applications to complex dynamic multi-level models


  • Daniele, Patrizia


In this paper we consider a supply chain network model with three tiers of decision-makers (manufacturers, retailers, and consumers) in the case when prices and shipments are evolving on time. Moreover, we assume that excesses of production and excesses of demand of the commodity are present. For such a framework we furnish, using the infinite dimensional duality theory, the equilibrium conditions for the representatives of each tier of the supernetwork, the time-dependent variational formulation governing the complete supply chain supernetwork, and we provide some existence theorems and a numerical example.

Suggested Citation

  • Daniele, Patrizia, 2010. "Evolutionary variational inequalities and applications to complex dynamic multi-level models," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(6), pages 855-880, November.
  • Handle: RePEc:eee:transe:v:46:y:2010:i:6:p:855-880

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    Cited by:

    1. Nagurney, Anna & Nagurney, Ladimer S., 2012. "Dynamics and equilibria of ecological predator–prey networks as nature’s supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 89-99.
    2. Barbagallo, Annamaria & Daniele, Patrizia & Giuffrè, Sofia & Maugeri, Antonino, 2014. "Variational approach for a general financial equilibrium problem: The Deficit Formula, the Balance Law and the Liability Formula. A path to the economy recovery," European Journal of Operational Research, Elsevier, vol. 237(1), pages 231-244.
    3. Yamada, Tadashi & Imai, Koji & Nakamura, Takamasa & Taniguchi, Eiichi, 2011. "A supply chain-transport supernetwork equilibrium model with the behaviour of freight carriers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 887-907.


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