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An Evolutionary Variational Inequality Formulation of Supply Chain Networks with Time-Varying Demands

In: Network Science, Nonlinear Science and Infrastructure Systems

Author

Listed:
  • Anna Nagurney

    (Harvard University
    University of Massachusetts)

  • Zugang Liu

    (University of Massachusetts)

Abstract

This paper first develops a multitiered supply chain network equilibrium model with fixed demands and proves that the governing equilibrium conditions satisfy a finite-dimensional variational inequality. The paper then establishes that the static supply chain network model with its governing equilibrium conditions can be reformulated as a transportation network equilibrium model over an appropriately constructed abstract network or supernetwork. This identification provides a new interpretation of equilibrium in supply chain networks with fixed demands in terms of path flows. The equivalence is then further exploited to construct a dynamic supply chain network model with time-varying demands (and flows) using an evolutionary (time-dependent) variational inequality formulation. Recent theoretical results in the unification of projected dynamical systems and evolutionary variational inequalities are presented and then applied to formulate dynamic numerical supply chain network examples and to compute the curves of equilibria. An example with step-wise time-dependent demand is also given for illustration purposes.

Suggested Citation

  • Anna Nagurney & Zugang Liu, 2007. "An Evolutionary Variational Inequality Formulation of Supply Chain Networks with Time-Varying Demands," International Series in Operations Research & Management Science, in: Terry L. Friesz (ed.), Network Science, Nonlinear Science and Infrastructure Systems, chapter 0, pages 269-304, Springer.
    • Handle: RePEc:spr:isochp:978-0-387-71134-8_12
    DOI: 10.1007/0-387-71134-1_12
    as

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