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

Anna Nagurney and Zugang Liu
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Anna Nagurney: Harvard University
Zugang Liu: University of Massachusetts

Chapter Chapter 12 in Network Science, Nonlinear Science and Infrastructure Systems, 2007, pp 269-304 from Springer

Abstract: 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.

Keywords: supply chain; variational inequalities; evolutionary processes; dynamics (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-0-387-71134-8_12

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DOI: 10.1007/0-387-71134-1_12

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