An Evolutionary Variational
Inequality Formulation of
Supply Chain Networks with Time-Varying
Demands
Anna Nagurney
Radcliffe
Institute Fellow
Radcliffe
Institute for Advanced Study
and
Department of Finance and Operations Management
Zugang
Liu
Department of Finance and Operations Management
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.