An evolutionary variational inequality formulation of supply chain networks with time-varying demands

Anna Nagurney, Zugang Liu

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationInternational Series in Operations Research and Management Science
PublisherSpringer New York LLC
Pages269-304
Number of pages36
StatePublished - Jan 1 2007

Publication series

NameInternational Series in Operations Research and Management Science
Volume102
ISSN (Print)0884-8289

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Science Applications
  • Strategy and Management
  • Management Science and Operations Research
  • Applied Mathematics

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    Nagurney, A., & Liu, Z. (2007). An evolutionary variational inequality formulation of supply chain networks with time-varying demands. In International Series in Operations Research and Management Science (pp. 269-304). (International Series in Operations Research and Management Science; Vol. 102). Springer New York LLC.