Journal of Global Optimization

, Volume 75, Issue 2, pp 439–460 | Cite as

Global supply chain networks and tariff rate quotas: equilibrium analysis with application to agricultural products

  • Anna NagurneyEmail author
  • Deniz Besik
  • Ladimer S. Nagurney


In this paper, we develop a global supply chain network model in which profit-maximizing firms engage in competition in the production and distribution of products in the presence of quantitative trade policy instruments in the form of tariff rate quotas. Tariff rate quotas are two-tiered tariffs, in which a lower in-quota tariff is applied to the units of imports until a quota or upper bound is attained and then a higher over-quota tariff is applied to all subsequent imports. They are utilized to protect domestic producers in the case of a wide range of products, from agricultural ones to fabrics and even steel, and can be challenging to formulate. We construct the governing set of novel equilibrium conditions associated with the product flows and Lagrange multipliers, which correspond to quota rent equivalents, and derive the variational inequality formulation. Qualitative properties are presented along with an effective algorithm, which is then applied to compute solutions to numerical examples comprising an agricultural product case study on avocados and global trade. This work is the first to model and solve general, competitive supply chain network problems consisting of oligopolistic firms with multiple production sites and demand markets in multiple countries subject to tariff rate quotas.


Supply chains Tariff rate quotas Global trade Networks Variational inequalities Agricultural products 



The authors are grateful to the two anonymous reviewers and to the Editor for helpful comments and suggestions on an earlier version of this paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Operations and Information Management, Isenberg School of ManagementUniversity of MassachusettsAmherstUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of HartfordWest HartfordUSA

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