Supply Chain Network Competition with Multiple Freight Options

  • Anna Nagurney
  • Dong Li
Part of the Springer Series in Supply Chain Management book series (SSSCM, volume 2)


This chapter extends the results in Chap. 5 to include multiple freight options for the manufacturers to ship their products from their manufacturing plants to consumers at the demand markets. We first develop a static supply chain network model of Cournot-Nash competition with product differentiation, multiple freight options, and quality competition. Each manufacturing firm seeks to maximize its own profit by determining its product shipments and product quality. We utilize variational inequality theory for the formulation of the governing Cournot-Nash equilibrium. We then construct the projected dynamical systems model, which provides a continuous-time evolution of the product shipments of the firms and the product quality levels, and whose set of stationary points coincides with the set of solutions to the variational inequality problem. We establish stability analysis results using a monotonicity approach and construct a discrete-time version of the continuous-time adjustment processes, which yields an algorithm, with closed form expressions at each iteration. The algorithm is then utilized to compute the solutions to several numerical examples. A sensitivity analysis on changes in the demand price functions is also conducted.


Variational Inequality Quality Level Demand Market Supply Chain Network Freight Transport 
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  1. Arrow, K., & Hurwicz, L. (1977). Studies in resource allocation processes. New York: Cambridge University Press.Google Scholar
  2. Ben-Aliva, M., Meersman, H., & Van der Voorde, E. (Ed.). (2013). Freight transport modelling. Bingley: Emerald Group Publishing.Google Scholar
  3. Bonilla, D., & Whittaker, C. (2009, December). Freight transport and deployment of bioenergy in the UK (Working Paper Number 1043). Oxford: Transport Studies Unit, Oxford University.Google Scholar
  4. Bookbinder, J. H., & Prentice, B. E. (2013). The future. In J. H. Bookbinder (Ed.), Handbook of global logistics: Transportation in international supply chains (pp. 531–546). New York: Springer.Google Scholar
  5. Boyce, D., & Williams, H. (2015). Forecasting urban travel: Past, present future. Cheltenham: Edward Elgar.Google Scholar
  6. Cournot, A. A. (1838). Researches into the mathematical principles of the theory of wealth, english translation. London: MacMillan.Google Scholar
  7. Dafermos, S., & Nagurney, A. (1987). Oligopolistic and competitive behavior of spatially separated markets. Regional Science and Urban Economics, 17, 245–254.Google Scholar
  8. Dupuis, P., & Nagurney, A. (1993). Dynamical systems and variational inequalities. Annals of Operations Research, 44, 9–42.Google Scholar
  9. Floden, J. (Ed.). (2015). Sustainable intermodal biofuel transport. Gothenburg: BAS Publishing.Google Scholar
  10. Gabay, D., & Moulin, H. (1980). On the uniqueness and stability of Nash equilibria in noncooperative games. In A. Bensoussan, P. Kleindorfer, & C. S. Tapiero (Eds.), Applied stochastic control in econometrics and management science (pp. 271–294). Amsterdam: North-Holland.Google Scholar
  11. Groothede, B., Ruijgrok, C., & Tavasszy, L. (2005). Towards collaborative, intermodal hub networks: A case study of the fast moving consumer goods market. Transportation Research E, 41(6), 567–583.Google Scholar
  12. Nagurney, A., Ke, K., Cruz, J., Hancock, K., & Southworth, F. (2002). Dynamics of supply chains: A multilevel (logistical/information/financial) network perspective. Environment and Planning, 29B, 795–818.Google Scholar
  13. Nagurney, A., Li, D., Wolf, T., & Nagurney, L. S. (2013a). A network economic game theory model of a service-oriented internet with choices and quality competition. Netnomics, 14(1–2), 1–25.Google Scholar
  14. Nagurney, A., Masoumi, A. H., & Yu, M. (2015). An integrated disaster relief supply chain network model with time targets and demand uncertainty. In P. Nijkamp, A. Rose, & K. Kourtit (Eds.), Regional science matters: Studies dedicated to walter isard (pp. 287–318). Cham: Springer.Google Scholar
  15. Nagurney, A., & Nagurney, L. S. (2010). Sustainable supply chain network design: A multicriteria perspective. International Journal of Sustainable Engineering, 3, 189–197.Google Scholar
  16. Nagurney, A., & Yu, M. (2011). Fashion supply chain management through cost and time minimization from a network perspective. In T. M. Choi (Ed.), Fashion supply chain management: Industry and business analysis (pp. 1–20). Hershey: IGI Global.Google Scholar
  17. Nagurney, A., & Yu, M. (2012). Sustainable fashion supply chain management under oligopolistic competition and brand differentiation. International Journal of Production Economics, 135, 532–540.Google Scholar
  18. Nagurney, A., Yu, M., Masoumi, A. H., & Nagurney, L. S. (2013b). Networks against time: Supply chain analytics for perishable products. New York: Springer.Google Scholar
  19. Nagurney, A., & Zhang, D. (1996). Projected dynamical systems and variational inequalities with applications. Boston: Kluwer Academic.Google Scholar
  20. Nash, J. F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, USA, 36, 48–49.Google Scholar
  21. Nash, J. F. (1951). Noncooperative games. Annals of Mathematics, 54, 286–298.Google Scholar
  22. Okuguchi, K., & Szidarovszky, F. (1990). The theory of oligopoly with multi-product firms (Lecture notes in economics and mathematical systems, Vol. 342). Berlin: Springer.Google Scholar
  23. Palmeri, C. (2014, April 10). Disney’s ‘Frozen’ dress sets off $1,600 frenzy by parents. Bloomberg News.
  24. Qiang, Q., Nagurney, A., & Dong, J. (2009). Modeling of supply chain risk under disruptions with performance measurement and robustness analysis. In T. Wu, J. Blackhurst (Eds.), Managing supply chain risk and vulnerability: Tools and methods for supply chain decision makers (pp. 91–111). Berlin: Springer.Google Scholar
  25. Tavasszy, L., & de Jong, G. (Eds.). (2014). Modeling freight transport. Waltham: Elsevier.Google Scholar
  26. Vives, X. (1999). Oligopoly pricing: Old ideas and new tools. Cambridge: MIT.Google Scholar
  27. Wigan, M. A., & Southworth, F. (2005). What’s wrong with freight models? Proceedings of the European transport conference. Strasbourg: Association of European Transport.Google Scholar
  28. Wilson, M. C. (2007). The impact of transportation disruptions on supply chain performance. Transportation Research E, 43, 295–320.Google Scholar
  29. Wolf, T., Griffioen, J., Calvert, K., Dutta, R., Rouskas, G., Baldine, I., & Nagurney, A. (2012). Choice as a principle in network architecture. In Proceedings of ACM SIGCOMM 2012, Helsinki, 13–17 August 2012.Google Scholar
  30. Zhang, D., & Nagurney, A. (1995). On the stability of projected dynamical systems. Journal of Optimization Theory and Its Applications, 85, 97–124.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Anna Nagurney
    • 1
  • Dong Li
    • 2
  1. 1.Isenberg School of ManagementUniversity of MassachusettsAmherstUSA
  2. 2.Department of Management and Marketing College of BusinessArkansas State UniversityState UniversityUSA

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