Dynamic supernetworks for the integration of social networks and supply chains with electronic commerce: modeling and analysis of buyer–seller relationships with computations

  • Tina Wakolbinger
  • Anna Nagurney


In this paper, we develop a dynamic supernetwork framework for the modeling and analysis of supply chains with electronic commerce that also includes the role that relationships play. Manufacturers are assumed to produce a homogeneous product and to sell it either through physical or electronic links to retailers and/or directly to consumers through electronic links. Retailers, in turn, can sell the product through physical links to consumers. Increasing relationship levels in our framework are assumed to reduce transaction costs as well as risk and to have some additional value for both sellers and buyers. Establishing those relationship levels incurs some costs that have to be borne by the decision-makers in the supernetwork, which is multilevel in structure and consists of the supply chain and the social network. The decision-makers, who are located at distinct tiers in the supernetwork, try to optimize their objective functions and are faced with multiple criteria including relationship-related ones and weight them according to their preferences. We establish the optimality conditions for the manufacturers, retailers, and consumers, derive the equilibrium conditions, and provide the variational inequality formulation. We then present the projected dynamical system, which describes the disequilibrium dynamics of the product transactions, relationship levels, and prices on the supernetwork, and whose set of stationary points coincides with the set of solutions of the variational inequality problem. We also illustrate the dynamic supernetwork model through several numerical examples, for which the explicit equilibrium patterns are computed.


electronic commerce projected dynamical systems relationships social networks supernetworks supply chains 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R.P. Bagozzi, Reflections on relationship marketing in consumer markets, J. Acad. Marketing Sci. 23 (1995) 272–277. Google Scholar
  2. [2]
    M.S. Bazaraa, H.D. Sherali and C.M. Shetty, Nonlinear Programming: Theory and Algorithms (Wiley, New York, 1993). Google Scholar
  3. [3]
    K.M. Carley, Dynamic network analysis, in: Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers, eds. R. Breiger, K. Carley and P. Pattison, Committee on Human Factors, National Research Council (2003) pp. 133–145. Google Scholar
  4. [4]
    V.P. Crawford, Relationship-specific investment, Quart. J. Economics 105 (1990) 561–574. Google Scholar
  5. [5]
    B. Donaldson and T. O’Toole, Classifying relationship structures: Relationship strength in industrial markets, J. Business Industr. Marketing 15 (2000) 491–506. Google Scholar
  6. [6]
    J. Dong, D. Zhang and A. Nagurney, Supply chain networks with multicriteria decision-makers, in: Transportation and Traffic Theory in the 21st Century, ed. M.A.P. Taylor (Pergamon, Amsterdam, 2002) pp. 179–196. Google Scholar
  7. [7]
    P. Dupuis and A. Nagurney, Dynamical systems and variational inequalities, Ann. Oper. Res. 44 (1993) 9–42. MathSciNetMATHGoogle Scholar
  8. [8]
    L.C. Freeman, Social network analysis: definition and history, in: Encyclopedia of Psychology, ed. A.E. Kazdan (Oxford Univ. Press, New York, 2000) pp. 350–351. Google Scholar
  9. [9]
    D. Gabay and H. Moulin, On the uniqueness and stability of Nash equilibria in noncooperative games, in: Applied Stochastic Control of Econometrics and Management Science, eds. A. Bensoussan, P. Kleindorfer and C.S. Tapiero (North-Holland, Amsterdam, 1980). Google Scholar
  10. [10]
    S. Ganesan, Determinants of long-term orientation in buyer–seller relationships, J. Marketing 58 (1994) 1–19. Google Scholar
  11. [11]
    S.L. Golicic, J.H. Foggin and J.T. Mentzer, Relationship magnitude and its role in interorganizational relationship structure, J. Business Logistics 24 (2003) 57–75. Google Scholar
  12. [12]
    M. Granovetter, Economic action and social structure: The problem of embeddedness, Amer. J. Sociology 91 (1985) 481–510. Google Scholar
  13. [13]
    D. Iacobucci, ed., Networks in Marketing (Sage Publications, Thousand Oaks, CA, 1996). Google Scholar
  14. [14]
    C. Jones, W.S. Hesterly and S.P. Borgatti, A general theory of network governance: Exchange conditions and social mechanisms, Acad. Managm. Rev. 22 (1997) 911–945. Google Scholar
  15. [15]
    P.L. Joskow, Asset specificity and the structure of vertical relationships: Empirical evidence, J. Law Econom. Organization 4 (1988) 95–117. Google Scholar
  16. [16]
    R.L. Keeney and H. Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs (Cambridge Univ. Press, Cambridge, 1993). Google Scholar
  17. [17]
    D. Krackhardt, Modeling structures of organizations, in: Computational Modeling of Behavior in Organizations: The Third Scientific Discipline, eds. D.R. Ilgen and C.L. Hulin (Amer. Psycholog. Assoc., Washington, DC, 2000) pp. 269–273. Google Scholar
  18. [18]
    J.R. Lincoln, M.L. Gerlach and P.K. Takahashi, Keiretsu networks in the Japanese economy: A dyad analysis of intercorporate ties, Amer. Sociolog. Rev. 57 (1992) 561–585. Google Scholar
  19. [19]
    A. Muthoo, Sunk costs and the inefficiency of relationship-specific investment, Economica 65 (1998) 97–106. Google Scholar
  20. [20]
    A. Nagurney, Network Economics: A Variational Inequality Approach, 2nd and revised ed. (Kluwer Academic, Dordrecht, 1999). Google Scholar
  21. [21]
    A. Nagurney and J. Dong, Supernetworks: Decision-Making for the Information Age (Edward Elgar Publishing, Chelthenham, England, 2002). Google Scholar
  22. [22]
    A. Nagurney, J. Dong and D. Zhang, A supply chain network equilibrium model, Transport. Res. E 38 (2002) 281–303. Google Scholar
  23. [23]
    A. Nagurney, K. Ke, J. Cruz, K. Hancock and F. Southworth, Dynamics of supply chains: A multilevel (logistical/informational/financial) network perspective, Environment Planning B 29 (2002) 795–818. Google Scholar
  24. [24]
    A. Nagurney, J. Loo, J. Dong and D. Zhang, Supply chain networks and electronic commerce: A theoretical perspective, Netnomics 4 (2002) 187–220. Google Scholar
  25. [25]
    A. Nagurney and F. Toyasaki, Supply chain supernetworks and environmental criteria, Transport. Res. D: Transport. Environment 8 (2003) 185–213. Google Scholar
  26. [26]
    A. Nagurney and D. Zhang, Projected Dynamical Systems and Variational Inequalities with Applications (Kluwer Academic, Boston, MA, 1996). Google Scholar
  27. [27]
    J.F. Nash, Equilibrium points in N-person games, Proc. National Acad. Sci. USA 36 (1950) 48–49. Google Scholar
  28. [28]
    J.F. Nash, Noncooperative games, Ann. Math. 54 (1951) 286–298. Google Scholar
  29. [29]
    J.N. Sheth and A. Parvatiyar, Relationship marketing in consumer markets: Antecedents and consequences, J. Acad. Marketing Sci. 23 (1995) 255–271. Google Scholar
  30. [30]
    T. Takayama and G. Judge, Spatial and Temporal Price and Allocation Models (North-Holland, Amsterdam, 1971). Google Scholar
  31. [31]
    B. Uzzi, The sources and consequences of embeddedness for the economic performance of organizations: The network effect, Amer. Sociolog. Rev. 61 (1996) 674–698. Google Scholar
  32. [32]
    B. Uzzi, Embeddedness in the making of financial capital: How social relations and networks benefit firms seeking financing, Amer. Sociolog. Rev. 64 (1998) 481–505. Google Scholar
  33. [33]
    J. Vickers and M. Waterson, Vertical relationships: An introduction, J. Industr. Economics 39 (1991) 445–450. Google Scholar
  34. [34]
    O.E. Williamson, Credible commitments: Using hostages to support exchange, Amer. Econom. Rev. 73 (1983) 519–540. Google Scholar
  35. [35]
    D.T. Wilson, An integrated model of buyer–seller relationships, J. Acad. Marketing Sci. 23 (1995) 335–345. Google Scholar
  36. [36]
    D. Zhang and A. Nagurney, On the stability of projected dynamical systems, J. Optim. Theory Appl. 85 (1995) 97–124. Google Scholar
  37. [37]
    D. Zhang and A. Nagurney, Stability analysis of an adjustment process for oligopolistic market equilibrium modeled as a projected dynamical systems, Optimization 36 (1996) 263–285. Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Tina Wakolbinger
    • 1
  • Anna Nagurney
    • 1
  1. 1.Department of Finance and Operations Management, Isenberg School of ManagementUniversity of MassachusettsAmherstUSA

Personalised recommendations