The Generalized Network Model: Algorithms and Application to Manufacturing Operations

  • Spyros Tzafestas
  • George Kapsiotis
Part of the Advanced Manufacturing book series (ADVMANUF)


The growth of computer industry has had a profound influence on many areas; Management and Manufacturing Sciences are undoubtedly two of them. The exploitation of the available computational power of the new technology has rendered possible the development and solution of realistic models, which capture many of the intricacies and take into account the plethora of data involved in most of the real-life problems. Network programming is one of the most extensively studied areas, and there has been a lot of work carried out on network formulation and computer implementation techniques. The major reasons that network modelling is such a popular tool among decision-makers are: i) many of the problems coming up in real-life applications have a network structure; the shortest path, assignment, scheduling, transportation and transshipment problems are the most common ones, ii) the pictorial nature of the model permits the easy statement of the problem, the conceptualzation, interpretation and verification of it and of the optimal solution, and also, the communication of relating ideas to non-scientific staff, iii) finally, the enhancement of the pure network model to the so-called Generalized Network (GN) model makes the model applicable to a great variety of problems ranging from integrated production and distribution planning to such exotic areas like file reduction and plastic-limits analysis.


Candidate Node Demand Node Cumulative Cost Complementary Slackness Dual Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Bertsekas P.D., Linear Network Optimization: Algorithms and codes, MIT Press, 1992.Google Scholar
  2. [2]
    Bertsekas P.D. and P. Tseng, “Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems”, Oper. Res., Vol. 36, pp. 93–114, 1988.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Brown J. and R. McBride, “Solving Generalized Networks”, ManagementSci., Vol. 30, pp.1497–1523, 1984.MathSciNetMATHGoogle Scholar
  4. [4]
    Dantzig B.G., Linear Programming and Extensions, Princeton University Press, Princeton, N.J., 1963.MATHGoogle Scholar
  5. [5]
    Dembo S.R., Mulvey M.J., and A.S. Zenios, “Large-Scale Nonlinear Network Models and their Applications”, Operations Res., Vol. 37, pp. 353–372, 1989.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Elam J., Glover F. and D. Klingman, “A strongly Convergent Primal Simplex Algorithm for Generalized Networks”, Math. Oper. Res., Vol.4, pp. 39–59, 1979.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Glover F., Jones J., Karns D., Klingman D. and J. Mote, “An Integrated Production, Distribution and Inventory Planning System”, Interfaces, Vol. 9, pp. 21–35, 1979.CrossRefGoogle Scholar
  8. [8]
    Glover F., Hultz J., Klingman D., “Improved Computer-Based Planning Techniques, Part I”, Interfaces, Vol. 8, pp. 16–25, 1978.CrossRefGoogle Scholar
  9. [9]
    Glover F., Hultz J., Klingman D. and J. Stutz, “Generalized Networks: A Fundamental Computer-Based Planning Tool”, Management Sci., Vol. 24, pp. 1209–1220, 1978.CrossRefGoogle Scholar
  10. [10]
    Glover F., Hultz J., Klingman D., “Improved Computer-Based Planning Techniques, Part II”, Interfaces, Vol. 9, pp. 12–20, 1979.CrossRefGoogle Scholar
  11. [11]
    Gongran M., Minoux M. and S. Vajda, Graphs and Algorithms, John Wiley 1984.Google Scholar
  12. [12]
    Jensen A.P. and G. Bhaumic, “A Flow Augmentation Approach to the Network with Gains Minimum Cost Flow Problem”, Management Sci., Vol. 23, pp. 631–643, 1977.MATHCrossRefGoogle Scholar
  13. [13]
    Jewell S.W., “Optimal Flow through Networks with Gains”, Operations Res., Vol. 10, pp. 476–499, 1962.MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    Maurras J.F., “Optimization of the Flow through Networks with Gains”, Mathematical Programming, Vol. 3, pp. 135–144, 1972.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    McBride R. “Solving Embedded Generalized Network Problems”, Eur. J. Opl. Res., Vol. 21, pp. 82–92, 1985.MATHCrossRefGoogle Scholar
  16. [16]
    Reveliotis S. and G. Kapsiotis, “Genet-Optimiser”, ESPRIT CMSO Report, DECE-IRAL, NTUA, Athens, 1990.Google Scholar
  17. [17]
    Tzafestas S., Kapsiotis G. and S. Reveliotis, “A Dual Algorithm for Post-Optimization of the Generalized Network Optimal Flow Problem”, Foundation of Computing & Decision Sci., Vol. 16, No.1, pp.39–54, 1991.MathSciNetMATHGoogle Scholar
  18. [18]
    Tzafestas S., Kapsiotis G. and S. Reveliotis, “The Generalized Network Approach to Optimized Decision Making and Planning”, In: Systems and Simulation (A. Sydow Editor), North Holland 1992.Google Scholar
  19. [19]
    Zahorik A., Thomas J. and W. Trigeiro, “Network Programming Models for Production Scheduling in Multi-stage, Multi-item Capacitated Systems”, Management Sci., Vol. 30, pp. 308–325, 1984.MATHCrossRefGoogle Scholar
  20. [20]
    Tzafestas S., Pimenidis T. and G. Kapsiotis, “Expert Decision Support Based on the Generalized Network Model: An Application to Transportation Planning”, EUROSIM’ 95: European Simulation Congress, Technical University of Vienna, Vienna, Austria (Sept. 11–15, 1995).Google Scholar

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© Springer-Verlag London Limited 1997

Authors and Affiliations

  • Spyros Tzafestas
  • George Kapsiotis

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