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Viability analysis: A formulation aid for all classes of network models

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  • John W. Chinneck

Abstract

Nonviable network models have edges which are forced to zero flow simply by the pattern of interconnection of the nodes. The original nonviability diagnosis algorithm [4] is extended here to cover all classes of network models, including pure, generalized, pure processing, nonconserving processing, and generalized processing. The extended algorithm relies on the conversion of all network forms to a pure processing form. Efficiency improvements to the original algorithm are also presented.

Suggested Citation

  • John W. Chinneck, 1992. "Viability analysis: A formulation aid for all classes of network models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(4), pages 531-543, June.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:4:p:531-543
    DOI: 10.1002/1520-6750(199206)39:43.0.CO;2-K
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    References listed on IDEAS

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    1. F. Glover & J. Hultz & D. Klingman & J. Stutz, 1978. "Generalized Networks: A Fundamental Computer-Based Planning Tool," Management Science, INFORMS, vol. 24(12), pages 1209-1220, August.
    2. John W. Chinneck, 1990. "Formulating processing network models: Viability theory," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 245-261, April.
    3. John W. Chinneck & Erik W. Dravnieks, 1991. "Locating Minimal Infeasible Constraint Sets in Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 3(2), pages 157-168, May.
    4. Chou-Hong J. Chen & Michael Engquist, 1986. "A Primal Simplex Approach to Pure Processing Networks," Management Science, INFORMS, vol. 32(12), pages 1582-1598, December.
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    1. Pannell, David J. & Kingwell, Ross S. & Schilizzi, Steven, 1996. "Debugging Mathematical Programming Models: Principles and Practical Strategies," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 64(01), pages 1-15, April.
    2. Wiesława T. Obuchowska, 2015. "Irreducible Infeasible Sets in Convex Mixed-Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 747-766, September.
    3. Chinneck, J. W. & Moll, R. H. H., 1995. "Processing network models for forest management," Omega, Elsevier, vol. 23(5), pages 499-510, October.
    4. Draman, Murat & Kuban Altinel, I & Bajgoric, Nijaz & Tamer Unal, Ali & Birgoren, Burak, 2002. "A clone-based graphical modeler and mathematical model generator for optimal production planning in process industries," European Journal of Operational Research, Elsevier, vol. 137(3), pages 483-496, March.

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