Abstract
We describe the use of network methods to aid model formulation and analysis, particularly when using certain approaches, notably GAMs or Structured Modeling. When mapping a relational description to an algebraic representation, it is desirable to check logical consistency, redundancy and forcing structures that may be present, Sometimes these could be purposeful, but often they reflect modeling errors. In either case it is useful to reveal these properties efficiently. Here we describe an algorithmic framework, based on topological sorting, which applies not only to mathematical programming modeling, but also to, rule-base management in an expert system.
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References
Aho, A.V., Garey, M.R., and Ullman, J.D., ‘The transitive reduction of a directed graph’, SIAM J. Comput. 1 (1972) 131–137.
Balinski, M.L., ‘On a selection problem’, Mgt. Sci. 17 (1970) 230–231.
Blair, C.E., Jeroslow, R.G., and Lowe, J.K., ‘Some results and experiments in programming techniques for propositional logic’, to appear in Comp. and OR.
Bramer, M.A., ‘Expert Systems: The vision and the reality’, in Research and Development in Expert Systems, M.A. Bramer (ed.), Cambridge University Press, 1985, pp. 1–12.
Ford, Jr. L.R. and Dulkerson, D.R., Flows in Networks, Princeton University Press, 1962.
Geoffrion, A.M., ‘Integrated modeling systems’, Computer Science in Economics and Management 2 (1989) 3–15 (this issue).
Glover, F., Klingman, D., Mote, J., and Whitman, D., ‘Comprehensive Evaluation and Enhancement of Maximum Flow Algorithms’, Applications of Management Science 3 (1983) 109–175.
Greenberg, H.J., Lundgren, J.R., and Maybee, J.S., ‘Inverting graphs of rectangular matrices’, Disc. Appl. Math. 8 (1984) 255–265.
Greenberg, H.J., Lundgren, J.R., and Maybee, J.S., ‘Digraph inversion’, University of Colorado.
Harary, F. Norman, R.Z. and Cartwright, D., Structural Models: An Introduction to the Theory of Directed Graphs, Wiley, 1965.
Jeroslow, R.G., ‘Computation-oriented reductions of predicate to propositional logic’, to appear in Dec. Supp. Systems.
Johnson, E.L., and Padberg, M.W., ‘Degree-two inequalities, clique facets, and biperfect graphs’, Annals Disc. Math. 16 (1982) 169–187.
Knuth, D.E., The Art of Computer Programming, Volume 1: Fundamental Algorithms, Addison-Welsey, Reading, MA, 1968.
Meeraus, A., ‘General Algebraic Modeling System,’ to appear.
Picard, J.C. ‘Maximal Closure of a Graph and Applications to Combinatorial Problems’, Mgt. Sci. 22 (1976) 1268–1272.
Rhys, J.M.W., ‘Shared fixed cost and network flows’, Mgt. Sci. 17 (1970) 200–207.
Sethi, R., ‘Testing for the Church-Rosser property’, J. ACM 21 (1974) 671–679.
Valdes, J., Tarjan, R.E. and Lawler, E.L., ‘The recognition of series parallel digraphs’, SIAM J. Comput. 11 (1982) 298–313.
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Glover, F., Greenberg, H.J. Logical testing for new approaches to mathematical programming modeling and analysis. Computer Science in Economics and Management 2, 49–64 (1989). https://doi.org/10.1007/BF00454704
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DOI: https://doi.org/10.1007/BF00454704