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Models and algorithms for multiple criteria linear cost network programs

Published online by Cambridge University Press:  17 February 2009

X. Q. Yang  and
C. J. Goh
X. Q. Yang
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands WA 6907, Australia.
C. J. Goh
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands WA 6907, Australia.
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Abstract

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In this paper, we discuss a general model for multiple criteria linear cost network flow problems. This model includes several classes of existing models in the operations research literature as special cases. Based on this model, a search algorithm for finding a feasible solution of the concurrent flow problem is suggested and illustrative numerical examples are given. This search algorithm is also extended to obtain a new algorithm for finding the efficient frontier of a multiple criteria linear program.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 4 , April 1999 , pp. 568 - 581
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Aneja, Y. P. and Nair, K. P. K., “Bicriteria transportation problem”, Management Science 25 (1979) 73–78.CrossRefGoogle Scholar
[2]Dantzig, G. B., Linear Programming and Extensions (Princeton University Press, Princeton, NJ, 1963).Google Scholar
[3]Evans, J. R. and Martin, K., “A note on feasible flows in lower-bounded multicommodity networks”, J. Open Res. Soc. 29 (1978) 923–927.CrossRefGoogle Scholar
[4]Geoffrion, A. M., “Strictly concave parametric programming, Part I: Basic theory”, Management Science 13 (1966) 244–253.CrossRefGoogle Scholar
[5]Goh, C. J. and Yang, X. Q., “Analytic efficient solution set for multi-criteria quadratic program”, European J. Oper. Res. 89 (1996) 483–491.Google Scholar
[6]Gondran, M. and Minoux, M., Graphs and Algorithms (Wiley-Interscience, New York, 1984).Google Scholar
[7]Kennington, J. L. and Helgason, R. V., Algorithms for Network Programming (Wiley, New York, 1980).Google Scholar
[8]Ruhe, G., Algorithmic Aspects of Flows in Networks (Kluwer Academic Publishers, London, 1991).CrossRefGoogle Scholar
[9]Sawaragi, Y., Nakayama, H. and Tanino, T., Theory of Multi-Objective Optimization (Academic Press, New York, 1985).Google Scholar
[10]Tung, C. T. and Chew, K. L., “A multicriteria pareto-optimal path algorithm”, European J. Oper. Res. 62 (1992) 203–209.CrossRefGoogle Scholar
[11]Yang, X. Q. and Goh, C. J., “Osn intersections of two particular convex sets”, J. Optimiz. Theory Appl. 89 (1996) 483–491.CrossRefGoogle Scholar
[12]Yu, P. L., Multiple-Criteria Decision Making - Concepts, Techniques, and Extensions (Plenum Press, 1985).CrossRefGoogle Scholar
[13]Yu, P. L. and Zeleny, M., “Linear multiparametric programming by multicriteria simplex methods”, Management Science 23 (1976) 159–170.Google Scholar