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Geometric programming with probabilistic decision variables

Published online by Cambridge University Press:  17 February 2009

T. R. Jefferson  and
C. H. Scott
T. R. Jefferson
Affiliation:
School of Mechanical and Industrial Engineering, University of N.S.W., P.O. Box 1, Kensington, N.S.W. 2033, Australia
C. H. Scott
Affiliation:
School of Mechanical and Industrial Engineering, University of N.S.W., P.O. Box 1, Kensington, N.S.W. 2033, Australia
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Abstract

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Here we consider a particular class of stochastic geometric programs in which the randomness occurs in the decision variables. Specifically we analyse a program in which we specify a joint normal probability for the dicision variables and require the constraint set to be satisfied in the chance constrained mode. A numerical example is given to illustrate the approach.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 2 , October 1980 , pp. 229 - 236
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Avriel, M. and Wilde, D. J., “Stochastic geometric programming”, in Proceedings of the Princeton Symposium on Mathematical Programming, Kuhn, H. W. ed. (Princeton, New Jersey: Princeton University Press, 1970).Google Scholar
[2]Charnes, A., Cooper, W. W. and Symonds, G. H., “Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil”, Management Science 4 (1958), 235–263.CrossRefGoogle Scholar
[3]Dembo, R. S., “Current state of the art of algorithms and computer software for geometric programming”, J.O.T.A. 26 (1978) 149–184.CrossRefGoogle Scholar
[4]Duffin, R. J., Peterson, E. L. and Zener, C., Geometric programming (New York: John Wiley and Sons, 1967).Google Scholar
[5]Hastings, C., Approximation for digital computers (Princeton, New Jersey: Princeton University Press, 1955).Google Scholar
[6]Jefferson, T. R., Geometric programming with an application to transportation planning (Ph.D. Dissertation, Northwestern University, 1972).Google Scholar
[7]Jefferson, T. R. and Scott, C. H., “Avenues of geometric programming”, N.Z. Operational Research 6 (1978), 109–136.Google Scholar
[8]Prekopa, A., “On probabilistic constrained programming”, in Proceedings of the Princeton Symposium on Mathematical Programming, Kuhn, H. W. ed. (Princeton, New Jersey: Princeton University Press, 1970).Google Scholar
[9]Rijckaert, M. J. and Martens, X. M., “Comparison of generalized geometric programming algorithms”, J.O.T.A. 28 (1978), 205–242.CrossRefGoogle Scholar
[10]Saima, V. L. N., Martens, X. M., Reklaitis, G. V. and Rijckaert, M. J., “A comparison of computational strategies, for geometric programs”, J.O.T.A. 28 (1978), 185–204.Google Scholar
[11]Sengupta, J. K., Stochastic programming (Amsterdam: North-Holland, 1972).Google Scholar
[12]Vajda, S., Probabilistic programming (New York: Academic Press, 1972).Google Scholar