Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-29T09:58:18.058Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuous-time quadratic cost flow problems with applications to water distribution networks

Published online by Cambridge University Press:  17 February 2009

A. T. Ernst
A. T. Ernst
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands WA 6009.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper deals with a class of network optimization problems in which the flow is a function of time rather than static as in the classical network flow problem, and storage is permitted at the nodes. A solution method involving discretization will be presented as an application of the ASG algorithm. We furnish a proof that the discretized solution converges to the exact continuous solution. We also apply the method to a water distribution network where we minimize the cost of pumping water to meet supply and demand, subject to both linear and nonlinear constraints.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 4 , April 1996 , pp. 530 - 548
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Anderson, E. J. and Philpott, A. B., “A continuous-time network simplex algorithm”, Networks 19 (1989) 395–425.CrossRefGoogle Scholar
[2]Boland, N. L., Ernst, A. T., Goh, C. J. and Mees, A. I., “A faster version of the ASG algorithm”, Appl. Math. Utters 7 (1994) 23–27.Google Scholar
[3]Boland, N. L., Goh, C. J. and Mees, A. I., “An algorithm for solving quadratic network flow problems”, Appl. Math. Letters 4 (1991) 61–64.CrossRefGoogle Scholar
[4]Boland, N. L., Goh, C. J. and Mees, A. I., “An algorithm for non-linear network programming: implementation, results and comparisons”, J. Opl. Res. Soc. 42 (1992) 979–992.CrossRefGoogle Scholar
[5]Brebbia, C. A. and Ferrante, A. J., Computational hydraulics (Butterworths, London, 1983).Google Scholar
[6]Buie, R. N. and Abrham, J., “Numerical solutions to continuous linear programming problems”, Zeitschrift fur Open Res. 42 (1973) 107–117.Google Scholar
[7]Collins, M., Cooper, L., Helgason, R., Kennington, J. and Blanc, L. Le, “Solving pipe network analysis problems using optimization techniques”, Mang. Sci. 24 (1978) 747–760.CrossRefGoogle Scholar
[8]Ford, L. R. and Fulkerson, D. R., Flows in networks (Princeton University Press, Princeton, 1962).Google Scholar
[9]Markowitz, H. M., Portfolio selection: efficient diversification of investments (Wiley, New York, 1959).Google Scholar
[10]Pullan, M., Separated continuous linear programs: theory and algorithms, Ph. D. Thesis, Judge Institute of Management Studies, University of Cambridge, 1992.Google Scholar
[11]Teo, K. L., Goh, C. J. and Wong, K. H., A unified computational approach to optimal control problems (Wiley, New York, 1991).Google Scholar