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Flow ratio design of primal and dual network models of distribution

Published online by Cambridge University Press:  17 February 2009

G. A. Mohr
G. A. Mohr
Affiliation:
International Arts and Sciences College, 68 Tulip Grove, Cheltenham VIC 3192, Australia.
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Abstract

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The finite element method can be used to provide network models of distribution problems. In the present work ‘flow ratio design’ is applied to such models to obtain approximate minima and maxima for both the primal and dual FEM models. The resulting primal MIN and dual MAX solutions are equal to or close to the exact solutions but, intriguingly, the primal MAX and dual MIN solutions are approximately equal to an intermediate saddle point solution.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 4 , April 2004 , pp. 573 - 583
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Bartol, K. M. and Martin, D. C., Management, 2nd ed. (McGraw-Hill, New York, 1994).Google Scholar
[2]Gallagher, R. H. and Zienkiewicz, O. C., Optimum structural design (Wiley, London, 1973).Google Scholar
[3]Gilmour, P., Logistics management: an Australian framework (Longman Cheshire, Melbourne, 1993).Google Scholar
[4]Hillier, F. S. and Lieberman, G. J., Introduction to operations research, 3rd ed. (Holden-Day, Oakland CA, 1980).Google Scholar
[5]Kirsch, U., “On singular topologies in optimal structural design”, Structural Optimiz. 2 (1990) 133–142.CrossRefGoogle Scholar
[6]Michell, A. G. M., “The limits of economy in frame structures”, Phil. Mag. Ser. 68 (1904) 589–597.CrossRefGoogle Scholar
[7]Mohr, G. A., “Elastic and plastic predictions of slab reinforcement requirements”, Civ. Engrg Trans Inst. Engrs Aust. CE21 (1979) 16–20.Google Scholar
[8]Mohr, G. A., “Finite element formulation by nested interpolations: application to a quadrilateral thin plate bending element”, Civ. Engrg Trans Inst. Engrs Aust. CE25 (1983) 211–218.Google Scholar
[9]Mohr, G. A., Finite elements for solids, fluids, and optimization (Oxford University Press, Oxford, 1992).CrossRefGoogle Scholar
[10]Mohr, G. A., “Optimization of critical path models using finite elements”, Civ. Engng Trans Inst. Engrs Aust. CE36 (1994) 123–126.Google Scholar
[11]Mohr, G. A., “Finite element modeling of distribution problems”, Appl. Math. Comput. 105 (1999) 69–76.Google Scholar
[12]Mohr, G. A., “Optimization of primal and dual network models of distribution”, Comp. Meth. Appl. Mech. Engng 188 (2000) 135–144.CrossRefGoogle Scholar
[13]Mohr, G. A., “The patch method: a nodal equation method based on FEM”, Adv. Engng Software 32 (2001) 327–335.CrossRefGoogle Scholar
[14]Mohr, G. A., Finite elements and optimization for modern management (International Publishers, Melbourne, 2002).Google Scholar
[15]Mohr, G. A., “Finite element modeling and optimization of traffic flow networks”, Road and Transport Research (submitted).Google Scholar
[16]Rozvany, G. I. N. and Gollub, W., “Michell layouts for various combinations of line supports. Part 1”, Int. J. Mech. Sci. 32 (1990) 1021–1043.CrossRefGoogle Scholar
[17]Schroeder, R. G., Operations management, 3rd ed. (McGraw-Hill, New York, 1989).Google Scholar
[18]Slaybough, C. J., “Pareto's law and modern management”, Management Services (03–04 1967).Google Scholar
[19]Spillers, W. R. and Al-Banna, S., “Optimization using iterative design techniques”, Comput. Struct. 3 (1973) 1263–1270.CrossRefGoogle Scholar