References and Bibliography 581
element consists of selecting values for the diameter of the pipe, the slope of the
pipe, and the mean depth of the pipe (Di,hi− 1 , andhi) The construction cost of an.
element,Ri, includes cost of the pipe, cost of the upstream manhole, and earthwork
related to excavation, backfilling, and compaction. Some of the constraints can be stated
as follows:
1.The pipe must be able to discharge the specified flow.
2.The flow velocity must be sufficiently large.
3.The pipe slope must be greater than a specified minimum value.
4.The depth of the pipe must be sufficient to prevent damage from surface
activities.
The optimum design problem can be formulated and solved as a dynamic programming
problem.
References and Bibliography
9.1 R. S. Schechter,The Variational Method in Engineering, McGraw-Hill, New York,
1967.
9.2 R. E. Bellman, Dynamic Programming, Princeton University Press, Princeton, NJ,
1957.
9.3 G. Hadley,Nonlinear and Dynamic Programming, Addison-Wesley, Reading, MA, 1964.
9.4 L. S. Lasdon,Optimization Theory for Large Systems, Macmillan, New York, 1970.
9.5 B. G. Neal,Structural Theorems and Their Applications, Pergamon Press, Oxford, UK,
1964.
9.6 R. E. Bellman and S. E. Dreyfus,Applied Dynamic Programming, Princeton University
Press, Princeton, NJ, 1962.
9.7 G. L. Nemhauser,Introduction to Dynamic Programming, Wiley, New York, 1966.
9.8 S. Vajda,Mathematical Programming, Addison-Wesley, Reading, MA, 1961.
9.9 O.L.R. Jacobs,An Introduction to Dynamic Programming, Chapman & Hall, London,
1967.
9.10 R. J. Aguilar,Systems Analysis and Design in Engineering, Architecture, Construction
and Planning, Prentice-Hall, Englewood Cliffs, NJ, 1973.
9.11 A. C. Palmer, Optimal structure design by dynamic programming,ASCE Journal of the
Structural Division, Vol. 94, No. ST8, pp. 1887–1906, 1968.
9.12 D. J. Sheppard and A. C. Palmer, Optimal design of transmission towers by dynamic
programming,Computers and Structures, Vol. 2, pp. 455–468, 1972.
9.13 J. A. S. Ferreira and R. V. V. Vidal, Optimization of a pump–pipe system by dynamic
programming,Engineering Optimization, Vol. 7, pp. 241–251, 1984.
9.14 G. A. Walters and A. B. Templeman, Non-optimal dynamic programming algorithms
in the design of minimum cost drainage systems,Engineering Optimization, Vol. 4,
pp. 139–148, 1979.
9.15 J. S. Gero, P. J. Sheehan, and J. M. Becker, Building design using feedforward nonserial
dynamic programming,Engineering Optimization, Vol. 3, pp. 183–192, 1978.
9.16 J. S. Gero and A. D. Radford, A dynamic programming approach to the optimum lighting
problem,Engineering Optimization, Vol. 3, pp. 71–82, 1978.
