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Title: DESIGN OF ENGINEERING SYSTEMS USING STOCHASTIC DECOMPOSITION: WATER SUPPLY PLANNING APPLICATION

Authors
 Elshorbagy, W - UNIV. OF ARIZ. Yakowitz, Diana Lansey, K - UNIV. OF ARIZ.

 Submitted to: Journal of Engineering Optimization Publication Type: Proceedings Publication Acceptance Date: October 8, 1996 Publication Date: N/A Interpretive Summary: To efficiently design many engineering systems, the future operation of the system which usually has many uncertain factors must be considered. A mathematical programming model in two-stages can satisfy this requirement. The first stage of this formulation is the design stage at the present time when a decision must be made subject to some constraints on the design. The second stage represents the future operation or response to the design where other actions are to be taken after future random input. To solve this type of problem, a mathematical algorithm known as Regularized Stochastic Decomposition was modified and employed to better handle real engineering problems. In this paper the resulting algorithm is applied to a regional water supply problem that seeks the best design sizes of recharge facilities, water and secondary wastewater plants, and tertiary wastewater treatment plants to meet future demands. The advantages of using gthis design approach in engineering applications along with other problems are evaluated. Results for the example indicate that a savings of 5% can be obtained by considering this formulation. Other results are discussed for different forms of uncertainties and objectives. Technical Abstract: To efficiently design many engineering systems, the future, uncertain, operation of the system must be considered. A two-stage stochastic programming formulation can satisfy this requirement. The first stage of this formulation represents the design criteria at the time when the decision to build must be made. The second stage represents the future operation of the system where other actions (recourse decisions) are to be made after observing the random input. To solve this type of problem, the Regularized Stochastic Decomposition (RSD) algorithm was employed and modified to better handle real engineering problems. The resulting algorithm is applied to a regional water supply problem that seeks the optimal design capacities of recharge facilities and, water, and secondary wastewater, and tertiary wastewater treatment plants while meeting future demands. Results are shown for different forms of uncertainties and objectives. One case indicates a 5% improvement by using the stochastic approach. The advantages of using this design approach in engineering applications and other problems are evaluated.