Design of engineering systems using stochastic decomposition: Water supply planning application

To effectively design engineering systems, the future operation of the system which usually involves many uncertainties must be considered. A two-stage stochastic programming formulation can aid in satisfying this requirement. The first stage of this formulation represents the design criteria at the present time when a decision must be made. The second stage represents the future operation or the system response to the design where other actions (recourse decisions) are to be made after observing the random input. To solve this type of problem, the Regularized Stochastic Decomposition algorithm, which allows the consideration of continuous random variables, was employed and extensions to better handle real engineering problems were investigated. The algorithm is applied to a regional water supply problem that seeks the optimal design capacities of water treatment plants, secondary and tertiary wastewater treatment plants, and recharge facilities while meeting future demands. Results are generated based on different forms of uncertainties for both linear and nonlinear first-stage objective functions. The advantages of using stochastic programming in engineering decision making are evaluated.