Robust Optimization for Water Quality Management under Uncertainty

Nguyen Thi Huynh Nga

School of Civil and Environmental Engineering, Nanyang Technological University, Nanyang Avenue, Singapore

Qin Xiao Sheng

School of Civil and Environmental Engineering, Nanyang Technological University, Nanyang Avenue, Singapore

Robust optimization was applied to solve the water quality management problem under uncertainty. The study case included four industrial plants which discharge waste water into the river system. The treatment efficiency for CBOD and NBOD were determined by the robust optimization model. To demonstrate the effectiveness of robust optimization in water quality management, the total operational cost function is adopted and applied in the robust model framework. Operational variables are treatment efficiencies of carbonaceous biological oxygen demand (CBOD) and nitrogenous biological oxygen demand (NBOD). These are called design variables and they are independent with uncertain parameters and cannot be adjusted when specific uncertain parameters are observed.

In the Changsha section of Xiangjiang River in China, there are four discharge points from Leatheroid plant, Paper mill, Textile plant, and Chemical plant. The waste water flow rates from each industry fluctuate with their probabilities. The cost function depends on the waste water flow rates, and the treatment efficiency of CBOD and NBOD. To tackle the uncertainties and to minimize operational cost for each scenario, robust optimization is applied to find the treatment efficiency of CBOD, NBOD and penalties due to constraints’ violation. The model is restrained by the effluent standard and the surface water quality standard of BOD and DO. In waste water treatment, water quality management is as important as development of innovative technologies because one of the ultimate concerns is the cost. Therefore, this study does not focus on the technologies, but rather addresses the management of the operational variables and uncertainties to achieve the minimum total operational cost. At the same time, it also proposes solutions complying with environmental standards.

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