Surface water quality management using a multiple‐realization chance constraint method

Abstract

Abstract. Traditional chance-constrained programming (CCP) and simulationoptimization methods of incorporating input information uncertainty in pollution management models are unsuitable for complex river systems with several critical water quality segments. Using the CCP method, characterization of the joint probability distribution of coefficients of the management model is often difficult because stream information is limited and the model formulation is generally difficult to understand and solve. For the simulation-optimization method most of the solutions produced are inferior. The multiple realization model, which includes several scenarios of design conditions simultaneously in an optimization model, overcomes such weaknesses by not requiring the joint probability distribution of the stochastic model coefficients and by producing noninferior solutions. Heuristic and neural network techniques are developed to reduce the computational time required to solve the multiple realization model, through identification and utilization of only potentially important stream and water quality information that influence the optimal solution. These techniques are applied to develop trade-off relationships between waste treatment cost and reliability of achieving dissolved oxygen objectives for an example river basin. Results show that the heuristic technique is computationally efficient when <1000 realizations are included in the model, while the neural network method is suitable when several thousand realizations are needed to adequately represent the stochastic water quality system.

Solving Chance-Constrained Stochastic Programs via Sampling and Integer Programming

“…In addition to the facility location, telecommunication, and finance examples cited earlier, chance-constrained models have been used in numerous other applications, including production planning (Murr and Prékopa [22], Lejeune and Ruszczyński [16]), chemical processing (Henrion et al [15], Henrion and Möller [14]), and water resources management (Prékopa and Szántai [29], Takyi and Lence [31]). See Prékopa [28] for a background and an extensive list of references.…”

Non-Uniform Flow Effect on Optimal Waste Load Allocation in Rivers

“…Camp (1963) and Dobbins (1964) proposed modifications to the Streeter-Phelps (S-P) model to include sedimentation or scour rate, algal and benthic oxygen demands, and a non-point source input rate. The S-P model with Camp-Dobbins extensions has also been used by a number of researchers (Ellis, 1987;Fujiwara et al, 1988;Takyi and Lence, 1999) in water quality management models. One of the main advantages of using the S-P model in water quality management studies is that it is possible to use the Linear Programming technique to solve the optimization problem.…”

Fuzzy waste load allocation model: a multiobjective approach

“…There are three widely adopted approaches for addressing randomness in water-quality management models (Takyi & Lence 1999). These are (i) chance-constrained optimization (Lohani & Thanh 1978, 1979Burn & McBean 1985Ellis 1987;Fujiwara et al 1986Fujiwara et al , 1987, (ii) combined simulation -optimization (Burn 1989;doi: 10.2166/hydro.2010 Takyi & Lence 1994) and (iii) multiple realization approach (Burn & Lence 1992;Takyi & Lence 1999).…”