Fuzzy credibility–constrained quadratic optimization for booster chlorination of the water distribution system under uncertainty

To keep chlorine concentration at acceptable levels, chlorine is usually injected into the water distribution system (WDS). To protect the health of human beings, the chlorine concentration at consumers’ nodes should be kept at appropriate levels. However, these levels are difficult to determine due to the presence of fuzzy uncertainties. To deal with fuzziness at both sides of the constraints in the optimization model of booster chlorination, we propose a fuzzy credibility–constrained quadratic programming (FCCQP) model with a consideration of credibility levels and weight coefficients. The proposed model is applied to two WDSs to obtain the booster cost under uncertain conditions. The results indicate that the booster cost increases with the credibility level for lower chlorine concentration ζL. In addition, the booster cost decreases with the weight coefficient w. The booster cost function curves along with the variation of weight coefficients are concave and convex for scenario 1 and scenario 2, respectively. These results can help managers to make informed decisions on disinfection injection under conditions of fuzzy uncertainties.