Inexact ${\mathrm{m}}_{\uplambda }$ fuzzy chance-constrained programming of booster chlorination for water distribution system under uncertainty

Abstract

To sustain water quality in water distribution system (WDS), disinfectant generally chlorine is boosted to water distribution system. However, the concentration of chlorine should be limited to acceptable scope. The upper bound of the scope is set for preventing the occurrence of disinfectant byproduct, which is harmful to human health. The lower bound of the scope is set for controlling the growth of microorganism as well as reducing the cost. As such, the optimization model was applied to solve the water quality issue in WDS. However, in WDS, chlorine decays and varies with time and space, affected by pipe material, temperature, pH value, and chlorine injection. Therefore, in this paper, an inexact ${\mathrm{m}}_{\uplambda }$ fuzzy chance-constrained programming (IMFCCP) model was proposed to optimize the chlorine injection to maintain chlorine in WDS at an acceptable level with consideration of uncertainty in water quality simulation. The results indicated that the upper bounds, the lower bounds, and intervals of the injection mass increased with preference parameter λ, which means that the results are more unreliable with higher preference parameter λ. However, the effect of reliability level ζ on the injection mass is determined by the relationship between the preference parameter λ and reliability level ζ. In case of $\uplambda \le {\upzeta }_{\mathrm{U}}={\upzeta }_{\mathrm{L}}$, the effect is not more significant than the case of $\uplambda >{\upzeta }_{\mathrm{U}}={\upzeta }_{\mathrm{L}}$. The results can help managers determine the injection strategy under uncertainty.