A mixed integer fuzzy-interval credibility-constrained programming for booster optimization in water distribution system under uncertainty

Abstract

Generally, boosters should be placed in water distribution system (WDS) to preserve the required residual disinfectant concentration at the far-ends. To cope with the fuzzy and interval uncertainties in the optimization of boosters, a mixed integer fuzzy-interval credibility-constrained programming (MIFICCP) model was formulated for disinfection booster design, location, and operation, which is solved by transforming the model into two linear sub-models. The results indicated that: The booster injection rates, operational injection costs (BCI), and booster capital costs (BCD) increased with the credibility levels; The lower and upper booster costs under fuzzy-interval set (FIS) with trapezoidal distribution are higher than FIS with triangular distribution for various credibility levels except for the credibility level of 0.5; With the increase of maximum booster number, the values of BCI decreased, the value of BCD increased, and the total costs may increase or decrease, which depend on the relative magnitude of BCI to the total costs. The results obtained can give more information for managers to make decisions on the booster strategies to uniform chlorine distribution along WDS scientifically and reasonably, especially under dual uncertainties of fuzzy and interval.