Fractional Stochastic Interval Programming for Optimal Low Impact Development Facility Category Selection under Uncertainty

Uncertainties in nature and human society influence low impact development (LID) facility category selection during LID facility optimization distribution, however the investigation of this area is seldom. There are still two problems with uncertainty which influence LID facility distribution 1) how uncertainty factors affect LID facility selection and 2) in the case of a number of LID facilities of multiple categories are to be set, how to construct the LID facility optimization distribution model for LID facility category selection under uncertainty. To handle the problems, this study develops a fractional stochastic interval programming model to process LID facility category selection under the influence of uncertainty. The model can either process multiple objectives via objective maximization and minimization or process the stochastic uncertainty and interval uncertainty. The study shows that the uncertainties which influence LID facility category selection exist in rainfall, infiltration rate, release coefficient, unit price and budget. and the study reveal that the key constraint of LID facility category selection is the uncertainty parameter characteristic of the LID facility, in which different parameters lead to various LID facility optimization schemes. Results of the model include a series of LID facility optimization distribution schemes in multiple scenarios.Results also provide a series of feasible schemes for decision makers, and the manager can select the most appropriate scheme according to water processing level or budget. The developed model could 1) identifying the uncertainty which impact the LID facility distribution. 2) processing the LID facility category selection under interval uncertainty and stochastic uncertainty during LID facility optimization distribution. The method can also be used to estimate the rationality of the LID facility optimization scheme. Moreover, the proposed method is universal and could be extended to other cases of LID facility category selection under uncertainty.