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

Abstract

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.

Appendix

i :

the type i of LID facility

j :

the location site of LID facility

a _ij :

the characteristics of LID facility i on site j

b _ij :

the characteristics of LID facility i on site j

c _ij :

the characteristics of LID facility i on site j

d _ij :

the characteristics of LID facility i on site j

k _ij :

the unknown decision variable of the LID facility i on site j

r :

the bottom radius of percolation well

f _per :

permeability of percolation well

V _{retained. i} :

the retained rainwater in the LID facility i

V _{through. i} :

the rainwater that flows through the LID facility i

V _effluent :

the volume of effluent rainwater from the LID facility

f _per :

the permeability of percolation well

V _ij :

the effective storage of linear reservoir

re _ij :

The release coefficient of LID facility i on site j (unit:1/time)

V _ij :

The effective volume of LID facility i on site j

∆t :

The duration time of urban rainfall

C _r :

The rainwater pollutant contamination r

E _ijr :

The treated rainwater pollutant contamination r in LID facility i on site j

ε _ijr :

The pollution treatment efficiency of LID facility i on site j

k _ij :

The known variable, it means the capacity of the i − th type of LID facility at the j − th site, and the k_ij is predetermined and conforms to existing standard

P _ij :

The cost for each volume of the i − th type of LID facility at the j − th site

F _ij :

The fixed cost for installation of the i − th type of LID facility at the j − th siteindependent of the facility size.

x _ij :

The binary integer variable.

B :

The total budget

I _j :

the volume of rain water arrive at the j − th site

I _ctrl :

water control standard for retained rain water

TMDL _r :

The regulatory r − pollution concentration of rain water discharged from the district

Q :

the total volume of rain water discharged from the district

M _r :

the total pollution of urban rain water discharged from the district

F :

Infiltration rate of LID

h ₀ :

Surface ponding

K _sat :

Saturated hydraulic conductivity of soil surface

φ :

Soil suction at the wetting front

∆θ :

Difference between saturated moisture content and initial moisture