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Development of a Fuzzy-Boundary Interval Programming Method for Water Quality Management Under Uncertainty

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Abstract

This study develops a fuzzy-boundary interval programming (FBIP) method for tackling dual uncertainties expressed as crisp intervals and fuzzy-boundary intervals. An interactive algorithm and a vertex analysis approach are proposed for solving the FBIP model and solutions with α-cut levels have been generated. FBIP is applied to planning water quality management of Xiangxi River in the Three Gorges Reservoir Region, China. Biological oxygen demand (BOD), total nitrogen (TN), and total phosphorus (TP) are selected as water quality indicators to determine the pollution control strategies. Results reveal that the highest discharge of BOD is observed at the Baishahe chemical plant, among all point and nonpoint sources; crop farming is the main nonpoint source with the excessive nitrogen loading due to too much uses of livestock manures and chemical fertilizers; phosphorus discharge derives mainly from point sources (i.e. chemical plants and phosphorus mining companies). Abatement of pollutant discharges from industrial and agricultural activities is critical for the river pollution control; however, the implementation of management practices for pollution control can have potentials to affect the local economic income. These findings can help generate desired decisions for identifying various industrial and agricultural activities in association with both maximizing economic income and mitigating river-water pollution.

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Abbreviations

i:

Chemical plant, 1 = Gufu (GF), 2 = Baishahe (BSH), 3 = Pingyikou (PYK), 4 = Liucaopo (LCP), 5 = Xiangjinlianying (XJLY)

j:

Agricultural zone, and j =1, 2, 3, 4

k:

Main crop, 1= citrus, 2 = tea, 3 = wheat, 4 = potato, 5 = rapeseed, 6 = alpine rice, 7 = second rice, 8 = maize, 9 = vegetables

p:

Phosphorus mining company; 1 = Xinglong (XL) 2 = Xinghe (XH), 3 = Xingchang (XC), 4 = Geping (GP), 5 = Jiangjiawan (JJW), 6 = Shenjiashan (SJS)

r:

Livestock, 1 = pig, 2 = ox, 3 = sheep, 4 = domestic fowls

s:

Town, 1 = Gufu, 2 = Nanyang, 3 = Gaoyang, 4 = Xiakou

t:

Planning time period, 1 = dry season, 2 = wet season

Lt :

Length of period (day)

BC ±it :

Net benefit from chemical plant i in period t (RMB¥/t)

PLC ±it :

Production level of chemical plant i in period t (t/day)

BP ±pt :

Average benefit for per unit phosphate ore (RMB¥/t)

PLM ±pt :

Production level of phosphorus mining company p during period t (t/day)

BW ±st :

Net benefit from water supply to municipal uses (RMB¥/m3)

QW ±st :

Quantity of water supply to town s in period t (m3/day)

\( \tilde{{\mathrm{CY}}_{\mathrm{jkt}}^{\pm }} \) :

Yield of crop k planted in agricultural zone j during period t (t/ha)

BA ±jkt :

Average benefit for agricultural product (RMB¥/t)

PA ±jkt :

Planning area of crop k in agricultural zone j during period t (ha)

BL ±r :

Average benefit from livestock r (RMB¥/unit)

NL ±r :

Number of livestock r in the study area (unit)

WC ±it :

Wastewater generation rate of chemical plant i during period t (m3/t)

CC ±it :

Wastewater treatment cost of chemical plant i during period t (RMB¥/m3)

FW ±it :

Water consumption of per unit production of chemical plant i during period Rt (m3/t)

WSP ±t :

Price for industrial water supply (RMB¥/m3)

GT ±st :

Wastewater generation rate at town s during period t (m3/m3)

CT ±st :

Cost of municipal wastewater treatment (RMB¥/m3)

CM ±jt :

Cost of manure collection/disposal in agricultural zone j during period t (RMB¥/t)

CF ±jt :

Cost of purchasing fertilizer in agricultural zone j during period t (RMB¥/t)

AM ±jkt :

Amount of manure applied to agricultural zone j with crop k during period t (t)

AF ±jkt :

Amount of fertilizer applied to agricultural zone j with crop k during period t (t)

WSC ±t :

Price for agricultural water supply (RMB¥/ha)

TPC ±st :

Capacity of wastewater treatment capacity (WTPs) (m3/day)

TPD ±it :

Capacity of wastewater treatment capacity (chemical plants) (m3/day)

IC ±it :

BOD concentration of raw wastewater from chemical plant i in period t (kg/m3)

η ±BOD,it :

BOD treatment efficiency in chemical plant i during period t (%)

ABC ±it :

Allowable BOD discharge for chemical plant i in period t (kg/day)

BM ±st :

BOD concentration of municipal wastewater at town s during period t (kg/m3)

η '  ±BOD,st :

BOD treatment efficiency of WTPs at town s during period t (%)

\( \tilde{{\mathrm{ABW}}_{\mathrm{st}}^{\pm }} \) :

Allowable BOD discharge for WTPs at town s during period t (kg/day)

AML ±rt :

Amount of manure generated by livestock r during period t [t/ (unit·day-1)]

AMH ±t :

Amount of manure generated by humans [t/ (unit·day-1)]

RP ±t :

Total rural population in the study area during period t (unit)

MS ±t :

Manure loss rate in period t (%)

ε ±NM :

Nitrogen content of manure (%)

ACW ±t :

Wastewater generation of per capita water consumption during period t [m3/ (unit·day-1)]

DNR ±t :

Dissolved nitrogen concentration of rural wastewater during period t (t/m3)

ANL ±t :

Maximum allowable nitrogen loss from rural life section in period t (t)

NS ±jk :

Nitrogen content of soil in agricultural zone j planted with crop k (%)

SL ±jkt :

Average soil loss from agricultural zone j planted with crop k in period t (t/ha)

RF ±jkt :

Runoff from agricultural zone j with crop k in period t (mm)

DN ±jkt :

Dissolved nitrogen concentration in runoff from agricultural zone j planted with crop k in period t (mg/L)

MNL ±jt :

Maximum allowable nitrogen loss in agricultural zone j during period t (t/ha)

TA ±jt :

Tillable area of agricultural zone j during period t (ha)

PCR ±it :

Phosphorus concentration of raw wastewater from chemical plant i in period t (kg/m3)

η ±TP,it :

Phosphorus treatment efficiency in chemical plant i in period t (%)

ASC ±it :

Amount of slag discharged by chemical plant i in period t (kg/t)

SLR ±it :

Slag loss rate due to rain wash in chemical plant i during period t (%)

PSC ±it :

Phosphorus content in slag generated by chemical plant i in period t (%)

\( \tilde{{\mathrm{APC}}_{\mathrm{it}}^{\pm }} \) :

Allowable phosphorus discharge for chemical plant i in period t (kg/day)

ε ±PM :

Phosphorus content of manure (%)

DPR ±t :

Dissolved phosphorus concentration of rural wastewater during period t (t/m3)

APL ±t :

Maximum allowable phosphorus loss from rural life during period t (t)

PCM ±st :

Phosphorus concentration of municipal wastewater at town s in period t (kg/m3)

η ±TP,st :

Phosphorus treatment efficiency of WTP at town s in period t (%)

APW ±st :

Allowable phosphorus discharge for WTP at town s in period t (kg/day)

WPM ±pt :

Wastewater generation from phosphorus mining company p in period t (m3/t)

MWC ±pt :

Phosphorus concentration of wastewater from mining company p in period t (kg/ m3)

η ±TP,pt :

Phosphorus treatment efficiency in mining company p (%)

ASM ±pt :

Amount of slag discharged by mining company p during period t (kg/t)

PCS ±pt :

Phosphorus content in generated slag (%)

SLW ±pt :

Slag loss rate due to rain wash (%)

\( \tilde{{\mathrm{APM}}_{\mathrm{pt}}^{\pm }} \) :

Allowable phosphorus discharge for mining company p during period t (kg/day)

PS ±jk :

Phosphorus content of soil in agricultural zone j planted with crop k (%)

SL ±jkt :

Average soil loss from agricultural zone j planted with crop k in period t (t/ha)

DP ±jkt :

Dissolved phosphorus concentration in runoff from agricultural zone j with crop k (mg/L)

MPL ±jt :

Maximum allowable phosphorus loss in agricultural zone j during period t (t/ha)

MSL ±jt :

Maximum allowable soil loss agricultural zone j in period t (t/ha)

NVF ±t :

Nitrogen volatilization/denitrification rate of fertilizer in period t (%)

NVM ±t :

Nitrogen volatilization/denitrification rate of manure in period t (%)

ε ±NF :

Nitrogen content of fertilizer (%)

ε ±PF :

Phosphorus content of fertilizer (%)

ε ±NM :

Nitrogen content of manure (%)

ε ±PM :

Phosphorus content of manure (%)

NR ±jkt :

Nitrogen requirement of agricultural zone j with crop k during period t (t/ha)

PR ±jkt :

Phosphorus requirement of crop k in agricultural zone j during period t (t/ha)

TAH ±jt :

Dry farmland of agricultural zone j during period t (ha)

TAS ±jt :

Paddy farmland of agricultural zone j during period t (ha)

MFP ±t :

The government requirement for minimum area of farmland during period t (ha)

PLC ±it, min :

Minimum production level of chemical plant i in period t (t/day)

PLC ±it, max :

Maximum production level of chemical plant i in period t (t/day)

NL ±r, min :

Minimum number of livestock r in the study area (unit)

NL ±r, max :

Maximum number of livestock r in the study area (unit)

QW ±st, min :

Minimum quantity of water supply to town s in period t (m3/day)

QW ±st, max :

Maximum quantity of water supply to town s in period t (m3/day)

PLM ±pt, min :

Minimum production level of phosphorus mining company p during period t (t/day)

PLM ±pt, max :

Maximum production level of phosphorus mining company p during period t (t/day)

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Acknowledgments

This research was supported by the National Natural Science Foundation (51225904 and 51190095), the 111 Project (B14008), and the Program for Innovative Research Team in University (IRT1127). The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

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Authors and Affiliations

  1. MOE Key Laboratory of Regional Energy Systems Optimization, S-C Resources and Environmental Research Academy, North China Electric Power University, Beijing, 102206, China

    J. Liu, Y. P. Li & G. H. Huang

  2. Faculty of Engineering and Applied Sciences, University of Toronto, Toronto, ON, M5S 1A4, Canada

    S. Nie

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  1. J. Liu
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Correspondence to Y. P. Li.

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Liu, J., Li, Y.P., Huang, G.H. et al. Development of a Fuzzy-Boundary Interval Programming Method for Water Quality Management Under Uncertainty. Water Resour Manage 29, 1169–1191 (2015). https://doi.org/10.1007/s11269-014-0867-9

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