INEXACT OPTIMIZATION MODELING
FOR WATER QUALITY MANAGEMENT
IN XINGSHAN COUNTY OF THE XIANGXI RIVER BASIN
A Thesis
Submitted to the Faculty of Graduate Studies and Research
in Partial Fulfillment of the Requirements
for the Degree of
Master of Applied Science
in Environmental System Engineering
University of Regina
By
Zhong Li
Regina, Saskatchewan
January, 2012
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FACULTY OF GRADUATE STUDIES AND RESEARCH
SUPERVISORY AND EXAMINING COMMITTEE
Zhong Li, candidate for the degree of Master of Applied Science in Environmental Systems Engineering, has presented a thesis titled, Inexact Optimization Modeling for Water Quality Management in Xingshan County of the Xiangxi River Basin, in an oral examination held on December 19, 2011. The following committee members have found the thesis acceptable in form and content, and that the candidate demonstrated satisfactory knowledge of the subject material.
External Examiner: Dr. Amr Henni, Industrial Systems Engineering
Supervisor: Dr. Guo H. Huang, Environmental Systems Engineering
Committee Member: Dr. Shahid Azam, Environmental Systems Engineering
Committee Member: Dr. Tsun Wai Kelvin Ng, Environmental Systems Engineering
Chair of Defense: Dr. Rod Dolmage, Faculty of Education ABSTRACT
The Three Gorges Reservoir (TGR), the largest reservoir in China, has confronted the local development with many environmental challenges. Xingshan County, located in vicinity of the TGR, is one of the areas that have been significantly influenced. It lies within the middle reaches of the Xiangxi River, with a total area of 2,327 km •y. In recent years, changes to the County including rapid economic development and interventions of the TGR have brought about many pressing water quality problems. A sustainable development strategy is urgently needed to mitigate water deterioration and sustain economic growth. However, water quality systems are often associated with various uncertainties, which would strongly affect the related decision making processes.
Therefore, this research aims to provide scientific support for achieving sustainable development strategy for the County under uncertainties, with a focus on integrated water quality management.
An inexact two-stage stochastic programming water quality management (ITSP-WQM) model is established for the County. Various environmental, resource, and economic factors are integrated within the optimization framework. Interval solutions are obtained, and four scenarios are analyzed to reflect tradeoffs between the predefined economic targets and the associated environmental penalties. Moreover, in order to further tackle the fuzzy information, an inexact two-stage stochastic credibility constrained programming water quality management (ITSCCP-WQM) model is developed. The proposed model extends upon the ITSP-WQM model by introducing credibility
i constrained programming, and thus, fuzziness of the pollution load capacities can be reflected. Interval solutions that contain a spectrum of potential pollution abatement options are obtained. Sensitivity analysis regarding the total phosphorus control is conducted.
The proposed models can effectively communicate uncertainties expressed as intervals, probabilistic and possibilistic distributions into the optimization processes, and generate mitigation schemes with varied levels of system-failure risk. Results indicate that no pollution control would be required when the incoming water quality is Grade I. However, when the incoming water quality degrades to Grade II or III, certain mitigation should be conducted. This study is a first attempt to apply optimization approaches into water quality management at the watershed level in the TGR. It can provide scientific bases for regional sustainable development and planning. ACKNOWLEDGEMENT
First and foremost, I would like to express my utmost gratitude to my supervisor, Dr.
Gordon Huang, for his constant support and patient guidance during my graduate study.
His wisdom, knowledge and experience have been exceedingly helpful with respect to the successful competition of my thesis. I will forever treasure the learning experiences I enjoyed over the past two years.
I gratefully acknowledge the Faculty of Graduate Studies and Research, the Faculty of
Engineering, and the China Scholarship Committee for their financial support during my studies at the University of Regina.
My further appreciation goes to Dr. Yanpeng Cai, Dr. Qian Tan, Dr. Yimei Zhang, and Dr.
Hua Zhang for their constructive suggestions regarding my research, as well as to Dr.
Yuling Huang, Dr. Qianguo Lin, Dr. Xianghui Nie, and Dr. Xiaodong Zhang for their valuable advice. I would like to extend a thank you to Mr. Wei Sun, Mr. Renfei Liao, Mr.
Gongchen Li, Ms. Zhu Hua, Mr. Chunjiang An, Ms. Jia Wei, Mr. Guanhui Cheng, Mr.
Yurui Fan, Mr. Yao Yao, Mr Yang Zhou, Mr. Shuo Wang and the many other dearest friends from the Institute for Energy, Environment and Sustainable Communities at the
University of Regina for their kind help.
Finally, I would like to thank my parents, Mr. Bulong Li and Ms. Fenli Zhang, for their unconditional love and support. Their love means the world to me.
iii TABLE OF CONTENTS
ABSTRACT i ACKNOWLEDGEMENT iii LIST OF TABLES vii LIST OF FIGURES viii CHAPTER 1. INTRODUCTION 1 CHAPTER 2. LITERATURE REVIEW 6 2.1. Water Quality Management in the Xiangxi River Basin 6 2.2. Mathematical Programming Approaches to Water Quality Management under Uncertainties 8 2.3. Two-stage Stochastic Programming 11 2.4. Credibility Constrained Programming 12 2.5. Summary 14 CHAPTER 3. STUDY AREA 17 3.1. Study Area 17 3.1.1. Location 17 3.1.2. Geological and Geomorphologic Condition 20 3.1.3. Hydrological and Climatic Conditions 20 3.1.4. Vegetation Conditions 21 3.1.5. Socio-Economic Conditions 21 3.2. Water Quality Problems 22 3.2.1 Point Source Pollution 29 3.2.2 Non-point Source Pollution 30 CHAPTER 4. AN INEXACT TWO-STAGE STOCHASTIC PROGRAMMING WATER QUALITY MANAGEMENT MODEL 32 4.1. Background 32 4.2. Methodology ...... 34 4.2.1. Two-stage Stochastic Programming 34 4.2.2. Inexact Two-stage Stochastic Programming 36
iv 4.3. Model Development 39 4.3.1. Model Configuration 39 4.3.2. Model Formulation 41 4.3.3. Scenario Development 50 4.4. Data Collection 51 4.5. Result Analysis 59 4.5.1. Solutions under Scenario 1 62 4.5.2. Comparisons of the Results under Scenarios 1 to 4 77 4.6. Summary 93 CHAPTER 5. AN INEXACT TWO-STAGE STOCHASTIC CREDIBILITY CONSTRAINED PROGRAMMING WATER QUALITY MANAGEMENT MODEL 96 5.1. Background 96 5.2. Methodology 99 5.2.1. Credibility 99 5.2.2. Inexact Credibility Constrained Programming 103 5.2.3. Inexact Two-stage Credibility Constrained Programming 107 5.3. Model Development 110 5.4. Data Collection 115 5.4.1. Basic Data 115 5.4.2. Right-hand Side Value of the Fuzzy Constraints 116 5.4.3. Credibility Level 116 5.5. Result Analysis 119 5.5.1. Results of the ITSCCP-WQM Model 119 5.5.2. Comparison of the ITSP-WQM Model and the ITSCCP-WQM Model 129 5.6. Summary 140 CHAPTER 6. CONCLUSIONS 142 6.1. Summary 142 6.2. Research Achievements 143 6.3. Recommendations for Future Research 144
V REFERENCES 146 APPENDICES 162 Appendix A - Annual targets of the economic activities under Scenarios 1 to 4 in the ITSP-WQM model 162 Appendix B - ITSP-WQM model Solutions to Decision Variables under Scenario 1 166 Appendix C - ITSP-WQM model Solutions to Decision Variables under Scenario 2 170 Appendix D - ITSP-WQM model Solutions to Decision Variables under Scenario 3 174 Appendix E - ITSP-WQM model Solutions to Decision Variables under Scenario 4 178 Appendix F - ITSCCP-WQM model Solutions to Decision Variables 182
vi LIST OF TABLES
Table 3.1 Economic statistics of the eight subareas in Xingshan County (2010) 24 Table 3.2 Sowing areas of agriculture production in 2009 and 2010 (km "y ) 25 Table 3.3 Livestock production in 2009 and 2010 26 Table 3.4 Major industrial production in 2009 and 2010 27 Table 3.5 China's environmental quality standards for surface water (mg/L) 28 Table 4.1 Annual economic targets in each subarea 53 Table 4.2 Economic profits of the economic activities 54 Table 4.3 Mitigation costs of the four pollutants 56 Table 4.4 Pollution discharge rate of the four pollutants 57 Table 4.5 Probability of the occurrence of incoming water quality 58 Table 4.6 Maximum allowable pollution discharges of the four pollutants 60 Table 4.7 Water demands of the economic activities 61
Table 4.8 Results of decision variable xopt under Scenario 1 63
Table 4.9 Mitigation schemes under Scenarios 1 to 4 when the incoming water quality is Grade II 85 Table 5.1 b, b, and b value of the right-hand side fuzzy set 117 Table 5.2 Eleven scales of linguistic terms 118 Table 5.3 Mitigation amounts of the five industries under three incoming water quality levels 124 Table 5.4 Solutions to the economic target decision variables of the ITSCCP-WQM model 134
vii LIST OF FIGURES
Figure 3.1 Locations of Xingshan County and the Three Gorges Reservoir 18 Figure 3.2 Stream network of the Xiangxi River in Xingshan County 19 Figure 3.3 Administrative townships of Xingshan County 23 Figure 4.1 (1) Targeted income segments of the five industries under the optimized scheme of Scenario 1 (Lower bound) 65 Figure 4.1 (2) Targeted income segments of the five industries under the optimized scheme of Scenario 1 (Upper bound) 66 Figure 4.2 (1) Target segments of the agricultural activities under the optimized scheme of Scenario 1 67 Figure 4.2 (2) Target segments of the forestry activities under the optimized scheme of Scenario 1 68 Figure 4.2 (3) Target segments of the industrial activities under the optimized scheme of Scenario 1 69 Figure 4.3 (1) Targeted income from the five industries in Subareas 1 to 8 under the optimized scheme of Scenario 1 (Lower bound) 73 Figure 4.3 (2) Targeted income from the five industries in Subareas 1 to 8 under the optimized scheme of Scenario 1 (Upper bound) 74 Figure 4.4 Results of targeted income and mitigation costs of the eight subareas under the optimized scheme of Scenario 1 75 Figure 4.5 Mitigation amounts of the four pollutants under the three levels of incoming water quality 76 Figure 4.6 Results of the targeted income, mitigation costs, and net system benefit under Scenarios 1 to 4 78 Figure 4.7 (1) Targeted income of the five industries under Scenarios 1 to 4 (Lower bound) 80 Figure 4.7 (2) Targeted income of the five industries under Scenarios 1 to 4 (Upper bound) 81 Figure 4.8 (1) Targeted income of the eight subareas under Scenarios 1 to 4 (Lower
V1U bound) 82 Figure 4.8 (2) Targeted income of the eight subareas under Scenarios 1 to 4 (Upper bound) 83 Figure 4.9 (1) Percentage of mitigation amounts of agricultural production under the incoming water quality of Grade III (Lower bound) 86 Figure 4.9 (2) Percentage of mitigation amounts of agricultural production under the incoming water quality of Grade III (Upper bound) 87 Figure 4.10 (1) Percentage of mitigation amounts of fish farming under the incoming water quality of Grade III (Lower bound) 88 Figure 4.10 (2) Percentage of mitigation amounts of fish farming under the incoming water quality of Grade III (Upper bound) 89 Figure 4.11 Percentage of mitigation amounts of livestock husbandry under the incoming water quality of Grade III 90 Figure 4.12 (1) Percentage of mitigation amounts of industrial production under the incoming water quality of Grade III (Lower bound) 91 Figure 4.12 (2) Percentage of mitigation amounts of industrial production under the incoming water quality of Grade III (Upper bound) 92 Figure 5.1 Fuzzy membership, possibility, necessity and credibility of afuzzyset 102 Figure 5.2 (1) Targeted income from the five industries in the eight subareas (Lower bound) 120 Figure 5.2 (2) Targeted income from the five industries in the eight subareas (Upper bound) 121 Figure 5.3 Expected Value of the mitigation costs in the five industries 124 Figure 5.4 Expected Value of the mitigation costs of the eight subareas 125 Figure 5.5 (1) Stacked columns of mitigation amounts for TP, TN, and COD when the incoming water quality is Grade III 127 Figure 5.5 (2) Stacked columns of mitigation amounts for TP, TN, and COD when the incoming water quality is Grade II 128 Figure 5.6 (1) Changes in the targeted income when the TP discharge constraints are
IX loosened 130 Figure 5.6 (2) Changes in the mitigation costs when the TP discharge constraints are loosened 131 Figure 5.6 (3) Changes in the net system benefit when the TP discharge constraints are loosened 132 Figure 5.7 Targeted income, mitigation costs, and net system benefit of the ITSP-WQM model and the ITSCCP-WQM model 133 Figure 5.8 Targeted income of the five industries in the ITSP-WQM model and the ITSCCP-WQM model 137 Figure 5.9 (1) Mitigation cost (lower bound) segments of the five industries under the optimized schemes in the ITSP-WQM model and the ITSCCP-WQM model 138 Figure 5.9 (2) Mitigation cost (upper bound) segments of the five industries under the optimized schemes in the ITSP-WQM model and the ITSCCP-WQM model 139
X CHAPTER 1
INTRODUCTION
Xingshan County lies within the middle reaches of the Xiangxi River Basin, central
China. The Xiangxi River originates from the Shennongjia mountainous area, and flows north and then south through the County before draining into the Yangtze River. It is the major source water for the water consumption of municipal, agricultural, industrial and fishery sectors, as well as navigation. Relying on the abundant resources of hydropower, minerals (especially phosphorite), and forestry, the local economy has developed rapidly in recent years. However, the fast economic growth has been supervened with various environmental problems, such as water pollution, soil erosion and ecological damage. In particular, the deteriorating water quality has posed a serious challenge to local sustainable development. Agriculture, fisheries, navigation, and other resources provided by the Xiangxi River are vulnerable to changes in the water quality. Water quality deterioration is threatening public health, the health of the aquatic ecosystem and local economic development.
The need for economic development and environmental protection strategies is particularly urgent for Xingshan County given its reliance on the Xiangxi River for water resources and the County's limited capacity of wastewater treatment. This situation has been exacerbated by the newly-built Three Gorges Reservoir (TGR). The Xiangxi River
Basin is in vicinity of the TGR and it is also the largest catchment of the TGR. The TGR is the biggest reservoir in China and the world's largest hydropower project. It has a 1 water-storage capacity of over 3.93 * 1010 m3 with an installed capacity of 2.03 * 1010 W.
The TGR is a key regional resource in South China for a variety of socio-economic sectors such as agriculture, fishery, navigation, and electricity production. The construction of the TGR has confronted the Xiangxi River Basin with environmental, hydrological, ecological, and economic challenges. With respect to the water environment, the Xiangxi River is being impacted by the large-scale hydraulic interventions caused by the TGR. A large backwater area has been formed in the river following the impounding of the reservoir since 2003, leading to decreased flow velocity and reduced natural water purification capacity. The water quality problem has been particularly intensified by the frequent occurrence of water eutrophication. During 2004 -
2011, algal blooms occurred in the Xiangxi River every spring, which has been endangering the water supply, drinking water security, as well as local development. It is widely agreed that the operation of the TGR has greatly affected the water quality of the
Xiangxi River (Heggelund, 2004; Yang et al., 2006; Cai and Hu, 2006; Chai et al., 2009;
Ehret et al., 2010; Yang et al., 2010; Zheng et al., 2011). Therefore, there is an urgent need to mitigate the adverse influence of the TGR and control the environmental damage while maintaining local economic growth.
Moreover, the impoundment of the TGR has led to the loss of large areas of land. Parts of
Xingshan County, including 3 towns and 23 villages, were flooded during the impoundment. The submerged areas included cultivated, forestry, industrial and residential land. Consequently, over 34,000 farmers in Xingshan County were relocated; and the capital of the county, two towns, over 60 industrial enterprises and thousands of
2 houses were moved, and a new capital was built in the upper stream area of the Xiangxi
River. Xingshan County is at a new starting point for development, facing not only water problems but also new challenges with regard to regional planning.
Given the importance of water for socio-economic development throughout Xingshan
County (including the growing influence of the TGR), a water quality management and regional development plan is desired. The proposed plan is expected to create effective tradeoffs between economic targets and environmental objectives, based on a comprehensive analysis of the water system in the Xiangxi River Basin. However, due to the random characteristics of natural events, estimation errors of system parameters and vagueness of system objectives and constraints, the water quality management system is coupled with numerous uncertainties. For instance, spatiotemporal variation exists in system components such as economic targets and pollution control costs; system parameters such as pollution discharge rates and the water demands of each economic activity are related to many uncertain factors; and environmental capacities are functions of stochastic and/or inexact factors. Such uncertainties and their interactions would ultimately lead to considerable under- or over-estimations during the decision making process. For this reason, it is important for the County to effectively consider and tackle the uncertainties in the regional water quality management and planning.
In summary, it is clear that regional development planning under various uncertainties should be undertaken for Xingshan County based on a deeper understanding of the tradeoff between economic development and water quality control. This study proposes
3 two water quality management models using system analysis approaches. The Two-stage
Stochastic Programming (TSP) framework, used in these two models, is capable of providing effective compromises between predefined economic targets and the associated environmental penalties. The proposed models can provide bases for regional sustainable development and planning, with a focus on water quality management. This study entails the following objectives:
• Examine the water quality management system of Xingshan County in the
Xiangxi River Basin. Literature review and site studies will be conducted to
identify the system components and their interrelationships, as well as to
investigate the system complexities and uncertainties. Data support will be
provided for the configuration of the water quality management models.
• Build an inexact two-stage stochastic programming water quality management
(ITSP-WQM) model for Xingshan County. The proposed model will reveal the
environmental implications of local economic activities and plan for economic
and environmental development within the inexact two-stage stochastic (ITSP)
framework. Uncertainties described as probability distributions and discrete
intervals will be addressed. Decision support for regional sustainable development
will be provided.
• Develop an inexact two-stage stochastic credibility constrained programming
(ITSCCP) method and an inexact two-stage stochastic credibility constrained
programming water quality management (ITSCCP-WQM) model. The ITSCCP
method will be able to encode the fuzzy information of environmental capacities
4 via introducing an inexact credibility constrained programming method to the
ITSP framework. The ITSCCP-WQM model will be applied in Xingshan County
and provide decision alternatives for local planning.
This study will be a first attempt to apply inexact optimization approaches into the water quality management at the watershed level in the TGR. Comprehensive investigation regarding the predefined economic plans and their corresponding environmental damages in the middle reaches of the Xiangxi River Basin will be conducted, and decision support will be provided to improve upon the severe water deterioration while maintaining the economic growth. Furthermore, a credibility constrained programming method will be incorporated into the conventional ITSP j&amework for the first time. The introduction of a credibility constrained programming method will enable the water quality management model to tackle the uncertainties of environmental capacities resulting from the fuzzy water quality standards, so that more complexities can be reflected without unrealistic simplifications. The results of the two models are valuable in supporting the adjustment or justification of the existing economic development patterns, the identification of a desired pollutant-loading allocation and abatement plan among various economic activities, and the formulation of local sustainability strategies under various uncertainties.
The proposed method will also contribute to the field of water quality management.
5 CHAPTER 2
LITERATURE REVIEW
2.1. Water Quality Management in the Xiangxi River Basin
The Three Gorges Reservoir (TGR) in China is the largest newly-built reservoir worldwide (Fu et al., 2006). The environmental, hydrological, ecological, and economic impacts of the TGR have gained attention from researchers all over the world (Park et al.,
2003; Wu et al., 2003; Heggelund, 2004; Yang et al., 2006; Ehret et al., 2010).
Particularly, water quality is one of the most challenging problems resulted from the construction and operation of the TGR (Cai and Hu, 2006; Chai et al., 2009; Yang et al.,
2010; Zheng et al., 2011). The 2003 impoundment of the TGR formed a large backwater area and lowered the flow velocity in the upstream, which led to a pressing eutrophication problem and many other serious water quality problems (Chai et al., 2009;
Zheng et al., 2011). Over the past decades, there have been many studies regarding the
TGR. Fang (1999) discussed the impacts of the Three Gorge Dam on hydraulics and water quality. Heggelund (2004) analyzed the water resource as well as other environmental policies of the TGR project. Liu et al. (2004) studied the effect of nitrogen and phosphorus on the water quality in the TGR during and after its construction. Muller et al. (2008) investigated the water quality downstream from the TGR. Shen et al. (2008) analyzed the parameter uncertainty of the non-point source pollution in the TGR area.
Luo et al. (2011) studied seasonal variations of dissolved inorganic nutrients transported to the river basin of the TGR. Zheng et al. (2011) studied the impacts of water release
6 operations on algal blooms in a tributary bay of the TGR.
Being the largest tributary of the TGR, the Xiangxi River Basin is one of the areas that have been significantly influenced by the TGR (Ye et al., 2009; Ehret et al., 2010; Jahnig and Cai, 2010; Schonbrodt et al., 2010; Seeber et al., 2010). The natural water purification and environmental capacity of the water body have been lowered by the operation of the TGR. Moreover, due to intense human activities along the Xiangxi River in Xingshan County, especially the phosphorite mining industry, very high nutrient loads have been released (Fu et al., 2006). Consequently, algal blooms occur frequently in the
Xiangxi River (Fu et al., 2006). In response to these water quality problems, many studies have been conducted. Zhou et al. (2006) investigated and analyzed the spatial and temporal distribution of plankton rotifers in the Xiangxi River after the impoundment of the TGR. Fu et al. (2006) studied the phosphorus levels and their change in the sediment profile of the Xiangxi River. Fang et al. (2006) compared the phosphorus and nitrogen pollution status of the Xiangxi River Basin before and after the impoundment of the TGR.
Yang et al. (2010) studied the influence of the impounding process upon the TGR with respect to water eutrophication in the Xiangxi River. Whilst informative, the previous studies were generally limited to water quality monitoring, algal successions, water quality simulation and the related policy analysis. Very little has been done regarding comprehensive system analysis, and regional water quality management and planning.
The decision makers often find it challenging to maintain rapid with depleting natural resources and degrading environmental conditions. Thus, an effective water quality management model, which systematically examines the water quality systems and covers
7 aspects related to economic development, environmental impact, resource conservation and even political consideration for the Xiangxi River Basin is desirable.
2.2. Mathematical Programming Approaches to Water Quality Management under
Uncertainties
There are many complexities and uncertainties existing in water quality management systems due to the diversity of land use, underlying surface conditions, hydrological processes, water demands and socioeconomic status within different areas (Huang, 1998;
Arabi et al., 2007; Li et al., 2011). To address the uncertainties, system analysis and optimization approaches have been developed and widely applied. The majority of the optimization approaches for uncertain programming are related to Interval Mathematical
Programming (IMP) (Deininge.Ra, 1969; Huang, 1996; Cai et al., 2011), Stochastic
Mathematical Programming (SMP) (Lohani and Thanh, 1978; Tan et al., 2011), and
Fuzzy Mathematical Programming (FMP) (Chang et al., 1997; Sasikumar and Mujumdar,
2000; Zhang et al., 2011).
Based on these mathematical programming approaches, multiple uncertainties described as intervals, fuzzy sets and probability events can be tackled (Benayoun et al., 1971;
Bloemhof-Ruwaard et al., 1995; Bass et al., 1997; Chang and Wang, 1997; Triantis and
Girod, 1998; Li et al., 2006). Morgan et al. (1993) developed a mixed-integer chance-constrained programming (MICCP) method, derived from stochastic programming, for aquifer remediation design under uncertainty to find the globally
8 optimal tradeoff curve for maximum reliability versus a minimum pumping objective.
Cardwell and Ellis (1993) presented stochastic dynamic programming models for waste load allocation from multiple point sources, which included both parameter (Type II) and model (Type I) uncertainty. Huang (1996) proposed an interval parameter water quality management model and its application to a case study of water pollution control planning within an agriculture system. Change et al. (1996) applied the grey fuzzy multi-objective linear programming (GFMOLP) method for the evaluation of sustainable management strategies with respect to optimal land development in a reservoir watershed, and quantified the uncertainties in water resource management systems using specific fuzzy membership functions and grey numbers in a multi-objective analytical framework. Zou et al. (2000) proposed an inexact multi-objective mixed integer programming (IMOMIP) approach to deal with the uncertainty and complexity involved in decision making for regional sustainable development, with regarding to economic benefit, water resources, and water and air quality. Mathematical programming approaches have been widely applied in environmental system management.
More recently, Karmakar and Mujumdar (2006) developed a grey fuzzy optimization model for water quality management of river systems to address uncertainty involved in fixing the membership functions for different goals of the Pollution Control Agency
(PCA) and dischargers. Li et al. (2008) developed an interval-parameter robust quadratic programming (IRQP) method by incorporating techniques of robust programming and interval quadratic programming within a general optimization framework to support water quality management under uncertainties. Nie et al. (2008) proposed an inexact
9 fuzzy water management model based on an interval-parameter fuzzy robust programming approach, and applied it to a case study of water quality management within an agricultural system. Qin and Huang (2009) provided a multi-segment stream water quality (MSWQ) simulation model to establish the relationship between environmental responses and pollution control actions, and developed an inexact chance-constrained quadratic programming (ICCQP) model for stream water quality management. Qin (2009) developed a simulation-based interval quadratic waste load allocation (IQWLA) model for supporting river water quality management, and demonstrated the proposed model using a study case in the Changsha section of
Xiangjiang River in China. Han et al. (2011) proposed a multi-objective linear programming model with interval parameters wherein an interactive compromising algorithm was introduced, and applied the model to allocate of multi-source water resources with different water qualities to multiple users with different water quality requirements for the Dalian city, China. Tan et al. (2011) developed a radial interval chance-constrained programming (RICCP) approach to support source-oriented non-point source pollution control under uncertainty. Zhang (2011) developed a model-based decision support system to support water quality management under hybrid uncertainties, based on a hybrid uncertain programming (HFICP) model with fuzzy and interval coefficients. There has been a long history of applying optimization techniques to environment management problems, and they are considered suitable for the integrated water quality management and planning under uncertainties.
10 2.3. Two-stage Stochastic Programming
Two-stage Stochastic Programming (TSP) can provide support to management that requires decisions be made periodically (Huang and Loucks, 2000). TSP was first identified in the 1960's (Schultz et al., 1976). The relevant methodologies, solution algorithms and applications of TSP have been widely explored since that time. Pereira and Pinto (1985) initially published a dual dynamic programming algorithm for two-stage problems. Wang and Adams (1986) proposed a two-stage optimization method for the planning of reservoir operations. Kali (1979) proposed a set of computational methods to solve two-stage stochastic linear programming problems. Birge and Louveaux (1988) proposed a multi-cut algorithm for two-stage stochastic linear programming. The solution algorithm of TSP was further summarized by Birge and Louveaux in 1997. Pereira and
Pinto's algorithm (1985) was improved by Velasquez et al. in 1999, via adding a term in order to meet the Benders decomposition requirements. Sen and Sherali (2006) discussed alternative decomposition methods in which the second-stage integer sub-problems are solved using branch-and-cut methods, and laid the foundation for such decomposition methods for two-stage stochastic mixed-integer programs. The methodologies of TSP has been well developed to facilitate its application.
In the past decade, the TSP method, sometimes further incorporated with other uncertain programming methods such as inexact programming methods, has been widely applied in the environmental management area. Maqsood and Huang (2003) developed a two-stage interval-stochastic programming model for waste management under uncertainty. Leung
11 and Wu (2005) proposed a two-stage stochastic programming model with a recourse model for cross-border distribution with fleet management. Li et al. (2009) applied TSP to optimize chemical production planning under uncertainties. Rodriguez et al. (2009) established a TSP model to schedule replacements in sow farms. Guo et al. (2010) proposed a two-stage programming approach for water resource management. Lv et al.
(2011) developed a two-stage inexact joint-probabilistic programming method for air quality management under uncertainty. As for water management, there also have been several applications of TSP. Huang (1998) proposed a hybrid inexact-stochastic water management model for a river in Xiamen, China. Luo et al. (2006) developed a simulation-based interval two-stage stochastic model for agricultural non-point source pollution control through land retirement. Shastri and Diwekar (2006) formulated a two stage stochastic programming problem with recourse to optimize the distribution of sensors in water quality monitoring networks. Harrison (2007) developed a Bayesian
Programming method to optimize the two-stage adaptive water quality management process. Li and Huang (2009) studied two-stage planning for sustainable water management. However, the previous research mainly focused on the water resource management and allocation. Very few studies of TSP have been conducted to reflect the water quality response in the large-scale regional water management systems.
2.4. Credibility Constrained Programming
Fuzzy programming, derived from fuzzy possibility theory, was proposed as an alternative to the stochastic programming method (Zadeh, 1978). Fuzzy possibility theory
12 has been widely used in environmental management to account for uncertainties that can be expressed as possibilistic distribution (Mujumdar and Sasikumar, 2002; Onkal-Engin et al., 2004; Al-Shayji et al., 2008; Zhao and Chen, 2008). Hulsurka et al, (1997) presented an application of fuzzy programming approach to the multi-objective stochastic linear programming problem. In their work, fuzzy programming approach was applied to find the compromise solution after the proposed stochastic programming problem was converted into a deterministic problem. Cai et al (2007) proposed a mixed interval-parameter fuzzy-stochastic robust programming (MIFSRP) model and applied the model to the planning of solid waste management system under uncertainty. Maeda et al. (2009) developed a fuzzy optimization model to allocate allowable total nitrogen loads to distributed non-point sources and point sources in a watershed for river water quality management using the linear programming technique. Rehana and Mujumdar (2009) developed an imprecise fuzzy waste load allocation model (IFWLAM), which is capable for the computation of imprecise fuzzy risk of low water quality, for water quality management of a river system subject to uncertainties arising from partial ignorance. Li and Chen (2011) used the Nguyen's method to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, and proposed a fuzzy-stochastic-interval linear programming (FSILP) method by integrating Nguyen's method with conventional linear programming method to support municipal solid waste management.
Credibility is a definition derived from fuzzy possibility theory (Zhang and Huang, 2010).
The concept of credibility was proposed recently as a new self-dual measure for the
13 confidence level in fuzzy environment, and it is effective in tackling uncertainties expressed as fuzzy sets (Liu and Liu, 2002; Huang, 2006; Zhang and Huang, 2010).
There have been several studies on the application of the credibility constrained programming method. Luo et al, (2004) considered the general Hartley measure based on credibility for fuzzy numbers, and proposed a mathematical model determining the decision-making level of fuzzy programming based on the maximal unspecificity. Huang
(2006) proposed two types of fuzzy possibility chance-constrained programming models using credibility to measure the confidence level while solving a problem of capital budgeting in a fuzzy environment. Rong and Lahdelma (2008) presented the fuzzy credibility chance constrained model with which to optimize the scrap charge in steel production. Zhang and Huang (2010) incorporated the concepts of credibility-based chance-constrained programming and robust programming and proposed a fuzzy robust credibility constrained program for solid waste management and planning. In 2011, they further developed an inexact credibility constrained programming method to deal with multiple formats of uncertainties in parameters and variables for an agricultural water planning system. However, there are very few studies that applied credibility to reflect the fuzzy information in water quality management systems. Besides, the credibility constrained programming method has never been incorporated with the TSP framework to support water quality management.
2.5. Summary
The Xiangxi River Basin in the TGR is facing serious water pollution problems,
14 especially euthrophication (Chai et al., 2009; Zheng et al., 2011). Many studies have been conducted with respect to water quality monitoring and assessment. However, no comprehensive system analysis regarding regional water quality management has been conducted in this area. In order to minimize the water environmental damages and maintain local economic growth, systematic water quality management and planning is desirable.
The water quality management system is always firaught with numerous complexities and uncertainties. To address the uncertainties among system components and their interrelationships, many mathematical programming approaches have been developed. It has been demonstrated that optimization approaches are effective to deal with various uncertainties and provide decision support for environmental management and planning under various uncertainties. Two-stage Stochastic Programming (TSP) is a remarkable mathematical programming method that provides periodical decision support, and it is able to reflect the latter environmental penalty of previously regulated economic targets.
Credibility Constrained Programming (CCP) is another effective method that is capable of tackling uncertainties expressed as fuzzy sets. However, there have been very few applications of TSP or CCP methods in regional water quality management, and no applications have been conducted with regard to the Xiangxi River Basin.
Therefore, this review reveals the necessity to develop water quality management models based on the TSP methodology to incorporate economic and environmental concerns within a general optimization framework under a variety of uncertainties, as well as the
15 necessity to introduce CCP and further reflect the fiizziness that exist in the system. Such attempts to propose approaches for water quality management would contribute to the
Xiangxi River Basin, and also the field of environmental systems engineering.
16 CHAPTER 3
STUDY AREA
3.1. Study Area
3.1.1. Location
Xingshan County (110°45'-113o43'E, 31°14'-32°N) is located in western Hubei Province,
China (Figure 3.1). It lies within the middle reaches of the Xiangxi River Basin. It is 66 km in length from east to west and 54 km in width from south to north. Its total area is approximately 2,327 km2. The Xiangxi River Basin is the largest tributary of the TGR, located 40 km upstream of the reservoir. It covers Xingshan Coxmty and parts of
Shennongjia County and Zigui County, with a total area of 3,099 km2. The Xiangxi River originates in the Shennongjia mountain area, passes from north to south and drains into the Yangtze River. Its length is 33 km, with 21 km in Xingshan County and 12 km in
Zigui County. The stream network: of the Xiangxi River in Xingshan County is shown in
Figure 3.2.
The TGR is the largest reservoir in China. It started impounding on June 1st, 2003. The water level of the TGR increased from 135m to 175m during the past eight years. The rise of the water level led to the submergence of a large area in the Xiangxi River Basin.
Parts of Xingshan County were flooded during the impoundment. It also formed a backwater area at the downstream of the Xiangxi River Basin, which brought a significant influence upon the water environment and aquatic ecosystem of the Xiangxi 17 Figure 3.1 Locations of Xingshan County and the Three Gorges Reservoir
18 Lafend BovwfryCourrty
Figure 3.2 Stream network of the Xiangxi River in Xingshan County
19 River Basin including Xingshan County.
3.1.2. Geological and Geomorphologic Condition
Xingshan County is at the junction of the Wushan Mountain and the Daba Mountain.
There are 3,580 mountains and 156 rivers in this area. The altitude is high in the east, west and north, and relatively low in the south, with a difference of 2,317 m. The highest peak of this area is 2,427 m above sea level, which is the Xiannv Mountain, while the bottom is 110 m, which is at the Youjia River. The primary topography of the area is mountainous, mainly in the northeast and southwest of the county, accounting for over eighty percent of the total area. Sixty percent of the study area is mountainous area with an altitude over 1,200 m, and seventy-three percent of this area's inclinations are over 20°.
Farming and settlement are not allowed in these steeply sloped mountainous areas and human activities are restricted to level areas and smoother slopes.
3.1.3. Hydrological and Climatic Conditions
This area possesses a subtropical continental monsoon climate. It exhibits significant temperature differences and plentiful precipitation in spring, concentrated rainfall and high temperatures during the summer, cloudy or rainy conditions during the autumn, and frequent early frost in winter. During 1961 to 1990, the annual average temperature was
16.9 °C, with a maximum temperature of 43.1 °C and a minimum temperature of -9.3 °C.
The average days without frost each year at low, middle and high hills are 272, 215 and o ^ 163, respectively. The average annual quantity of solar radiation is 2.90 x 10 kW/m . The average solar radiation quantity during April to September is 1.88 x 108 kW/m2. The annual precipitation is 900 to 1,200 mm, which shows a significant spatiotemporal variations. The precipitation in the north is higher than that in the south, and the rainfall is more intense in the summer than it is in the winter. Sixty nine percent of the rain falls between May and September, and the average stream flow is 40.18 m3/s.
3.1.4. Vegetation Conditions
The study area is a subtropical mountainous area with mixed needleleaf and broadleaf forests. The vegetation distribution in this area exhibits an obvious vertical gradient. The dominant vegetation types from the low altitude to high altitude are: broadleaf forest
(below 800 m), needleleaf forest (800 to 1,000 m), and shrub-grassland (above 1,800 m).
The land use is characterized by grain crop farming mixed with cash crop production, typically on terraced farmland. The main crops include dry land crops (rape, wheat, and maize), rice, nuts, and garden fruits. Particularly, since the climatic conditions appear to be favorable, orange are widely cultivated in this area.
3.1.5. Socio-Economic Conditions
The total population of Xingshan County is approximately 181,000. Xingshan County is sub-divided into eight towns: Gufu Town, Zhaojun Town, Xiakou Town, Nanyang Town,
Huangliang Town, Shuiyuesi Town, Gaoqiao Town, and Zhenzi Town. The administrative townships of Xingshan County are presented in Figure 3.3.
21 This County is designated as a poverty-stricken area by the provincial government.
However, there are abundant resources of hydropower and minerals (especially phosphorite), which have stimulated the development of local economy in the past decade. The reserves of phosphorite of Xingshan County are among the top three all over
China. In recent years, the local government carried out an economic strategy based on hydropower, mineral, and forestry industries, which has transformed the previous agriculture-dominated economy to a more diversified economy with growing industrial sectors. In 2010, the Gross Domestic Product (GDP) for Xingshan County reached RMB
44.10 x 108, which increased by 16.43% when compared to that of 2009. The three-industry structure of primary, secondary and tertiary industries is 16: 53: 31. The per capita disposable income of urban residents was RMB 1.19 x 104, and the per capita net income of rural residents was RMB 0.43 x 104. The economic statistics of the eight subareas in 2010 are given in Table 3.1. The agricultural, livestock and industrial productions in 2009 and 2010 are tabulated in Tables 3.2 - 3.4, respectively.
3.2. Water Quality Problems
The Xiangxi River originates in Shennongjia, one of the National Forest Nature Reserves in China, and the incoming water quality of Xingshan County is fairly good. The water quality usually meets China's standards of Grade I ~ III (China's environmental quality standards for surface water are given in Table 3.5). However, rapid economic development has brought massive pollution into the river. Agricultural, industrial and other activities are generating more and more wastewater as economic
22 Figure 3.3 Administrative townships of Xingshan County (The People's Government of Xingshan County, 2011)
23 Table 3.1 Economic statistics of the eight subareas in Xingshan County (2010) (The People's Government of Xingshan County, 2011)
Government General Budget Per Capita Subarea Revenue Revenue Net Income of Residents (RMB 104) (RMB 104) (RMB) Gufu 2,364 1,111 4,328 Zhaojun 621 244 4,202 Xiakou 1,052 470 3,972 Gaoqiao 135 99 3,095 Nanyang 326 203 3,854 Zhenzi 4,795 2,490 4,668 Huangliang 535 373 4,291 Shuiyuesi 3,614 1,626 4,538
24 • Table 3.2 Sowing areas of agriculture production in 2009 and 2010 (km2) (The People's Government of Xingshan County, 2011)
2009 2010
Subarea Grain Grain Total Tobacco Vegetables Others Total Tobacco Vegetables Others crops crops Gufix 52.78 27.39 0.37 15.3 9.72 52.24 27.23 0.37 14.79 9.85
Zhaojun 25.27 13.45 - 7.17 4.65 26.58 14.31 - 7.62 4.65
Xiakou 39.63 26.96 - 4.13 8.54 40.30 27.01 - 4.18 9.11 Gaoqiao 41.35 23.13 2.52 4.91 10.79 41.69 23.34 1.87 5.17 11.31 Nanyang 27.84 16.33 2.94 2.92 5.65 28.73 17.26 2.33 2.65 6.49 Zhenzi 32.92 11.79 11.01 8.95 1.17 31.51 12.37 9.20 8.83 1.11 Huangliang 60.07 29.14 8.67 8.90 13.36 60.79 29.40 6.00 12.00 13.39 Shuiyuesi 46.65 29.84 0.59 7.70 8.52 47.05 29.78 0.59 7.87 8.81
25 Table 3.3 Livestock production in 2009 and 2010 (The People's Government of Xingshan County, 2011)
2009 2010 Subarea Pigs Cattle Sheep Poultry Pigs Cattle Sheep Poultry (head) (head) (head) (103 head) (head) (head) (head) (103 head) Gufu 41,411 314 9,346 72,475 41,528 326 8,957 64,402 Zhaojun 28,308 99 8,023 33,400 26,170 100 10,796 30,200 Xiakou 55,800 241 5,860 62,973 56,074 251 7,895 67,289 Gaoqiao 40,180 476 15,014 36,456 42,119 515 17,154 37,306
Nanyang 24,104 - 8,115 24,850 25,145 4 10,255 23,570 Zhenzi 11,005 576 15,003 22,000 12,217 428 14,413 24,218 Huangliang 55,000 500 18,012 37,908 54,164 449 24,216 81,482 Shuiyuesi 55,074 501 10,008 51,100 55,102 551 13,563 50,130
26 Table 3.4 Major industrial production in 2009 and 2010 (The People's Government of Xingshan County, 2011)
Products type Unit 2009 2010 Coal ton 73,054 69,338 Phosphorite 104 ton 138 187 Electricity 104 kw-h 48,190 51,428 Phosphate ton 488,408 415,689 Pork products ton 41,917 41,664 Dimethyl sulphoxide ton 17,469 17,640 Cement 104 ton 51 90 Tea ton 82 122 Vitriol ton 75,798 97,174 Furniture piece 15,767 12,160 Plastic products ton 0 472
27 Table 3.5 China's environmental quality standards for surface water (mg/L) Indicator I II III IV V COD 15 15 20 30 40 TN 0.02 0.10 0.20 0.30 0.40 TP 0.2 0.5 1.0 1.5 2.0
"COD", "TN", and "TP" "S4" represent "Chemical Oxygen Demand", "Total Nitrogen", and 'Total Phosphorus" (TP), respectively.
28 development expands. On the other hand, the domestic water treatment level is very low.
Most residential and industrial wastewater, as well as polluted runoff, is untreated and discharged directly into the Xiangxi River. Moreover, the construction of the TGR, which lowered the flow velocity and natural water purification, has created even more water pollution challenges. Euthrophication and the overall water quality deterioration have become the two major water quality problems in Xingshan County (Fu et al., 2006; Yang et al., 2010; Zheng et al., 2011).
3.2.1 Point Source Pollution
The point source pollution in Xingshan County includes industrial and municipal wastewater. The production of industry, especially the phosphate processing industry and silicon processing industry, developed at a rapid pace in the past decade. However, the increase of pollution mitigation was disproportionate to the industrial production growth.
In recent years, the average amount of industrial wastewater that was discharged directly into the Xiangxi River was 5820.5 ton/day, among which the amount of total phosphorus discharge was 0.22 ton/day (Sheng, 2008; Zhang, 2008). Industrial activities in Xingshan
County includes the electric power, chemical, cement, coal, electronic, food industries, and other industrial activities such as the furniture manufacturing. Among these activities, pollution from the mineral mining, electronics, and food processing industries, is the critical point source pollution (Sun, 2008; Zhang, 2008). Pollutants such as organic matters, nutrients and heavy metals are discharged from these industrial activities into the water body. In particular, phosphorite mining and processing industry is the pillar
29 industry of Xingshan County, and it discharges considerable nutrient pollution into the
Xiangxi River.
Municipal wastewater is mainly the residential wastewater from Xiakou, Zhaojun, and
Gufu. Average wastewater discharge rates of the three towns are approximately 580,
1,710, and 3,080 ton/day, respectively. According to the previous studies, the amount of
Chemical Oxygen Demand (COD), ammonia nitrogen (NH4-N), Total Nitrogen (TN), and
Total Phosphorus (TP), which are generated from the residential communities, are approximately 530, 15, 16, and 14 ton/year, respectively (Sheng, 2008; Sun, 2008; Zhang,
2008).
3.2.2 Non-point Source Pollution
Subjected to the topographic conditions and precipitation characteristics, the water quality of the Xinagxi River is strongly affected by the non-point source pollution resulted from soil loss and rainfall-runoff. Non-point source pollution is difficult to control and there are very few treatments for the non-point source pollution in Xingshan
County.
The non-point source pollution includes discharges and runoff from agricultural, livestock husbandry, forestry and fish farming activities, as well as rural residential wastewater. The annual application amount of fertilizer in agriculture and forestry is approximately 88 tonnes. The excessive application of fertilizer results in a great deal of nutrient discharges into the river. The total nitrogen and total phosphorus equivalents of 30 the fertilizer are 0.22 and 0.18 ton/day, respectively. Besides, pig husbandry, which supports the commercial production of the pork processing industry, plays an important role in the livestock industry and brings a significant discharge of organic pollutants and nutrients.
31 CHAPTER 4
AN INEXACT TWO-STAGE STOCHASTIC PROGRAMMING WATER
QUALITY MANAGEMENT MODEL
4.1. Background
Serious water quality problems have been associated with the rapid economic development in the Xiangxi River Basin. In the past three decades, a large amount of wastewater has been discharging into local water bodies, particularly the Xiangxi River.
This has caused major concerns upon water quality in the Xiangxi River, which is continuing to decrease with increasing pollutant-discharging rates. On the other hand, natural water purification capacity of the river has been decreasing due to the effects of the backwater and eddy flows associated with operations of the Three Gorges Reservoir
(TGR). This represents that water pollution load capacities of the Xiangxi River are decreasing drastically. Such issues are causing many complexities and uncertainties in managing water resources from water quantity and quality perspectives, posing great challenges for local decision makers. In order to mitigate the adverse influence of the
TGR, prevent water quality deterioration, and maintain water security without disturbing local economic development, optimal water quality management plans are desired.
Water quality management involves a series of decision-making processes. Ideally, economic targets for all of the subareas in a basin are normally pre-defined before any pollution control plans are undertaken. Conventionally, the pollution discharge from
32 economic productions can be estimated using pollutant generation coefficients of each economic activity. At the same time, the amount of pollutants in the incoming water can be obtained through regular water quality monitoring. Thus, the total pollution loads of the water body can be calculated, and the corresponding pollution abatement schemes can be formulated accordingly. Along with the temporally increasing economic targets and changing incoming water quality, relevant pollution abatement efficiencies should be continuously improved to satisfy the water quality requirements and to mitigate the penalties associated with excess discharge.
In this scope, the benefit of economic production in proportion to the pre-regulated economic targets can be considered as system benefits, while cost for the associated pollution control can be considered as system recourse penalties. The objective of the desired water quality management is to satisfy the environmental requirements through conducting pollution control and achieve a maximum net system benefit. A desirable water quality management model should be able to consider the aforementioned dynamic interactions between economic targets and pollution control. Additionally, in real-world problems, many uncertainties exist in the water quality management system. For instance, the pre-defined economic targets are usually intervals estimated by decision makers based on their experience, and the incoming water quality is a random event. The existence and combinations of the uncertainties and complexities could strongly affect the exercises with which to generate water quality management plans.
Therefore, a water quality management model under uncertainties will be proposed for
33 the Xiangxi River Basin. A large-scale regional inexact two-stage stochastic programming water quality management (ITSP-WQM) model in this basin will be develop to tackle various uncertainties and optimize the planning of various activities within the study horizon. The proposed model will be capable of addressing uncertainties described as both probability distributions and intervals in the water quality management system. In addition, the model will reflect tradeoffs between system benefits and system-failure risks (e.g., failure to meet the water quality standards required by governmental authorities). The results will be valuable in supporting the adjustment or justification of the existing economic structure and identifying desired economic targets and pollution mitigation strategies under uncertainties.
4.2. Methodology
4.2.1. Two-stage Stochastic Programming
Two-stage Stochastic Programming (TSP) with recourse is effective in capturing tradeoffs between economic development and environmental protection, as well as reflecting the connections between anticipatory strategies and the associated adaptive adjustments. Uncertainties described as random short-term events can be tackled by TSP.
The classical TSP model can be written in its implicit form as (Birge and Louveaux,
1997):
Max/ = cTx - ^[min q(tof >>(©)] (4.1 a)
subject to: Ax < b (4. lb)
34 T( x>0,y(a)>0. (4-Id) The first-stage decisions are represented by the n, x 1 vector x. The first-stage decision is made before a number of random events co e Q occur. When the set of random variables co is observed, the second-stage problem data <7(00), ^(co) and h(co) can be obtained. g(co)Ty(a>) denotes the second-stage recourse costs. The second-stage adaptive decisions depend upon the realization of the first-stage random vector. For a given realization of 0), let Q(y,£,(«>)) = min{q((a)Ty |W((o)y = h((o)-T((a)x} (4.2) y^Q be the second-stage value function. Via correcting the discrepancy between /J(CO) and T((n)x by the recourse action, the constraints W(®)y + T(a)x = A(G>) can be satisfied and the second-stage cost q(cof >>(cd) can be minimized. Thus, the pre-regulated benefits, which is determined by the first-stage decisions, as well as the associated penalty, which is determined by the second-stage decisions, can both be taken into account. Consider a case where the random vector Q = {<»,, N (p,>0,and ^ p, = 1). Then, the expected second-stage value function can be defined as: i £[(?(M(®))] = £Jmin ^(cd/y(co)] = £/>,0(.y,co,) (4.3) i 35 Therefore, Model 4.1 can be reformulated into a deterministic optimization model, Model 4.4, as follows. Max/ = cTx~Y, P,Q(y, ©,) (4.4a) i subject \o:Ax r(a>;)x + fV((ot)y = h((D,), V/ = 1,2,..., N (4.4c) x > 0, y( Thus, the optimal results of x and y could be obtained by sloving Model 4.4 using the Simplex Method. 4.2.2. Inexact Two-stage Stochastic Programming Although the two-stage stochastic programming, illustrated by Equations 4.4a-d, can effectively reflect the impacts of the random events in an optimization system, it can hardly deal with uncertainties that may exist in the objective functions and the left-hand side constraints. In order to further compound this type of uncertainties, interval parameters were introduced into the conventional TSP framework, and an inexact two-stage stochastic programming (ITSP) model was developed (Huang, 1996; Huang and Loucks, 2000). Let x be a closed and bounded set of real numbers. x± is defined as a set of intervals with crisp lower and upper bounds but unknown distribution information for x (Huang, 1996): 36 JC* =[JC",X+] = {/EX|JC~ 4 ± ± ± ± Max/ = c x -^p,Q(y ,(ol ) (4. 6a) /=i subject to: A±x± < b± (4. 6b) T(of )x± + JF(cof)/ = A(of), V/ = 1,2,...,7V (4. 6c) x±>0,y±((of)>0. (4.6d) To identify the optimal value of x±, a set of decision variables z is introduced. Then Model 4.6 can be re-written as Model 4.7, where the intervals x± can be expressed as deterministic numbers: 1 ± Max/* = c (x~ + Axz)— ^ p/Q(y ,co/ ) (4.7a) subject to: A±x± < b* (4.7b) T((of)x± +W((of)y ± =A(cof), VI = 1,2,...,N (4.7c) x± >0,y±((of)>0. (4.7d) Model 4.7 can be solved through constructing into two deterministic sub-models, which correspond to the lower and upper bounds of the objective function value. This transformation process is based on an interactive algorithm originated by Huang (1994). 37 The solutions of this algorithm provide intervals for the objective function and decision variables and they can be interpreted to generate decision alternatives (Huang and Loucks, 2000, Li et al., 2010, and Li et al., 2006). In this case, as the objective is to maximize the net system benefit, the sub-model corresponding to the upper bound of the objective function value should be formulated and solved first (assume c* >0, At > 0 and 6* > 0): Max/+ = c+(x~ + Axz) -£ p,Q{y~(4.8a) i=i subject to: A~(x~ + Axz) < b* (4.8b) T(a>J)(x~ + Axz) + fV((oJ)y~ = h((0j), Vl = l,2,...,N (4.8c) Ax = x+-x~ (4.8d) x+ > x" > 0 (4.8e) y~ > 0 (4.8f) 0 Max/" = cxlp -]£p,Q(y+,co,+) (4.9a) /=i subject to: A+x* nvJK, +W{^)y*=h(^), Vl = l,2,...,N (4.9c) 38 Ax = x+ -x (4.9d) x+ > x~ > 0 (4.9e) y* - y'op, - o (4.9f) where y* are the decision variables. Let y* and f denote the solutions and the maximum objective function value of Model 4.9, respectively. Therefore, solutions for Model 4.7 can be obtained as follows: (4.10) (4.11) (4.12) 4 J. Model Development 4.3.1. Model Configuration Considering the deteriorating water environment pollution in the Xiangxi River Basin, it is critical to ensure that the local economic growth does not cause irreversible damages to the environment. Thus, it could be inferred that the objective of the model is to obtain a desired plan for various activities with consideration of economic and environmental tradeoffs. It could be also interpreted as the maximization of the net system benefit, which denotes the difference between the economic benefit and environmental penalty. Decision variables are economic activities that would generate excessive pollutants, which could be considered as pollution reduction required for each activity under the 39 economic, environmental, and policy obejctives. They could also been interpreted as the environmental penalties of the water quality management system. The eight towns (Gufu, Zhaojun, Xiakou, Gaoqiao, Nanyang, Zhenzi, Huangliang and Shuiyuesi) in Xingshan County are denoted as Subareas j = 1 to 8, respectively. The primary industries are comprised of agriculture, forestry, fishery, and livestock. Agriculture includes grain crops, tobacco, vegetables and other farming (denoted as i = 1 to 4, respectively). Forestry is divided into commercial forestry and ecological forestry (denoted as i = 1 and 2, respectively). Fishery denotes fish and prawn farming activities (denoted as i = 1). Activities in livestock include pigs, cattle, sheep and poultry husbandry (denoted as i = 1 to 4, respectively). The secondary industries include the electric power industry, chemical industry, cement industry, coal industry, electronic industry, food industry, and other industries such as the furniture building industry and packaging industry (denoted as i = 1 to 7, respectively). The constraints include water quality constraints, water quantity constraints as well as technical constraints. The local water quality and water quantity requirements for water resources are reflected in the constraints. The pollutants in the Xiangxi River include oganic matters, nutrients, heavy metals et al. However, the major water quality problem of the Xiangxi River Basin in Xingshan County is the discharge of organic compounds, nitrogen, phosphorous and soil loss (Sun, 2008; Zhang, 2008). Thus, Chemical Oxygen Demand(COD), Total Nitrogen (TN), Total Phosphorus (TP) and soil loss are chosen as the four pollutant types in this model, denoted as k = 1 to 4, respectively. Since the pollution mitigation policies are expected to be undertaken continuously along with the temporally increasing economic targets, the planning horizon of this model is one year. In the water quality management system, there are many uncertainties exist in multiple formats. For instances, short-term economic targets are often subjected to local economic long-term strategies and they are usually determined by decision makers based on their experiences. The available data is insufficient to provide a distribution or any further detailed information and thus, this type of parameters will be considered as intervals. Moreover, as for the incoming water quality, which is a critical factor that would greatly affect the pollution control strategies, is usually a random event. Thereby, it will be considered as a stochastic event in this model. 4.3.2. Model Formulation The formulation of the ITSP-WQM model is as below: (a) Objective Function The objective of this model is to maximize system net benefit, which is the difference of economic benefit and environmental penalty. The economic benefit denotes the profits of the economic production determined by the first-stage decisions regarding the economic development targets. The environmental penalty denotes the pollution abatement cost for the economic activities that caused an over generation of pollutants under a certain water quality level, determined by the second-stage decisions regarding the pollution control 41 schemes. Therefore, the objective function can be expressed as: Max/* = Benfit* - Cost1 (4.13) where Benefit = x(TA,~+ &TA,jVij) ' J i j +IJIlBF^(TFi+ATF,xt) (4.14) I j +YLblXtl,~+ajVS> * J +II^*<7V+'"7a> i j crf-IIIIP ,xc;xP4xDA,> i j I k +EZ£2>*c.**'ptf*D3S i j t k +ZIIZaxc,*XP^*x-DJV; (4.15) i j I k +ms>. * where (4.14): Targeted income of agriculture, forestry, fishery, livestock and industry; (4.15): Penalty costs for the excess pollutant discharges from agricultural activities, forestry, fish farming, livestock husbandry and industrial activities. (b) Constraints (1) Pollutant losses from agricultural activities vw (4.16) ' J 42 (2) Pollutant losses from forestry activities X {TT~ + MTijWij -DT*) < ET,l, Vk,l (4.17) i j (3) Pollutant losses from fish farming activities v*.' (4.18) ' j (4) Pollutant losses from livestock husbandry activities Z£M»*(rc,-+Arvs-z>4)<.m*, vt,; (4.19) i j (5) Pollutant losses from industrial activities ZZw> (6) Water quality requirements I r4*(TA,;+ATA„vt-D4) i +ZPTZ X(TT; +A77->vf-flJj) i +YIPF^(TFt-+ATF,x,J-DF^ (4.21) i pl +L i*<.TL,~+&TLlylt-£>£*,) I +I«X","+A77#z1,-D/,J)<»'a;, V*,/ i (7) Water quantity constraints 43 II NAf x(TA~ + MAijViJ) < J +IZ + ' j +11 NF^x(TF'+ATFvx9) (4.22) » j +11 NLfx(TL,-*&TL,y,) ' j +IZ NIfx(TI,-+*TI,,!,)<& I J (8) Technical constraints t TAij >DA?Jl >0, V/,y,/ (4.23) TTt;>DT*>Q, Vi,j,l (4.24) TF*>DF*>0,Vi,j,l (4.25) TL^>DL%>0,Vi,j,l (4.26) TL;>Dlfjt>0, ViJ,l (4.27) v 0 - ,y ^ 1, V/,_/ (4.28) 0 O^x^l, ViJ (4.30) 0<^. <1, V/J (4.31) 0 - z,y -1» Vi',y (4.32) where is the benefit from agricultural activity i in subarea j (RMB 104/km2) ; BI'* is the benefit from forestry activity / in subarea j (RMB 104/km2) ; 44 BFy is the benefit from fish fanning activity i in subarea j (RMB 104/km2) ; BL* is the benefit from livestock husbandry activity i in subarea j (RMB 104/103 head); J31*. is the benefit from industrial activity i in subarea j (RMB 104/RMB 107) ; C* is the reduction of net benefit for excess discharge of pollutant k (RMB 104/kg when k is the 1, 2, 3; RMB 104/ton when k = 4) ; DA*t is the decision variable representing the amount by which agricultural land area target TA*j exceeds standards in subarea j when the water quality target of the river is / (km2) ; DT*t is the decision variable representing the amount by which forestry land area target TTy exceeds the standards in subarea j when the water quality target of the river is / (km2); DF* is the decision variable representing the amount by which fish farming land area target TFy exceeds standards in subarea j when the water quality target of the river is / (km2) ; £>Z,*7 is the decision variable representing the amount by which livestock husbandry 7Z| exceeds standards in subarea j when the water quality target of the river is/ (103 head); DI*;, is the decision variable representing the amount by which industrial target Tlf- exceeds standards in subarea j when the water quality target of the river is / (RMB 107); 45 EAfk is the maximum allowable discharge of pollutant k for agricultural farming activities with probability pt of occurrence under river water quality grade / (kg when k - 1, 2, 3; ton when k = 4); ETtf is the maximum allowable discharge of pollutant k for forestry fanning activities with probability p{ of occunence under river water quality grade / (kg when k = 1,2, 3; ton when k = 4) ; EFtf is the maximum allowable discharge of pollutant k for fish farming activities with probability of occurrence under river water quality grade / (kg when k= \, 2, 3; ton when k = 4) ; EL*k is the maximum allowable discharge of pollutant k for livestock farming activities with probability Pj of occurrence under river water quality grade / (kg when k = 1, 2, 3; ton when k = 4) ; Elfk is the maximum allowable discharge of pollutant k for industrial farming activities with probability pt of occunence under river water quality grade / (kg when k = 1, 2, 3; ton when k = 4); NAf is the water demand of agricultural activity i (104m3/km2) ; NT* is the water demand of forestry activity i (104m3/km2) ; NF* is the water demand of fish fanning activity i (104m3/km2) ; NL* is the water demand of livestock husbandry activity i (104m3/103 head) ; Nlf is the water demand of industrial activity i (104m3/RMB 104); pl is the probability of occurrence of river water quality grade / (%); PA* is the discharge of pollutant k from agricultural activity i (kg/km2 when k= 1, 2, 3; ton/km2 when k = 4) ; PT£ is the discharge of pollutant k from forestry activity i (kg/km2 when k = 1, 2, 3; ton/km •j when k = 4); PF^ is the discharge of pollutant k from fish farming activity i (kg/km2 when k = 1, 2,3; ton/km2 when k = 4); 3 PL*k is the discharge of pollutant k from livestock husbandry activity i (kg/10 head when k = 1, 2,3; ton/103 head when k = 4) ; PI* is the discharge of pollutant k from industrial activity i (kg/RMB 104 when k = 1,2, 3; ton/ RMB 104 when k = 4) ; Q± is the quantity of available water for the development of primary and secondary industries (104m3); TAfj is the land area target for agricultural activity i in subarea j (km2/year) ; TT* is the land area target for forestry activity i in subarea j (km2/year); TFy is the land area target for fish farming i in subarea j (km2/year) ; TL\ is the target for livestock husbandry / in subarea j (103 head/year); 77* is the target for industrial activity i in subarea j (RMB 107/year) ; WQ* is the maximum allowable discharge of pollutant k for all activities with probability pt of occurrence under river water quality grade 1 (kg when k= \, 47 2, 3; ton when k = 4) ; is the symbol for economic activities: (1) Agricultural activities = 1 for grain crops = 2 for tobacco 3 for vegetables : = 4 for others; (2) Forestry activities i'=l for commercial forest i = 2 for ecological forest; (3) Fish fanning activities i — 1 for fish and prawn farming; (4) Livestock husbandry activities = 1 for pigs = 2 for cattle = 3 for sheep = 4 for poultry; (5) Industrial activities = 1 for electricity power industry = 2 for chemical industry = 3 for cement industry = 4 for coal industry = 5 for electronic industry i = 6 for food industry i' = 7 for other industries (furniture building and packaging industries); j is the symbol for subareas j -1,2, 3,4, 5, 6, 7, 8; k is the symbol for pollution types, namely: k = 1 for COD discharge k = 2 for TN discharge k = 3 for TP discharge & = 4 for Soil loss; / is the symbol for the water quality grade based on the China's Environmental Quality Standards for Surface Water, where 1=1 corresponds to Grade I 1 = 2 corresponds to Grade II / = 3 corresponds to Grade III; vv is the decision variable regarding the land area target for agricultural activity i in subarea j (0 < vi} < 1); w0. is the decision variable regarding the land area target for forestry activity i in subarea j (0 < Wy < 1); xtJ is the decision variable regarding the land area target for fish farming / in subarea j (0 < Xy <1); y0 is the decision variable regarding the target for livestock husbandry i in subarea j (0<^ 49 ztJ is the decision variable regarding the target for industrial activity /' in subarea j (0 < zij <1) • 4.3.3. Scenario Development One of the main advantages of the ITSP-WQM model is its capability to incorporate economic policies, in terms of economic targets, within the optimization framework via the introduction of the first-stage decision variables ( T* ). Given an economic development policy, if the water quality standards are satisfied, it could result in a system benefit (i.e. targeted income). However, when the pollution discharged from the pre-regulated economic activities violates the water quality standards, pollution control must be conducted to meet the water quality requirements, which could lead to environmental penalties and thus a reduction of system benefit (i.e., pollution mitigation costs). In order to exam the tradeoffs between economic development and environmental pollution control, four scenarios were examined: • Under Scenario 1, the economic targets of each industry will be identified based on ± ± the equation T =T~ +ATxopl ( AT = T —T~ and xopt e[0,l] ). xopt will be introduced into the model as decision variables to find the desired target of each economic activity. • Under Scenario 2, the economic targets of each industry will approach their lower bounds (i.e., T± = T~), where the decision maker is conservative for economic 50 development. * Under Scenario 3, the economic targets of each industry will approach their upper bounds (i,e.,T±=T+), where the decision maker is optimistic for economic development, regardless of the water quality violation risks that may exist. * Under Scenario 4, the economic targets of each industry will be identified based on the equation 7"* =(T~ +T*)/2 . This corresponds to a situation where the economic targets approach their mid-value, and the decision maker is of neutral attitude to economic development and environmental protection. 4.4. Data Collection In this study, the natural, socio-economic and environmental conditions of the Xiangxi River Basin in Xingshan County were investigated via an extensive literature survey and field trip. Massive data with respect to the following four categories were collected, verified and analyzed to support the development of the water quality management model. (1) Economic Targets and Benefits The economic target and benefit data are given in Tables 4.1 and 4.2. Economic target and benefit data include the annual targets and profits of economic activities of the following five industries: (a) Agriculture • Grain crops 51 • Tobacco • Vegetables • Others (b) Forestry • Commercial forestry • Ecological forestry (c) Fishery • Fish and prawn (d) Livestock • Pigs • Cattle • Sheep • Poultry (e) Industry • Electric power industry • Chemical industry • Cement industry • Coal industry • Electronic industry • Food industry • Others 52 Table 4.1 Annual economic targets in each subarea Subarea 1 Subarea 2 Subarea 3 Subarea 4 Subarea 5 Subarea 6 Subarea 7 Subarea 8 Agriculture (km2) Grain crops [27.23, 27.56] [13.45,16.20] [26.96,27.12] [23.13, 23.76] [16.33,19.28] [11.79,13.61] [29.14, 29.93] [29.78, 29.90] Tobacco [0.37, 0.38] 0 0 [1.87,2.57] [2.33, 3.00] [9.2,11.23] [6.00, 8.84] [0.59,0.60] Vegetables [14.79, 15.78] [7.17,8.59] [4.13,4.27] [4.91, 5.74] [2.65,3.17] [8.83, 9.06] [8.9,21.81] [7.70, 8.24] Others [9.85,10.90] [4.65, 8.80] [8.54,10.59] [11.44,12.45] [6.53,9.29] [1.69,4.46] [16.03, 18.22] [8.58,9.83] Forestry (km2) Commercial forestry [108.71,216.86] [36.32, 72.45] [52.65,105.03] [42.17, 84.12] [67.28, 134.20] [87.51,174.56] [59.72,119.13] [113.10,225.61] Ecological forestry [84.55, 192.70] [28.25, 64.38] [40.95, 93.33] [32.80,74.75] [52.33,119.25] [68.06,155.11] [46.45,105.86] [87.97, 200.48] Fishery (km2) Fish and prawn [0.06,0.10] [0.02,0.03] [0.03,0.05] [0.02,0.04] [0.04,0.06] [0.05,0.08] [0.03,0.05] [0.06,0.10] Livestock (103 head) Pigs [41.41,41.78] [26.17,28,85] [55.80,56.64] [40.18,46.26] [24.10,27.35] [11.01, 15.05] [54.16, 55.80] [55.07, 55.21] Cattle [0.31,0.35] [0.10,0.10] [0.24,0.27] [0.48,0.60] [0,0.02] [0.43, 0.47] [0.45,0.50] [0.50,0.67] Sheep [8.96,10.15] [8.02,19.56] [5.86, 14.32] [15.01,22.41] [8.12,16.38] [14.41, 16.20] [18.01,43.74] [10.01,24.90] Poultry [64.40, 77.93] [30.20,36.28] [62.97, 76.90] [36.46,39.04] [23.57,27.50] [22.00,29.36] [37.91,122.22] [50.13, 53.06] Industry (RMB 104) Electric power [12.92, 28.90] 0 [0.37,0.53] [1.47, 2.26] [0.05,0.07] [0.11,0.16] [0.09, 0.13] Chemical [531.76,643.43] 0 0 0 [40.91,49.50] 0 [33.97,41.11] Cement 0 0 [20.34,34.37] 0 0 0 0 Coal 0 0 [1.33,1.62] 0 0 0 0 Electronic [2.13,3.17] 0 0 0 0 0 0 Food [1.87,1.99] [146.99,177.66] 0 [0.56,0.95] 0 [1.28,2.17] [0.71,0.88] Others 0 [1.59,1.82] 0 0 0 0 [0.71, 1.20] 53 Table 4.2 Economic profits of the economic activities Agriculture (RMB 104/km2) Grain crops Tobacco Vegetables Others [68.92,71.03] [233.10,284.70] [300.00,400.00] [150.00, 200.00] Forestry (RMB 104/km2) Commercial forestry Ecological forestry [11.21,14.90] [2.00,3.00] Fishery (RMB 104/km2) Fish and prawn [303.20,467.20] Livestock (RMB 104/103head) Pigs Cattle Sheep Poultry [91.24,97.40] [168.60,210.80] [47.1,68.00] [1.56, 2.12] Industry (RMB 104/107 RMB) Electric power Chemical Cement Coal Electronic Food Others [138.06,162.42] [292.17,343.73] [170.48,200.56] [385.04,452.98] [269.41,316.95] [408.75,480.88] [147.12,173.08] 54 (2) Environmental Penalties Environmental penalty data include the pollution mitigation costs, namely the environmental penalties, for excess discharges of the following four types of pollutants, as well as the pollutant discharging rates of the four pollutants from the above-listed economic activities. (a) Chemical Oxygen Demand (COD) (b) Total Nitrogen (TN) (c) Total Phosphorus (TP) (d) Soil loss The environmental penalty data are given in Tables 4.3 and 4.4. (3) Physical Parameters Physical parameters include the water quality standards and the probability of occurrence of river water quality. In this study, China's environmental quality standards for surface water (GB2002-3838) are adopted. The probability distribution of incoming water quality is generated according to the water quality monitoring records. The physical parameters are given in Tables 3.5 and 4.5. (4) Water Pollution Control Parameters The data related to pollution control include the maximum allowable pollutant discharges for the five individual economic industries under the three levels of incoming water quality, the overall maximum allowable pollution discharges under the three levels of incoming water quality, as well as and the water demands of the above-listed economic 55 Table 4.3 Mitigation costs of the four pollutants Pollutant Type COD TN TP Soil loss Mitigation Costs (RMB 104/kg) [0.06, 0.08] [0.23, 0.28] [1.13,1.41] [0.30,0.38] 56 Table 4.4 Pollution discharge rates of the four pollutants COD (kg) TN (kg) TP (kg) Soil loss (ton) Agriculture (km2) Grain Crops 0 [1,500,1,750] [600,700] [600,700] Tobacco 0 [500,625] [200,250] [200,250] Vegetables 0 [625,750] [250,300] [250, 300] Others 0 [750,875] [300,350] [300, 350] Forestry (km2) Commercial forestry 0 [90,110] Ecological forestry 0 [80,90] Fishery (km2) Fish and prawn [74,115,100,055] [4,117, 5,559] [580,783] 0 Livestock (103 head) Pigs [7,982,9,756] [1,352,1,653] [510,623] 0 Cattle [74,460,91,007] [18,330,22,404] [3,022,3,694] 0 Sheep [6,667,9,667] [1,000,1,500] [433,600] 0 Poultry [719,879] [165,201] [91,112] 0 Industry (RMB 104) Electric power 0 0 0 0 Chemical [25,67] [12,16] [17,36] 0 Cement [99,123] 0 0 0 Coal [100,123] 0 0 0 Electronic [60,74] 0 0 0 Food [76,94] [34,43] [2,9] 0 Others [68,84] 0 0 0 57 Table 4.5 Probability of the occurrence of incoming water quality Incoming water quality i ii in TV V Probability 0.15 0.80 0.05 0 0 58 activities. The water quality requirement of the Xiangxi River is China's water quality standard Grade III. Accordingly, the parameters related to pollution load capacity can be calculated. The control parameters are tabulated in Tables 4.6 and 4.7. 4.5. Result Analysis Results are obtained through solving the ITSP-WQM model using the aforementioned two-step interactive solution algorithm. Optimized targets of the economic activities are generated under Scenario 1. The pre-determined targets of the economic activities are applied under Scenarios 2 to 4 according to the previously mentioned scenario design. The targets of Scenarios 1 to 4 are presented in Appendix A. The desired pollution mitigation amounts of the four pollutants from the eighteen economic activities under three incoming water quality levels are also obtained under the four scenarios. Detailed solutions under Scenarios 1 to 4 are provided in Appendix B. Consequently, the targeted income, mitigation costs, and net system benefit under the four scenarios can be generated to facilitate the decision-making process. Economic benefit denotes the profits of the economic productions, which is determined by the first-stage decisions regarding the economic development targets. The mitigation costs denotes the pollution abatement expense in order to meet a certain water quality level. It can also be considered as environmental penalty of the system, which is caused by the economic activities that caused an over generation of pollutants. The mitigation costs can be calculated based on the second-stage decisions regarding the pollution reduction Table 4.6 Maximum allowable pollution discharges of the four pollutants Incoming water quality Pollutant Type I II III COD (103 kg) [5,311,7,081] [3,541, 5,311] [2,656,3,541] TN (103 kg) [1,517,2,023] [1,012,1,517] [506, 1,012] TP (103 kg) [537,740] [358,555] [179.0,370] Soil loss (103 ton) [1012,1349] [674,1012] [337,674] 60 Table 4.7 Water demands of the economic activities Agriculture (104 m3/km2) Grain Crops Tobacco Vegetables Others [34.26,44.46] [2.25,2.69] [29.99,74.96] [37.48,52.47] Forestry (104 m3/km2) Commercial forestry Ecological forestry [70.00, 80.00] [20.00, 40.00] Livestock (104 m3/103head) Pigs Cattle Sheep Poultry [110.00,130.00] [130.00,150.00] [90.00,110.00] [20.00,30.00] Industry (104 m3/107 RMB) Electric power Chemical Cement Coal Electronic Food Others [19.74,78.96] [67.90,271.62] [18.03,72.11] [40.89,163.57] [12.90,51.59] [20.79,83.16] [36.60,146.41] 61 schemes. Net system benefit is the difference between the total targeted income and mitigation costs, which denotes the overall benefits of economic development and environmental protection in the studied area. 4.5.1. Solutions under Scenario 1 (1) Economic Targets The generated objective function value and solutions to most of the non-zero decision variables under Scenario 1 are intervals, demonstrating that the related decisions are sensitive to the uncertain modeling input. In the first scenario, the target variable xopt is ,± designed to adjust the economic targets, which are in the form of 7 = T~ + ATxopl. This allows the system to search for the optimal economic targets in the range of [T~,T+], so that the compromise between economic development and environmental management could be achieved and the highest system benefit could be obtained. Scenario 1 represents a situation wherein decision makers have no preference regarding the economic targets. Scenario 1 is also considered as the baseline scenario. The optimal results of the target variables x^ are given in Table 4.8. Under this scenario, the targets of several types of agricultural activities, forestry activities and all industrial activities excluding chemical industry would approach their upper bounds, while the optimized targets in fishery and livestock would approach their lower bounds. It is implied that, considering the tradeoff between economic development and 62 environment protection, the priorities of local development in Xingshan County should be forestry and industry whereas the development of fishery and livestock should be limited. According to the lower and upper bound value of the net benefit of each economic activity (Table 4.2) in the lower and upper bound models, the lower and upper bounds of the targeted income for each industry could be further calculated. The targeted income segments of the total five industries are presented in Figure 4.1. It is indicated that industry would account for the largest proportion (i.e. RMB [29.21, 31.25] * 108). The targeted incomes of agriculture, livestock, forestry and fishery would be RMB [5.68, 5.69] x 10®, [3.39, 3.72] x 108, [1.99, 2.15] * 108and [0.012, 0.014] x io8, respectively. It is signified that in the results of the lower bound model, where the water quality penalty cost approaches its upper bound value, the proportion of industry and forestry would increase (from 71.67 % to 71.94% and from 4.21% to 4.46%, respectively) while that of agriculture (from 15.35% to 15.21%) and livestock (from 8.76% to 8.35%) would decrease. In detail, the optimized targets of agricultural, forestry, and industrial activities under Scenario 1, are given in Figure 4.2. As for agriculture, grain crop fanning would be the primary activity. Grain crop farming, vegetable farming, tobacco farming and other farming activities would account for the proportions of 53.88, 20.53, 6.24 and 19.35%, respectively. As for forestry, the target of the commercial forest (i.e. 787.21 km2, 52.95%) would be slightly higher than that of the ecological forest (i.e. 699.52 km2,47.05%). This may result from the relatively high net benefit of commercial forestry. The optimal farming area of fishery would be 0.21 km2. Pigs and poultry husbandry would be the 63 Table 4.8 Solutions to decision variables *opt , under Scenario 1 Subarea 1 2 3 4 5 6 7 8 Agriculture Grain crops 0 0 0 0 0 0 0 0 Tobacco 0 0 0 0 0 0 0 0 Vegetables 1 0.07 1 1 1 1 0 1 Others 0 0 0 0 0 0 0 0 Forestry Commercial forestry 1 1 1 1 1 1 1 1 Ecological forestry 1 1 1 1 1 1 1 1 Fishery Fish and prawn 0 0 0 0 0 0 0 0 Livestock Pigs 0 0 0 0 0 0 0 0 Cattle 0 0 0 0 0 0 0 0 Sheep 0 0 0 0 0 0 0 0 Poultry 0 0 0 0 0 0 0 0 Industry Electric power 1 0 1 0 1 1 1 1 Chemical 0 0 0 0 0 0.45 0 0 Cement 0 0 1 0 0 0 0 0 Coal 0 0 1 0 0 0 0 0 Electronic 1 0 0 0 0 0 0 0 Food 1 1 0 0 1 0 1 1 Others 0 1 0 0 0 0 0 1 64 Lower bound Agriculture 15.21% Forestry / , Fishery 4.46% 0.03% Livestock 8.35% 71.94% Industry Figure 4.1 (1) Targeted income segments of the five industries under the optimized scheme of Scenario 1 (Lower bound) 65 Upper bound Agriculture / 15.35% Forestry / .Fishery 4.21% 0.03% Livestock 71.67% Industry Figure 4.1 (2) Targeted income segments of the five industries under the optimized scheme of Scenario 1 (Upper bound) 66 Agriculture (km2) Others 42.70 19% Grain Crops 118.89 54% Vegetable 45.29 21% 13.77 Figure 4.2 (1) Target segments of the agricultural activities under the optimized scheme of Scenario 1 67 Ecological Forestry (km2) Forest 699.52 Commercial Forest 787.21 52.95% Figure 4.2 (2) Target segments of the forestry activities under the optimized scheme of Scenario 1 68 Industry (RMB 10s) Food Other Electric Industry 1.82 Electronic 180.74 0.20% Power Industry 20.22% .Industry 3.17 37.04 0.36% 4.14% Coal Industry 1.62 0.18% Cement Industry 39.86 Chemical 4.46% Industry 629.75 70.44% Figure 4.2 (3) Target segments of the industrial activities under the optimized scheme of Scenario 1 69 major livestock activities. The optimal number of pigs and poultry would be 1.99 x 105 head and 2.40 x 108 head, respectively. One reason pig farming would be the primary livestock activity is that there are several pork-processing factories in Xingshan County, which increases the potential benefit of pig husbandry. At the mean time, the dominant industrial sector would be chemical industry (i.e. RMB 580.76 x 108), which mainly consists of the phosphorite mining and processing industry (accounting for 68.73% of the total industrial production in this basin). This is reasonable because of the abundant phosphorite in the Xiangxi River Basin. The second largest industrial activity would be the electric power industry which results from the intensive hydropower development along the Xiangxi River. The food industry, cement industry, electronic industry, coal industry and other industries would account for 21.39, 4.71, 0.38, 0.19 and 0.22% of the total industrial targets, respectively. The distribution of targeted income of agriculture, forestry, fishery, livestock, and industry within eight subareas is shown in Figure 4.3. It is shown that Subarea 7 would obtain the highest agricultural targeted income (i.e. RMB [1.05, 1.70] x 108). Both the lower and upper bounds of the agricultural incomes in all of the other seven subareas would be below RMB 1.00 x 108. The forestry targeted income distribution among the eight subareas would be fairly even, within the range of RMB [0.13, 0.42] x 108. The income of the fishery industry would fall in the range of RMB [119.21, 140.26] x 104, which is the lowest of the five indmtries. The total income of the livestock industry would be RMB [3.39, 3.72] x 108, the majority of which would be in Subareas 3, 7, and 8. The majority of industrial activities would be located in Subareas 1 and 2, with (i.e., • 70 RMB [16.44, 18.94] x 108 and RMB [8.55, 8.57] x 108, respectively). The reason the industrial production would be significantly high in Subarea 1 is due to the fact that the largest phosphorite mining and processing factories are located in this area. Industrial productions would be relatively low in Subareas 4, 5, and 7. It could also be observed from the figure that industry would be the major economic sector in Subareas 1 to 3,6, and 8. Comparatively, agriculture and livestock would be the dominant sectors in Subareas 4, 5, and 7. (2) Pollution Mitigation Optimal targeted income and the expected value of mitigation costs in the eight subareas are presented in Figure 4.4. The highest income (i.e. RMB [18.13,20.84] x 108) would be in Subarea 1, which is also the capital of Xingshan County, as well as where the major factories of the county are located. The second highest income (i.e. RMB [9.35, 9.50] x o 10 ) would be in Subarea 2. The incomes in Subareas 3 to 8 would be less than RMB o 3.00 x 10 . However, the cost distribution pattern of mitigation costs would be different from that of the optimal economic income. The variance of the mitigation costs in the eight subareas is not significant. The highest pollution abatement costs would occur in Subareas 1, 3, and 7. In Subarea 2, where the income would be relatively high, the mitigation costs would be low. The situations in Subareas 1 and 6 resemble a pattern wherein the mitigation costs and the targeted income would not be proportionate. It might be because the pollution in Subareas 1, 2 and 6 is mainly from industrial wastewater. Since the technologies of industrial point source pollution treatment are far more developed than other non-point source pollution control, the mitigation of point source 71 pollution is much less costly than that of non-point source pollution, such as agriculture and livestock. It is also disclosed that industrial activities would bring high benefit and relatively low pollution mitigation cost. Thus, pollution from industry should be given priority for treatment. Mitigation amounts of the four pollutants under the three levels of incoming water quality (Grade I, II, and III) are shown in Figure 4.5. The amounts of pollution that should be reducted would vary under different levels of incoming water quality, which would eventually result in different pollution reduction costs. When the incoming water quality meets the standards of Grade I, the four pollutants barely require reduction. However, when the incoming water quality degrades to Grade II, certain treatment should be undertaken to control COD, TN, TP and Soil loss. The pollution abatement amount would be [10.38, 134.60] * 103kg, [2.49, 71.20] x 103 kg, [5.59, 22.75] * 103kg, and [0, 14.89] x 103 ton, respectively. When the incoming water quality deteriorates and turns to Grade III, the mitigation demand for COD would increase dramatically (i.e. [1,064.40, 1,342.80] x 103kg), and that for TN, TP and Soil loss would increase to [365.46, 505.95] x 103 kg, [150.10, 206.03] x 103kg, and [21.25, 125.87] x 103 ton, respectively. According to China's environmental quality standards (Table 3.5), the standard concentration of TN is four times higher than that of TP (1.0 and 0.2 mg/L for TN and TP, respectively). However, under the pollution mitigation scheme of Scenario 1, the mitigation demand for TN is only 2.3 - 2.4 times that of TP ([300.42, 505.05] x 103 kg and [129.17, 215.35] x 103 kg for TN and TP, respectively). It is implied that TP control is vital to water quality management, and underlying attention and investment should be paid for TP control. 72 ' Lower Bound Industry Livestock Fishing Forestry Agriculture Subarea 1 Subarea 2 Subawa 3 SubareaA Subarea5 Subarea6 Subarea7 Subarea 8 bound) optimized scheme of Scenario 1 0-ower ies in Subareas 1 to 8 under the from the five industnes 4,3 (1) Targeted income 73 Upper Bound Industry Livestock Fishing Forestry Agriculture Subareal Su5area 2 Subarea 3 Subawa* subwa*5 SuMim6 suMmT Subarea 8 scheme of Scenario 1 (Upper bound) ies in Subareas 1 to S under the op' from the five industries Figure 4.3 (2) Targeted income 74 25 i 'Targeted income (Upper bound) •••Targeted income (Lower bound) 20 M Mitigation cost (Upper bound) —• 'Mitigation cost (Lower bound) 15 &y OQ z oc 10 1 2 3 4 5 6 Subarea Figure 4.4 Results of targeted income and mitigation costs of the eight subareas under the optimized scheme of Scenario 1 75 1600 COD TN TP Soil loss 1400 1200 1000 * 3 800 1 < C 0 600 1o> HE 400 200 II III I II III I Quality of the incoming water COD (lower bound) (kg) •COD (upper bound)(kg) •A" TN (lower bound)(kg) •TN (upper bound)(kg) TP (lower bound)(kg) •TP (upper bound)(kg) Soil loss (lower bound)(ton) •Soil loss (upper bound) (ton) Figure 4.5 Mitigation amounts of the four pollutants under the three levels of incoming water quality 76 4.5.2. Comparisons of the Results under Scenarios 1 to 4 The detailed solutions for the objective functions and decision variables under Scenarios 1 to 4 are provided in tabular form in Appendices A to E. In the following comparisons of the solutions under Scenarios 1 to 4, "SI", "S2", "S3" and "S4" represent "Scenario 1", "Scenario 2", "Scenario 3", and "Scenario 4", respectively. Results of the targeted income, mitigation costs, and net system benefit under Scenarios 1 to 4 are presented in Figure 4.6. As the optimal economic prodution under Scenario 3 are the highest among the four scenarios, the obtained objective function value would be the highest (i.e. [41.03, 48.84] x 108 RMB). However, the high mitigation costs might have to be paid accordingly, because the intense economic activities would result in excessive pollution discharges. The cost for pollution control under Scenario 3 would also be the highest (i.e. RMB [16.42, 34.54] x 108). Under Scenario 2, the targeted income would be the lowest (i.e. RMB [33.14, 39.22] x 108), which would lead to a relatively low mitigation cost (i.e. RMB [5.67, 13.19] x 108). The targeted incomes under Scenarios 1 and 4 would be RMB [39.06, 42.66] x I08and RMB [37.09, 44.03] x 108, respectively. o Correspondingly, the associated mitigation cost would be RMB [5.80, 13.80] x 10 and RMB [8.30, 26.50] x 108, respectively. The highest objective value (i.e. RMB [25.26, 36.86] x io8) would be achieved under Scenario 1, where the economic targets are prioritized. The net system benefit would be RMB [19.95, 33.55] x 108and RMB [10.59, 35.73] x 108 under Scenarios 2 and 4, respectively. The lowest objective value would be obtained under Scenario 3 (i.e. RMB [6.50,32.42] x io8), where the pre-regulated 77 •Upper bound ILower bound S1 S2 S3 S4 •Upper bound ILower bound £ 30 S2 S3 S4 •Upper bound • Lower bound S1 S2 S3 S4 Figure 4.6 Results of the targeted income, mitigation costs, and net system benefit under Scenarios 1 to 4 78 economic targets are the highest. It is demonstrated that different policies for pre-regulating the economic targets would result in different net system benefit and water quality violation risks. The results also imply that the system would achieve a low net benefit if the pre-determined economic targets were maximized without any consideration to environmental protection. (1) Economic Targets The targeted income intervals from the five industries under Scenarios 1 to 4 are presented in Figure 4.7. The values of the targeted income in the eight subareas under Scenarios 1 to 4 are presented in Figure 4.8. The four scenarios resemble a general economic target distribution pattern among the eight subareas and five industries, wherein the industrial production of Subareas 1 and 2 would be the dominant economic activities. The targets under Scenarios 2 would be the lowest, indicating that decision makers are conservative for economic development and concerned about environment protection. The targets under Scenario 3 are the highest, representing decision makers' aggressive attitude regarding economic development and their comparative optimism in environmental problems. The pre-defined target of each activity under Scenario 4 is the average of those under Scenarios 2 and 3, implying decision makers' neutral attitude regarding the economy and environment. The interval value of forestry and industrial productions under Scenario 1 would be higher than those under Scenario 4, whilst the interval incomes of agriculture, fishery, and livestock husbandry under Scenario 1 would be lower than those targets under Scenario 4. As for the pre-determined economic target distribution among the eight subareas, the lower and upper bound targets of Subareas 1, 7, and 8 under Scenario 1 would be lower than those in the other five subareas. It is implied 79 Lower bound 40 /" 35 & T- 30 ffl 2 gc. 25 o E 20 c8 15 p>® 10 5 Agriculture Forestry Fishery Livestock Industry • S1 »S2 "S3 BS4 Figure 4.7 (1) Targeted income of the five industries under Scenarios 1 to 4 (Lower bound) 80 Upper bound Agriculture Forestry Fishery Livestock Industry Figure 4.7 (2) Targeted income of the five industries under Scenarios 1 to 4 (Upper bound) 81 Lower bound Subarea 1 Subarea 2 Subarea 3 Subarea 4 Subarea 5 Subarea 6 Subarea 7 Subarea 8 • S1 • S2 i S3 •S4 Figure 4.8 (1) Targeted income of the eight subareas under Scenarios 1 to 4 (Lower bound) 82 Upper bound Subarea 1 Subarea 2 Subarea 3 Subarea 4 Subarea 5 Subarea 6 Subarea 7 Subarea 8 • S1 «S2 "S3 "S4 Figure 4.8 (2) Targeted income of the eight subareas under Scenarios 1 to 4 (Upper bound) 83 that in the optimized economic development scheme, emphasis would be given to Subareas 2 to 6. (2) Pollution Mitigation Solutions to the decision variables regarding pollution mitigation schemes, (i.e., the pollution reduction amount of each activities under the three levels of incoming water quality) indicate that under all of the four scenarios, when the quality of incoming water satisfies the standards of Grade I, no pollution control would be required. However, if the quality of incoming water degrades and meet the standards of Grade II or Grade III, pollution abatement should be conducted. Due to the low pollutant discharge rate of forestry and its relatively high profits, no pollution control would be required for forestry activities, whereas pollution abatement would be required for the production in agriculture, livestock, fishery, and industry. The mitigation scheme of the situation where the quality of incoming water is Grade II is tabulated in Table 4.9. The mitigation amounts would be the highest under scenario 3 in all of the five industries, while they would be the lowest under Scenario 2. The mitigation amounts under Scenario 1 would be much lower than those under Scenario 4, but slightly higher than those under Scenario 2. The detailed mitigation scheme of each industry of the situation where the incoming water quality is Grade III is presented in Figures 4.9 to 4.12. It is shown that, resulted 84 Table 4.9 Mitigation schemes under Scenarios 1 to 4 when the incoming water quality is Grade II SI S2 S3 S4 Agriculture (km2) [0,24.81] [0,22.02] [0,49.60] [4.36, 33.02] Forestry (km2) 0 0 0 0 Fishery (km2) 0 0 [0, 0.12] [0,0.02] Livestock (103 head) [0,1.75] [0,1.75] [141.22,197.87] [0, 80.54] Industry (RMB 104) 155.13 143.26 363.99 335.17 "SI", "S2", "S3" and "S4" represent "Scenario 1", "Scenario 2", "Scenario 3", and "Scenario 4", respectively. 85 Lower bound Subaraa 1 Subarsa 2 Subarea 3 Subarea 4 Subarea 5 Subaraa 6 Subarea 7 Subarea 8 • S1 "S2 "S3 "S4 Figure 4.9 (1) Percentage of mitigation amounts of agricultural production under the incoming water quality of Grade III (Lower bound) 86 Upper bound Sub area 1 Subaraa 2 Subarea 3 Subarea 4 Subarea 5 Subarea 6 Subaraa 7 Subaraa 8 • S1 "S2 "S3 IS4 Figure 4.9 (2) Percentage of mitigation amounts of agricultural production under the incoming water quality of Grade III (Upper bound) 87 Lower bound Subarea 1 Subarea 2 Subarea 3 Subarea 4 Subarea 5 Subarea 6 Subaraa 7 Subarea 8 • SI 1S2 BS3 1S4 Figure 4.10 (1) Percentage of mitigation amounts of fish farming under the incoming water quality of Grade III (Lower bound) 88 Upper bound 5? 8 4 Subaru 1 Subarea 2 Subaraa 3 Subarea 4 Subarea 5 Subarea 6 Subaraa 7 Subarea 8 »S1 • S2 • S3 • S4 Figure 4.10 (2) Percentage of mitigation amounts of fish farming under the incoming water quality of Grade III (Upper bound) 89 Subarea 1 Subarea 2 Subaraa 3 Subarea 4 Subarea 5 Subarea 6 Subarea 7 Subarea S iS1 • S2 • S3 • S4 Figure 4.11 Percentage of mitigation amounts of livestock husbandry under the incoming water quality of Grade III 90 Lower bound £ 20 1 i i 1 i 11 i 111.1 i i i i Subarea 1 Subarea 2 Subarea 3 Subarea 4 Subarea 5 Subarea 6 Subarea 7 Subarea 8 • S1 "S2 • S3 • S4 Figure 4.12 (1) Percentage of mitigation amounts of industrial production under the incoming water quality of Grade III (Lower bound) 91 Lower bound Subarea 1 Subarea 2 Subaroa 3 Subarea 4 Subarea S Subarea 6 Subarea 7 Subarea 8 • S1 *S2 "S3 BS4 Figure 4.12 (2) Percentage of mitigation amounts of industrial production under the incoming water quality of Grade III (Upper bound) 92 from the different economic targets under the four scenarios, the corresponding pollution reduction amount would vary greatly among scenarios. As for agricultural production, the upper bound mitigation costs of the eight subareas would be significantly high under Scenario 1. In addition, the upper bound mitigation amount under Subareas 1,3, and 7 would be relatively high. In the lower bound results, the agricultural pollution reduction amounts in Subareas 1, 7, and 8 would be high while those in Subareas 2, S, and 6 would be low. As for fish farming, the results resemble a distribution pattern among the subareas under the four scenarios, expect the mitigation amounts in Subarea 4 under Scenario 3 would be particularly high. Pollution control would be required in Subarea 6 under all the scenarios, whereas it would be necessary only under Scenario 3. The pollutant abatement in fishery should be mainly conducted in Subareas 1, 6, and 8. As for livestock husbandry, the lower and upper bounds of the results have the same value, which means the solutions are deterministic. In most of the subareas, mitigation in Scenarios 1 and 2 would be similarly low, and that in Scenario 3 would be the highest. More intense pollutant mitigation should be conducted in Subareas 1, 3, 7, and 8 than the other subareas. As for industrial production, the mitigation schemes are consistent among the four scenarios. The highest pollution treatment should be conducted in Subareas 1 and 2. Subareas 6 and 8 would require small amounts of abatement, while very little pollution control would be needed in Subareas 3,4, 5, and 7. 4.6. Summary In this study, a large-scale regional inexact two-stage stochastic programming water 93 quality management (ITSP-WQM) model were developed. This model is based on inexact two-stage programming, which is a hybrid method derived from Two-stage Stochastic Programming (TSP) and Interval-parameter Programming (IP). In the IP method, the uncertain elements only have crisp lower and upper bounds that determine the interval. No information regarding the distribution or membership between the lower and upper bounds would be required. In the TSP method, the probabilistic uncertainties of the random elements can be reflected through applying a specification of the probability distributions. Uncertainties expressed as both probability distributions and discrete intervals can be addressed within the optimization framework via incorporating the two methods. In addition, the ITSP-WQM model can provide an effective linkage between the pre-regulated economic policies and the corresponding environmental penalties attributed to the failure to comply with the water quality requirements. The ITSP-WQM model can be solved by transforming into two deterministic sub-models, which correspond to the lower and upper bounds of the objective function value, and then interval solutions can be obtained by solving the two sub-models sequentially. The developed ITSP-WQM model was applied to support water quality management in the Xiangxi River Basin in Xingshan County, Hubei Province, China. The results provided stable intervals for the objective function and decision variables with different levels of risk of violating the constraints. Eighteen activities of agriculture, forestry, fisheiy, livestock and industries have been taken into consideration. Four scenarios that represent tradeoffs between system benefits and system-failure risks have been designed and examined. Decision alternatives for local economic development plans and pollution 94 control schemes have been provided. The baseline scenario (i.e. Scenario 1) resulted in the highest objective function value, and this scenario has been analyzed. The targeted income, mitigation costs, and net system benefit under the four scenarios have also been analyzed. It is indicated different policies for economic targets correspond to different water quality and pollution penalties, and thus, lead to varied system benefit and system-failure risk. 95 CHAPTERS AN INEXACT TWO-STAGE STOCHASTIC CREDIBILITY CONSTRAINED PROGRAMMING WATER QUALITY MANAGEMENT MODEL 5.1. Background Water quality is increasingly being acknowledged as a central factor in the water crisis in the Xiangxi River Basin. In recent years, the pace of economic development and scope of water quality problems grew fast. However, the pollutant discharges increased drastically and the pollution load capacities decreased due to the construction of the Three Gorges Reservoir. Changes to the basin including increase in population, rapid urbanization, industrialization, and hydropower development have resulted in detrimental impacts on the water quality. Water quality management is an integral part of environmental management and an essential requirement for the continuing viability of most sections of our society. A cost-effective and sustainable water quality management strategy is in desperate need for this area. The water quality situation is highly variable reflecting social, economic and physical factors as well as state of development, which are inherent with a number of uncertainties in the water quality management system. In the previously proposed inexact two-stage stochastic programming water quality management (ITSP-WQM) model, only those uncertainties described as interval information and stochastic events can be address. However, in practice, it is hard for decision makers to obtain probability distributions for 96 all random variables, while simply representing the uncertainties by deterministic or interval value would lead to a waste of valuable information (Zhang and Huang, 2011). Some system components, such as pollutant loading capacities can be presented as fiizzy sets featured with subjective membership functions that are determined by decision makers. In this scope, it is often necessary to deal with fuzzy information during the decision-making process of pollution control. Thereby, a more advanced approach, which is capable of encoding the fuzzy information in the water quality management system, is desired. Fuzzy theory has been widely applied in environmental quality management (Mujumdar and Sasikumar, 2002; Onkal-Engin et al., 2004; Al-Shayji et al., 2008; Zhao and Chen, 2008). Sasikumar and Mujumdar (1998) applied fuzzy theory to incorporate the aspirations and conflicting objectives of the pollution control agency and discharges, and developed a fiizzy waste-load allocation model for the water quality management of a river system using fuzzy multiple-objective optimization. The significance of fuzzy memberships as environmental indices has also been demonstrated and recognized (Silvert, 2000; Lu and Lo, 2002). For instances, Lu et al. (1999) determined the individual membership functions of evaluated factors, established a fiizzy evaluation matrix for the trophic status assessment for the Fei-Tsui Reservoir ain Taiwan, and proved that fuzzy synthetic evaluation is better suited to rate the trophic status than the tranditional deterministic index. Qiao et al. (2008) established fuzzy collections of the pollution evaluation factors and applied the fiizzy comprehensive evaluation method to the water quality evaluation of the Yangtze River. Soroush et al. (2011) proposed a fiizzy 97 index to evaluate water quality for industrial uses, and demonstrated the index with a case study from the Zayandehrud River, located in Isfahan Province, Iran. Fuzzy mathematic programming has been proved as an effective method to reflect fuzzy information. The conventional fuzzy mathematic programming methods include fuzzy flexible programming and fuzzy robust programming (Zimmermann, 1978; Huang et al., 1995; Buckley and Feuring, 2000; Mula et al., 2006; Nie et al., 2007; Li et al., 2008). Credibility constrained programming is a recently proposed fuzzy mathematic programming method (Luo et al., 2004). It is derived from fuzzy possibility theory, as an alternative to probability theory as used in the stochastic programming method (Zadeh 1978). It is a remarkable method that can address fuzzy information (Luo et al., 2004; Huang, 2006; Zhang and Huang, 2010; Zhang and Huang, 2011). Therefore, in this study, fuzzy theory will be applied to reflect the fuzziness of water quality standards and thus tackle the uncertainty of environmental capacities. Fuzzy membership functions will be used to encode the possibilistic distribution of the parameters. The concept of credibility, as well as the credibility constrained programming method will be introduced into the aforementioned ITSP-WQM model to represent the satisfaction levels of the constraints. An Inexact Two-stage Stochastic Credibility Constrained Programming (ITSCCP-WQM) model will be developed and applied in the case study of the Xiangxi River Basin in Xingshan County. The results of the ITSCCP-WQM model will provide pollution mitigation alternatives, combining economic development policies with different of risk-violation levels to support local water quality management and sustainable development. 98 5.2. Methodology 5.2.1. Credibility The concept of credibility is derived from the fuzzy possibility theory, which was first introduced by Zadeh (1978) as an extension of his theory of fiizzy sets and fuzzy logic. Possibility theory appears as a mathematical counterpart of probability theory, which deals with uncertainty by means of fiizzy sets (Dubois et al., 2004). Let £ be a triangular fiizzy variable and let t_, t, t and r be real numbers (Zhang and Huang, 2009). The fuzzy membership function // of t; is given by: r-t if t_ M(r)= ^4 ift Whereas probability theory uses a single number (i.e., the probability) to describe how likely an event is to occur, possibility theory uses a pair of functions to describe the likelihood of an event occurring: the possibility and the necessity of an event. Let / be the function that has real value in set X with the highest value of max(/). The possibility of the fiizzy event wherein £ < r is the possibility that there exists at least one value x of £ that satisfies x 99 Pos{£ < r) = max //(X) = max!//, (JC) | x e R,x < r} (5.2) fl The necessity measure of the fuzzy event wherein £ < r is defined by: Nec{£ < r} = 1 — Pos{^ > r} = 1- max /i(x) (5.3) H>r Accordingly, the possibility of the fuzzy event wherein £ > r can be expressed as (Zhang and Huang, 2010): 1 if r The necessity of the fuzzy event wherein £ > r can be expressed as (Zhang and Huang, 2010): 1 t-r Nec(g > r) = if t_ Possibility theory is driven by the principle of minimal specificity. It is stated that any hypothesis not known to be impossible cannot be ruled out (Dubois, 1983). For instance, as for the fuzzy event of t >r, as long as r < t ? the value of the possibility is 1, which means that the state r < / is totally possible (Zhang and Huang, 2010). However, there is a chance that the fuzzy event would not hold when the realization value of r lies in the interval [£, /], even though the possibility value is 1. The possibility measure is unable to reflect the differences among the fuzzy events when t_ Credibility is a linear combination of possibility measure and necessity measure to avoid these disadvantages. The credibility Cr is determined by the average of the possibility and necessity, and it is defined by (Yang and Iwamura, 2008): Cr{% < r} = ^{Pos{4 Thereby, the credibility of the fuzzy event wherein £ > r can be expressed as (Zhang and Huang, 2011): 1 ifr To better illustrate the three concepts, the fuzzy membership function of as well as the possibility, necessity, and credibility of the fuzzy event wherein t < r are shown in Figure 5.1. The advantage of credibility is that it is a self-dual measure while either possibility or necessity is not (Zhang and Huang, 2011). According to Equation 5.7, the lower the credibility, the less likely there will be an occurrence of fuzzy events. When the credibility value is 1, the fuzzy event will certainly happen and when the credibility is 0, it will certainly not happen (Zhang and Huang, 2010). It is demonstrated that no feature of fuzzy sets will be missing by applying credibility measure, and it is a more practical 101 Fuzzy set o t t t Possibility o.s 0 t t t Necessity 0.5 0 t t t Credibility o.s « t t t Figure 5.1 Fuzzy membership, possibility, necessity and credibility of a fuzzy set (Zhang and Huang, 2011) 102 measure for fuzzy events (Zhang and Huang, 2010). 5.2.2. Inexact Credibility Constrained Programming Credibility can applied in optimization modeling to express fuzzy information. The formulation of a conventional Credibility Constrained Programming (CCP) model is as follows (Zhang and Huang, 2011): Max / = cTx (5.8a) subject to: Cr{Ax x>0 (5.8c) where x is a vector of decision variables; A denotes the coefficients, b is a fuzzy set, and A (0 < X < 1) denotes the level of credibility. The higher the value of X is, the more satisfied the constrained will be. Based on Equation 5.7, the credibility of Ax 1 if Ax In the optimization process for management and planning, it is usually assumed that the credibility level should be no less than 0.5 (Yang and Iwamura, 2008; Zhang et al., 2011). Thus, the Constraint 5.8b can be re-written as: 103 Cr{Ax Hence, the conventional CCP model can be transformed into a deterministic model as follows (Zhang and Huang, 2011): Max / = cTx (5.11a) subject Xo\ Ax x>0 (5.11c) Thereby, crisp solutions can be generated when the credibility level X is determined. In the CCP model, fuzzy information in the right-hand side coefficients can be addressed. However, in practice, uncertainties also exist in the system components in other formats such as the format expressed as intervals with deterministic lower and upper bounds. To solve this problem, Zhang et al., (2011) introduced inexact linear programming into the conventional CCP model and developed an inexact credibility constrained programming (ICCP) model. In the ICCP model, system parameters and decision variables are intervals, and the formulation of the ICCP model is as follows: Max /±=(c±)rjc± (5.12a) subject to: Cr{Ax± x*>0 (5.12c) According to Equation 5.10, the constraint 5.12b can be transformed into: 104 ^c±<6 + (l-2A±X^-fe) (5.13) Thus, the ICCP Model 5.12 is equivalent to (Zhang and Huang, 2011): Max/±=(c±)r*± (5.14a) subjectto: Ax* x±>0 (5.14c) Applying two-step interactive solution algorithms of the inexact linear programming, Model 5.14 can be solved by transforming into two deterministic sub-models, which correspond to the lower and upper bounds of the objective function value. The sub-model corresponding to the upper bound of the objective function value is formulated as follows (Zhang and Huang, 2011): Maxr = + Z c]x- (5.15a) subjectto: |" signia^x* + £ \aj f sign(a*)x~ */ >0,7=1,...,*, (5.15c) x~ >Q,j= k x,...,n (5.15d) where the coefficients c* (J -1 to ) are positive, and the coefficients c* (j = £, to n) are negative; sign(a*) denotes -1 when a* < 0 and it denotes 1 when a* > 0; and f* is the upper bound of the objective function value. Model 5.15 can be solved and the optimal solution Xj_opl for / = 1 to kt and x~ Jjis for 105 j - kx to n can be obtained. Then, the sub-model corresponding to the lower bound of the objective function value can be constructed as below (Zhang and Huang, 2011): Max/" = £c;x; + X c;*; (5.16a) y=i y=*i+i + subject to: ]£| a* | sign(aJ)Xj + ^ | a* \~ sign(a*)x* x* >x-_opl,j = ku...,n (5.16c) 0 < x~ < x)_op„j = 1 (5.16d) Optimal solution x^opi for j = 1 to k{ and JCJ for j = £, to « can be gained for Model 5.16. Therefore, solutions for the ICCP Model 5.12 can be obtained as follows: 4, =r/0;„/0;,] (5.i7) Xj-op, = ix'-opt > xj-op, ] (5-18) The ICCP model can deal with uncertainties expressed as intervals and fuzzy sets in water quality management, such as interval economic targets and discharge rates, as well as fuzzy water quality requirements and fuzzy environmental capacities. However, in dynamic decision-making process, such as water quality management process, decisions should be adjusted continually according to the occurrence of random events. Uncertainties that appears as stochastic events cannot be reflected in the ICCP model. 106 5.2.3. Inexact Two-stage Credibility Constrained Programming To tackle the uncertainties in the format of random events and their dynamic interactions with other system components, an inexact two-stage credibility constrained programming (ITSCCP) model is developed in this study. The ITSCCP model can be formulated as follows: ±7 Max/* = cV - E%{minfa(mf )] y (oof)} (5.19a) subject to: Cr{A±x± HO** +W((of)y± =h(af), V/ = 1,2,...,7V (5.19c) x± > 0,y±((of) > 0. (5.19d) where x* denotes the vector of the interval first-stage decision variables; c±x± is the first-stage system benefit; According to the solution algorithms of the conventional ICCP model and ITSP model, Model 5.19 can be transformed into: Max/* = cV - Ya P,Q(y±^f) (5.20a) I 107 subject to: Ax* <6+(1-2^)0-6) (5.20b) T(a>f)x* +W((of)y± =h((of), V/ = 1,2,...,N (5.20c) x±>0,y±((of)>0. (5.20d) where p, is the probability of the occurrence of the stochastic event a, ; and Q(y±,G)f ) denotes the second-stage recourse cost. If the second-stage recourse cost can be formulated as Q{y±,of) = qfyf, Model 5.20 can be further transformed into two deterministic sub-models, as described above. The sub-model corresponding to the upper bound of the objective function value is as follows: Ma x/+ = £c+x* + £ c*xj ~Y$LPi subject to:^ |a*|-Sig*(«;)*;+ E \a*\+ sign(a*)x- xf >0,j = 1,...,A, (5.21c) x~>0,j = k l,...,n (5.21 d) y~>0,j = \,...,k2 (5.21e) x* >0,j = k2,...,m (5.21f) where coefficients c* (j = 1 to ) are positive, coefficients cJ (/ = kx to ri) are negative; coefficients q~ (? = 1 to k2) are positive; and coefficients q~ (i = &2 to m) are ± + negative. sign{a j) denotes -1 when a* <0 and it denotes 1 when a* >0; and / is the upper bound of the objective function value. 108 for 1 X j-oP, j = to x-_opl for j = kx to n, yj^ for i = 1 to k2, and ylopt for i = k2 to m, the optimal solutions of Model 5.21 can be obtained. Then, the sub-model corresponding to the lower bound of the objective function value can be formulated as: Max/- + X c'x] (5.22a) M >=*, +1 subject to: a* |+ sign(a*)x~ + £ |a* sign(a*)x+< b+ (l-2A +)(b-b) (5.22b) j=> ;=*,+i x* > x'^, j = ,...,n (5.22c) 0 < x~ < x]_opt,7 = 1,...,*, (5.22d) y;>ywJ = l~,*2 (5.22e) 0 Thereby, optimal solution JCJ_o;)< for j = 1 to and jcJ_op< for j = A:, to », y*_opt for i = 1 to &2 , and >rop, for i = k2 to m can be gained for Model 5.22. Therefore, the following solutions for the ITSCCP Model 5.20 can be obtained: (523) Xj-opt ^[x'j-opn^j-op,] (5.24) yf-op, = [y'i-opt,] (5-25) The proposed ITSCCP model is capable of tackling uncertainties expressed as discrete 109 intervals, stochastic events, and fuzzy sets. Thereby, the influence of these uncertainties on the exercises of generating the desired water quality management schemes can be avoided. 5.3. Model Development Based on the ITSCCP methodology, the previous ITSP-WQM model can be improved by further compounding the expressions of fuzzy sets and thus, developed into inexact two-stage credibility constrained programming water quality management (ITSCCP-WQM) model. In the ITSCCP-WQM model, eighteen activities (i.e., grain crops farming, tobacco farming, vegetables farming, and other agriculture production, commercial forestry, ecological forestry, fish and prawn fanning, pigs husbandry, cattle husbandry, sheep husbandry, poultry husbandry, electric power industry, chemical industry, cement industry, coal industry, electronic industry, food processing industry, and other industrial production) in five industries (i.e., agriculture, forestry, fishery, livestock and industry) are investigated. The study area is divided into eight subareas including Gufii, Zhaojun, Xiakou, Gaoqiao, Nanyang, Zhenzi, Huangliang and Shuiyuesi. Three levels of incoming water quality (Grade I, II, and III according to China's water quality standards) are considered. The planning horizon is one year. In this model, system parameters such as annual economic targets, profits of economic 110 activities, pollutant discharging rates, and pollution mitigation costs will be considered as intervals. The incoming water quality will be considered as a random event. Furthermore, environmental capacities (i.e. maximum allowable pollutant discharges) will be considered as fuzzy sets. (1) Objective Function The objective of the ITSCCP-WQM model is to maximize the economic income while maintaining the water quality requirement. It can also be interpreted as to obtain a preferred plan for various economic activities by maximizing the net benefit of the water quality system, which is the subtraction of environmental penalty from economic benefit. It can be formulated as: Max4±=ZE^x(V+)-Z<5-26) • j i j I k where: By denotes the benefit from economic activity i in subarea j; Cf is the reduction of net benefit for excess discharge of pollutant k (RMB 104/kg when £=1,2, 3; RMB 104/ton when k = 4); Dfj, is the decision variables representing the amount by which the economic target exceeds the standards in subarea j when the water quality requirement of the river is /; Pi is the probability of occurrence of river water quality grade / (%); is the discharge rate of pollutant k from economic activity i; ill Ty is the target of economic activity i in subarea j\ ATy is the range of the economic target interval of economic activity i in subarea j, A7J= Tf-Tp-; if/jj is the decision variables regarding the target for economic activity i in subarea j (0 x (Ty +ATvy/ij) represents the overall economic benefit in all of the i j subareas; and Dfjt is the expected value of the overall environmental i j 1 k penalty under three different incoming water quality levels. (2) Constraints There are four types of constraints: 1) Pollution constraints in each industry, including agriculture, forestry, fishery, livestock, and industry: ZEtfx CT; + - K y2 K. • ' (5-27) ' J where Efk is the environmental capability of each of the five industries for pollutant k with the probability pt of occurrence under incoming water quality grade /. 2) Environmental capacity constraints for each pollutant: 112 w Cr{YJXP?k*(T,- +&TijviJ-D*)< Q,k}>A, Vk, I (5.28) • j where WQlk is the maximum allowable discharge of pollutant k for all activities with the probability p, of occurrence under incoming water quality grade /. 3) Water quantity constraints: EE*?+AT^o)* Q± <5-29> ' J where N* is the water demand of the economic activity / and Q± is the quantity of available water. 4) Technical constraints: T~ + ATytf/y >Dfj,>0, V», j, I (5.30) 0<^<1, ViJ (5.31) In this ITSCCP-WQM model, the fuzzy set is used to account for the uncertainties in the right hand side of the total phosphorus capacity constraints, and the credibility level is applied to measure the satisfaction degrees of the constraints. According to the solution algorithm of the ITSCCP model, it can be re-written as follows: Max^? +AW-EEIZa * subjectto: EE x(V +A7 ^<>v*'1 (5-32b) i ) 113 i j Xl^'xirr+A^jse* (5.32d) ' 7 T- + ATyVy >Dfj{>Q, V/, j, I (5.32e) 0<^<1, Vi.y (5.32f) Accordingly, Model 5.32 can be further transformed into two sub-models. The first sub-model, which corresponds to the upper bounds of the objective function value, is as follows: Ma*/;+A7>i*c;xPt**D:, subject to: x(T,- +&Tjr,-D~,) EEItf v*. / <5.33c> ' J + A7X>* Q+ (5.33d) ' j T~ + AT:^ >D~>0, V/, y, / (5.33e) 0 Solutions Wij-opt D7jl opt can be obtained by solving the deterministic optimization Model 5.33, and thus, the second sub-model corresponding to the lower bound of the objective function value can be formulated as follows: 114 Max /,~ =IZ^«(C + )-ZZZXp,*C;*p;xD;, (5.34a) / j I j I t subject to: V*, 1 (5.34b) ' 7 * J (5.34c) XIXxar+MiYw^e- (5.34d> ' y V/,y, l (5.34e) D^D^ZO-VUhl (5.34f) 5.4. Data Collection 5.4.1. Basic Data As described in Chapter 4, the targets and benefits of various economic activities were investigated from the annual reports by local authorities. The pollution discharge rates and water needs of the economic activities were collected from industrial coefficients handbooks. The pollution mitigation cost, the quality of the incoming water and the allowable pollution discharges of the water body were calculated according to previous research regarding water quality monitoring and environmental capacities. 115 5.4.2. Right-hand Side Value of the Fuzzy Constraints In the ITSCCP-WQM model, the right-hand sides of the water quality constraints, namely the maximum allowable pollutant discharges, are considered as triangular fuzzy sets (b, b, b). The minimum, maximum and the most likely value that define these fuzzy sets are tabulated in Table 5.1. 5.4.3. Credibility Level Since human subjective judgment is involved in the management and planning, linguistic terms are always encountered in the practical process of data acquisition. To interpret decision maker's preferences in linguistic terms and better facilitate the application of the model, a semantic correspondence for the different degrees of credibility has been established by Jimenez et al. (2007). Eleven semantic scales are proposed to present the credibility levels of constraints, namely the confidence levels of the fuzzy constraints. The linguistic description and the corresponding degree of credibility levels are listed in Table 5.2. Regarding the water quality management of the Xiangxi River Basin in Xingshan County, the constraints should be satisfied and not violated. Therefore, the acceptable interval credibility level X is set as [0.5, 0.9], indicating the constraints will at least not be violated and at best, practically satisfied. 116 Table 5.1 b, b, and b value of the right-hand side fuzzy set Incoming b b b water quality I II III I II III I II III Agriculture TN(105 kg3) 3.31 6.63 9.95 5.86 9.61 13.37 8.40 12.60 16.79 TP(105 kg3) 0.66 1.32 1.99 1.17 1.92 2.67 1.68 2.52 3.35 Fishery COD(l()3 kg3) 21.03 28.04 42.06 24.02 34.27 48.03 27.00 40.50 54.00 TN(103 kg3) 1.56 3.12 4.68 2.28 3.81 5.34 3.00 4.50 6.00 TP(103 kg3) 0.22 0.44 0.66 0.32 0.54 0.75 0.42 0.63 0.85 Livestock C()D(105kg3) 25.04 33.38 50.08 32.29 46.35 64.58 39.54 59.31 79.08 TNOO'kg3) 10.57 21.14 31.70 17.80 29.34 40.88 25.03 37.54 50.06 TP(105 kg3) 0.40 0.80 0.12 0.67 1.11 1.55 0.95 1.42 1.90 Industry COD(10skg3) 0.59 0.79 1.19 0.77 1.12 1.56 0.96 1.44 1.92 TN(105 kg3) 0.08 0.15 0.23 0.13 0.22 0.30 0.19 0.28 0.37 TP (10s kg3) 0.06 0.13 0.19 0.11 0.18 0.25 0.16 0.23 0.31 117 Table 5.2 Eleven scales of linguistic terms Credibility Linguistic term Constraint Linguistic term level ( X ) -violation risk 0 Completely UC 1 Completely VC 0.1 Practically UC 0.9 Practically VC 0.2 Almost UC 0.8 Almost VC 0.3 Very UC 0.7 Very VC 0.4 Quite UC 0.6 Quite VC 0.5 Neither SC nor UC 0.5 Neither IC nor UC 0.6 Quite SC 0.4 Qutie IC 0.7 Very SC 0.3 Very IC 0.8 Almost SC 0.2 Almost IC 0.9 Practically SC 0.1 Practically IC 1 Completely SC 0 Completely IC UC: Unsatiiied Constraint; SC: Satified Constraint; VC: Violated Constraint; IC: Inviolated Constraint (Zhang and Huang, 2011). 118 5.5. Result Analysis 5.5.1. Results of the ITSCCP-WQM Model Feasible solutions were obtained by solving the ITSCCP-WQM model. The solutions of most decision variables are intervals, indicating that the related decisions are sensitive to the uncertain modeling input. The objective function value, i.e., the net system benefit would be RMB [27.31, 35.28] x io8, the economic targeted income would be RMB [38.26,40.88] x 108, and the expected value of the environmental penalty would be RMB [10.95, 56.05] x 108. (1) Economic Targets The lower and upper bounds of the targeted income from agriculture, forestry, fishery, livestock, and industry in the eight subareas are presented in Figure 5.2. It is shown that industrial production would be the major economic activity type in Xingshan County. Livestock husbandry and agricultural activities would also account for a certain part of the economic development. The highest targeted income would come from the industrial production in Subarea 1 (i.e., RMB [16.10, 18.94] x 108), which denotes Gufu Town, the capital of Xingshan County. The industrial targeted income in this subarea would mainly consists of electric power generation and phosphate production. The industrial production in Subarea 2 (i.e., Zhaojun Town) would be the second highest economic income source. Its targeted income would be RMB [6.04, 7.01] x 108, mainly from pork products processing. Cement production from Subarea 3 (Xiakou Town), as well as phosphate production from Subareas 6 and 8 (Zhenzi Town and Shuiyuesi Town), would also 119 Lower bound 18.00 CO 0 00 2 fc 1 O u c •5 £0> P £ m, / Industry Livestock Subarea 1 Subarea 2 Fishing Subarea 3 Subarea 4 Forestry Subarea 5 Subarea 6 Agriculture Subarea 7 Subarea 8 Figure 5.2 (1) Tasted moome from the five industries in the eight subareas (Lower bound) 120 Upperbound o 16.00 « 12.00 Industry Livestock Fishing Forestry Subarea 1 Subarea2 Subarea3 Agriculture Subarea 4 Subarea5 Subarea6 Subarea 7 Subarea8 the eight subareas (Upper bound) Figure 5.2 (2) Targeted income from the five industries in 121 contribute much to the economic development. The targeted income of these three parts would be RMB [0.66, 0.77] * 108, [1.20, 1.41] x io8, and [1.23,1.48] * 108, respectively. The second largest economic activity types would be livestock husbandry and agriculture production. The targeted income of livestock would mainly come from Subareas 3, 4, 7, and 8 (i.e., Xiakou, Gaoqiao, Huangliang, and Shuiyuesi), while that of agriculture would mainly come from Subareas 1, 7, and 8 (i.e., Gufu, Huangliang, and Shuiyuesi). It is indicated that Subarea 1 and 2 would focus more on industrial production, while primary industry, such as agriculture and livestock, would play important roles in the development of the other six subareas. (2) Pollution Mitigation The cost of pollution control in the five industries under three incoming water quality levels is tabulated in Table 5.3. The distributions of the mitigation costs among the five industries and among the eight subareas, are figured in Figure 5.3 and 5.4. In the two figures, the mitigation cost denotes the expected value of the mitigation costs under the three incoming water quality levels, Grade I, II, and III. A great deal of pollution should be reduced for agriculture and livestock. The reason is that pollution from agriculture and livestock is non-point source, which is usually difficult to control. The expected value of mitigation costs for agriculture and livestock would be RMB [1.53, 7.45] x 108 and RMB [3.08, 3.43] x 108, respectively. The pollution reduction cost of industrial production would be relatively low (i.e., RMB [0.41, 0.64] x 108), even though the targeted income would be high. The reason is that technologies for industrial wastewater treatment are well developed and the cost of centralized treatment is low. 122 Table 5.3 Mitigation amounts of the five industries under three incoming water quality levels Incoming water quality grade Industry Type I II HI Agriculture (km2) 0 [0,28.13] [97.37, 277.51] Forestry (km2) 0 0 0 Fish fanning (km ) 0 0 [0.06, 0.09] Livestock (103 head) 0 0 [115.80,217.94] Industry (RMB 104) 0 [101.71,105.03] [379.03,469.39] 123 • Upper bound "Lower bound Agriculture Forestry Fishing Livestock Industry Figure 5.3 Expected value of the mitigation costs in the five industries 124 • Upper Bound • Lower Bound g 2.5 I 2 <3 1.5 § o> 1 w S 0.5 * ...... SubareaI 1 SubareaJj. 2 Subarea 3 Subarea 4 Subarea 5 Subarea .11 6 Subarea 7 Subarea 8 Figure 5.4 Expected value of the mitigation costs of the eight subareas 125 Relatively high mitigation cost would be expected in Subareas 1, 3, 7, and 8, due to the intense economic activities. Accordingly, the environmental cost would be lower in the other four subareas due to the less intense economic activities. The results of the ITSCCP-WQM model show that when the water quality of the incoming water meets the standards of Grade I, no pollution control would be necessary. However, when the incoming water quality could only meet the standards of Grade II or III, pollution control should be conducted. Percent stacked bars of the mitigation amounts (lower and upper bounds) of TP, TN, and COD under the incoming water quality Grade III are shown in Figure 5.5 (1). The amount of TN reduction would be [3.66, 4.68] x 10s kg, accounting for 19.62% - 27.09% of the three pollutants, while that of Soil loss should be [5.13, 11.06] x 104 tonnes. The percent stacked bars of the mitigation amounts (lower and upper bounds) for TP, TN, and COD under incoming water quality Grade II are shown in Figure 5.5 (2). In this case, the reduction amount of TN would be [0.16, 0.31] x 105kg ,taking 13.47% - 60.16% of the total reduction amount of TP, TN, and COD, and that of Soil loss would be [0, 1.17] x 104 tonnes. It is also shown that, when the water quality of the incoming water is deteriorated from Grade II to Grade III, the mitigation percentage of TP would rise significantly. The required reduction amount of TP would increase from [3.67, 13.41] x 103 kg under Grade II to [150.14, 190.70] x 103 kg under Grade III. The corresponding percentage would change from [8.05%, 11.04%] to [26.43%, 30.31%]. It is implied that when the water quality deteriorated drastically, TP would be the controlling pollutant in the practice of satisfying the water quality requirements. 126 100% • TP •TN • COO Upper bound Lower bound Figure 5.5 (1) Stacked columns of the mitigation amounts for TP, TN, and COD when the incoming water quality is Grade III 127 100% • TP •TN • COD Upper bound Lower bound Figure5.5 (2) Stacked columns of the mitigation amounts for TP, TN, and COD when the incoming water quality is Grade II 128 To better support TP pollution control, further analysis regarding TP discharge constraints was conducted. The TP discharge constraints were loosen one percent by one percent, up to ten percent. The changes of targeted income, mitigation cost and net system benefit are presented in Figure 5.6. It is shown that when the allowable TP discharge increases by 10%, the targeted income, mitigation costs, and net system benefit would change [3.13%, 3.55%], [-7.53%, 5.4%], and [2.24%, 5.31%], respectively. It is revealed that under the economic development and environment protection scheme of the ITSCCP-WQM model, allowing excessive TP discharge would not bring considerable increase of the net system benefit. Therefore, there is no need to risk loosing TP control for economic benefits. 5.5.2. Comparison of the ITSP-WQM Model and the ITSCCP-WQM Model The targeted income, mitigation costs and net system benefit of the two models are shown in Figure 5.7. The credibility constraints of the ITSCCP-WQM model, which are transformed from the fuzzy water quality constraints, are tighter than the interval water quality constraints of the ITSP-WQM model. Therefore, the flexible solution region of the ITSCCP-WQM model would decrease and the solution intervals would become narrower. The results of the two models are close, indicating similar suggested investment schemes for economic development and environment protection. The net system benefit of the ITSP-WQM and the ITSCCP-WQM model would be RMB [25.26, 36.86] x 108 and RMB [27.31, 35.28] * 108, respectively. The results of the ITSCCP-WQM model can be considered as alternatives to those of the ITSP-WQM model. 129 • Upper bound i Lower bound 43 42 & T- 41 £D s 40 «r 39 E 8 c 38 3 37 % C» 36 a K- 35 34 0 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% Looseness of the TP discharge constraints Figure 5.6 (1) Changes in the targeted income when the TP discharge constraints loosened 130 14 • Upper bound •Lower bound 12 ° 10 ffl s OC 8 o e c c £ 4 0 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% Looseness of the TP discharge constraints Figure 5.6 (2) Changes in the mitigation costs when the TP discharge constraints loosened 131 • Upper bound (Lower bound 0 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% Looseness of the TP discharge constraints Figure5.6 (3) Changes in the net system income when the TP discharge constraints loosened 132 45 iResults of ITSCCP model I Results of ITSP model 40 35 30 & m 25 s oc 20 15 10 5 0 Targeted Mitigation Net system income cost benefit Figure 5.7 Targeted income, mitigation costs, and net system benefit of the ITSP-WQM model and the ITSCCP-WQM model 133 Table 5.4 Solutions to the economic target decision variables of the ITSCCP-WQM model Subarea 1 2 3 4 5 6 7 8 Agriculture Grain Crops 0 0 0 0 0 0 0 0 Tobacco 0 0 0 0 0 0 0 0 Vegetables 0 0 0 0 0 0 0 0 Others 0 0 0 0 0 0 0 0 Forestry Commercial forestry 1 1 1 1 1 1 1 1 Ecological forestry 1 1 1 1 1 1 1 1 Fishery Fish and prawn 0 0 0 0 0 0 0 0 Livestock Pigs 0 0 0 0 0 0 0 0 Cattle 0 0 0 0 0 0 0 0 Sheep 0 0 0 0 0 0 0 0 Poultry 0 0 0 0 0 0 0 0 Industry Electric power 1 0 1 0 1 1 1 1 Chemical 0 0 0 0 0 0 0 0 Cement 0 0 1 0 0 0 0 0 Coal 0 0 1 0 0 0 0 0 Electronic 1 0 0 0 0 0 0 0 Food 0 0 0 0 1 0 0.28 1 Others 0 1 0 0 0 0 0 1 134 (1) Economic Targets ± The economic targets of the two models are denoted as T =T~ +ATxopt. xopl = 1 implies that the optimal target would approach its upper bound, while xopl = 0 means that the optimal target would approach its lower bound. Solutions to the economic target decision variables x^ of the two models are tabulated in Tables 4.8 and 5.4, respectively. According to the results of the ITSP-WQM model, the economic targets of forestry would approach the upper bounds, those of fishery and livestock would approach the lower bounds, and portions of the targets in industry and agriculture would approach the upper bounds. It is revealed by both models that forestry, industry and agriculture should be given development priorities. Whereas, the development of livestock and fishery should be kept within certain limits to prevent unexpected environmental penalties. In the ITSCCP-WQM model, since the pollution discharge constraints are tighter, the economic targets of agriculture should be cut and only the forestry targets and parts of the industrial targets should approach their upper bounds. It is implied that under environmental constraints, the priority for industrial production should be even higher than that of agricultural production. The targeted income under the optimized schemes of the ITSP-WQM model and the ITSCCP-WQM model are presented in Figure 5.8. The distribution patterns of the targeted income among the five industries in the two models are similar. In the optimized economic plans of the two models, industry would be the dominant economic activity type, while the targets for fish fanning would be very low. Although the targeted income 135 contains similarities, alternatives regarding economic development are nevertheless provided. As for agriculture, livestock and forestry, the targeted income of the ITSP-WQM model would be a little lower than that of the ITSCCP-WQM model. For instance, the industrial targets would be RMB [28.83, 31.25] x 108 and RMB [25.17, 29.61] x 108, in the two models, respectively. (2) Pollution Mitigation Mitigation cost segments of the five industries in the USP-WQM model and the ITSCCP-WQM model are further analyzed in Figure 5.9. The mitigation costs denote the expected value of pollution abatement costs for the five industries under different levels of incoming water quality, which is the environmental penalty of the water quality systems. Results of the two models demonstrate that the majority of the environmental penalties would come from non-point source pollution in agriculture and livestock. The cost of agricultural pollution control in the ITSP-WQM model and the ITSCCP-WQM model would be RMB [1.53, 7.65] x 108and RMB [1.53, 5.24] * 108, respectively. High environmental cost would also be required for livestock husbandry, which accounts for 40% - 59% and 37% - 61% in the two models, respectively. The cost would be the third highest for pollution reduction in industrial production (i.e., RMB [0.64, 0.85] x 108and RMB [0.51, 0.64] * 108 in the two models, respectively). The environmental penalties of forestry would be low due to the small pollutant discharge rates of the forestry activities. The low environmental cost of the fishery activities would also be low, and the reason might be the low target of fish farming activities. 136 Fishing • Results of ITSCCP •Results of ITSP Forestry Agriculture 10 15 20 25 30 35 T arget income (RMB 10s) Figure 5.8 Targeted income of the five industries in the ITSP-WQM model and the ITSCCP-WQM model 137 Results of ITSCCP Industry Lower bound Results of ITSP Agriculture Fishery Livestock Figure 5.9 (1) Mitigation cost (lower bound) segments of the five industries under the optimized schemes in the ITSP-WQM model and the ITSCCP-WQM model 138 Results of ITSCCP Industry Upper bound Results of ITSP Agriculture Livestock Figure 5.9 (2) Mitigation cost (upper bound) segments of the five industries under the optimized schemes in the ITSP-WQM model and the ITSCCP-WQM model 139 5.6. Summary In this study, an inexact two-stage stochastic credibility constrained programming (ITSCCP) method has been proposed and an inexact two-stage stochastic credibility constrained programming water quality management (ITSCCP-WQM) model has been developed for the Xiangxi River Basin in Xingshan County. This model is an improvement over the previous ITSP-WQM model, in terms of introducing the credibility constrained programming method. In the ITSP-WQM model, environmental standards are considered as intervals. However, in practice, this would lead to a waste of useful information when decision makers can provide membership functions of this type of parameters. In this scope, fuzzy programming was incorporated to account for the imprecision (fuzziness) associated with the goals of pollution control, and to make full use of the available information. Fuzzy membership functions are used to encode the possibilistic distribution of the parameters, and credibility was proposed to measure the satisfaction level of the fuzzy constraints. Uncertainties presented in fuzzy, probabilistic and interval formats can be all tackled within the ITSCCP framework to support water quality management and planning. Stable interval solutions have been obtained by solving the ITSCCP-WQM model. The results show that economic development priority should be given to forestry, industry, and agriculture. It is also indicated that a great deal of abatement should be conducted with regard to pollution from non-point sources such as livestock and agriculture. Detailed 140 results regarding the targets and mitigation schemes of various economic activities in the eight subareas have been generated, and the system sensitivities of total phosphorus control have been analyzed. The results are valuable for supporting local decision makers in generating cost-effective water quality management strategies. 141 CHAPTER 6 CONCLUSIONS 6.1. Summary In this research, an inexact two-stage stochastic programming water quality management (ITSP-WQM) model were developed for the Xiangxi River Basin in Xingshan County, China. A number of environmental and economic factors, as well as the inherent uncertainties in water quality management systems, were considered and integrated within an optimization framework. The model can reflect the dynamic relationship and tradeoffs between economic development plans and the associated pollution mitigation schemes. It can also address system uncertainties presented in interval and probabilistic formats. Interval solutions were obtained by using a two-step interactive solution algorithm. Four scenarios representing decision makers' various preferences regarding economic targets were designed and analyzed. In addition, an inexact two-stage stochastic credibility constrained programming water quality management (ITSCCP-WQM) model and its solution algorithms were proposed. The credibility constrained programming method, which is derived from fuzzy possibility theory, was incorporated into an optimization framework in order to account for environment managers' confidence level over the estimated parameters. Uncertainties expressed as intervals, probability distributions and possibility distributions, as well as their relationships, can be addressed in the ITSCCP-WQM model. Interval solutions were 142 obtained, and a sensitivity analysis regarding the right-hand side coefficients of the environmental constraints was conducted. Results of the two models indicated that among the various economic activities, priorities should be given to forestry and industrial production. It was also indicated that no pollution control would be necessary when the incoming water quality meets China's water quality Grade I. However, an excess amount of pollution would be produced when the incoming water quality is Grade II or III. Desired adjustments regarding the 18 economic production targets, as well as the corresponding pollution mitigation schemes for the excessive pollution, were provided by both models. The two models have different data requirements, and they represent different considerations of the system uncertainties. Thus, the results are capable of providing various useful bases to formulate the sustainable development strategies, wherein water quality requirements can be satisfied while economic growth is being maintained. 6.2. Research Achievements The development of the large-scale regional ITSP-WQM model in the Xiangxi River is a pioneer study of optimization modeling in the Three Gorges Reservoir (TGR). It could provide a basis for water quality management in other river basins of the TGR, as well as other areas which are facing conflicts between economic development and pollution reduction. 143 An ITSCCP method is proposed, and an ITSCCP-WQM model is developed and applied to a real-world case. The ITSCCP method extends upon the inexact two-stage stochastic programming (ITSP) method by introducing fuzzy theory and credibility constrained programming to measure the satisfaction degrees of the constraints. The development of the ITSCCP-WQM model could enhance the robustness of the optimization efforts and thus, provide decision support for regional water quality management and planning. 6.3. Recommendations for Future Research (1) The models could be improved by introducing other advanced optimization methods to tackle more uncertainties and complexities. For instance, mixed-integer linear programming method could be introduced to handle integer variables. Multi-stage programming method could be applied to consider the interaction between system components at different stages of the decision-making process. Multi-objective programming would be used to reflect the multiple objectives of water management, such as the maximization of economic benefits, the minimization of pollution discharges, and the minimization of water consumption. (2) In this study, the water quality constraints were pollution load constraints. The movement and transformation of pollutants after they have been discharged into the water body have not, as yet, been taken into consideration. The proposed models could be improved by integrating water quality simulation models so that the concentration of pollutants can be simulated and considered in the constraints. 144 (3) In the ITSCCP-WQM model, triangular membership functions were used to express fuzzy information regarding water quality constraints. 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Entropy method for determination of weight of evaluating indicators in fuzzy synthetic evaluation for water quality assessment. Journal of Environmental Sciences (China). 18(5): 1020-3. 161 APPENDICES Appendix A - Annual targets of the economic activities under Scenarios 1 to 4 in the ITSP-WQM model (1) Annual targets of the economic activities under Scenario 1 Subarea 1 2 3 4 5 6 7 8 Agriculture (km2) Grain Crops 27.23 13.45 26.96 23.13 16.33 11.79 29.14 29.78 Tobacco 0.37 0 0 1.87 2.33 9.20 6.00 0.59 Vegetables 15.78 7.26 4.27 5.74 3.17 9.06 8.90 8.24 Others 9.85 4.65 8.54 11.44 6.53 1.69 16.03 8.58 Forestry (km2) Commercial forestry 216.86 72.45 105.03 84.12 134.20 174.56 119.13 225.61 Ecological forestry 192.70 64.38 93.33 74.75 119.25 155.11 105.86 200.48 Fishery (km2) Fish and prawn 0.06 0.02 0.02 0.02 0.04 0.05 0.03 0.06 Livestock (103 head) Pigs 41.41 26.17 55.80 40.18 24.10 11.01 54.16 55.07 Cattle 0.31 0.10 0.24 0.48 0 0.43 0.45 0.50 Sheep 8.96 8.02 5.86 15.01 8.12 14.41 18.01 10.01 Poultiy 64.40 30.20 62.97 36.46 23.57 22.00 37.91 50.13 Industry (RMB 104) Electric power 34.17 0 0.53 0 2.26 0.07 0.16 0.13 Chemical 531.76 0 0 0 0 49.00 0 33.97 Cement 0 0 39.86 0 0 0 0 0 Coal 0 0 1.62 0 0 0 0 0 Electronic 3.17 0 0 0 0 0 0 0 Food 1.99 177.66 0 0 1.10 0 2.51 0.88 Others 0 1.82 0 0 0 0 0 1.40 162 (2) Annual targets of the economic activities under Scenario 2 Subarea 1 2 3 4 5 6 7 8 Agriculture (km2) Grain Crops 27.23 13.45 26.96 23.13 16.33 11.79 29.14 29.78 Tobacco 0.37 0 0 1.87 2.33 9.20 6.00 0.59 Vegetables 14.79 7.17 4.13 4.91 2.65 8.83 8.90 7.70 Others 9.85 4.65 8.54 11.44 6.53 1.69 16.03 8.58 Forestry (km2) Commercial forestry 108.71 36.32 52.65 42.17 67.28 87.51 59.72 113.10 Ecological forestry 84.55 28.25 40.95 32.80 52.33 68.06 46.45 87.97 Fishery (km2) Fish and prawn 0.06 0.02 0.03 0.02 0.04 0.05 0.03 0.06 Livestock (103 head) Pigs 41.41 26.17 55.80 40.18 24.10 11.01 54.16 55.07 Cattle 0.31 0.10 0.24 0.48 0 0.43 0.45 0.50 Sheep 8.96 8.02 5.86 15.01 8.12 14.41 18.01 10.01 Poultry 64.40 30.20 62.97 36.46 23.57 22.00 37.91 50.13 Industry (RMB 104) Electric power 12.92 0 0.37 0 1.47 0.05 0.11 0.09 Chemical 531.76 0 0 0 0 40.91 0 33.97 Cement 0 0 20.34 0 0 0 0 0 Coal 0 0 1.33 0 0 0 0 0 Electronic 2.13 0 0 0 0 0 0 0 Food 1.87 146.99 0 0 0.56 0 1.28 0.71 Others 0 1.59 0 0 0 0 0 0.71 163 (3) Annual targets of the economic activities under Scenario 3 Subarea 1 2 3 4 5 6 7 8 Agriculture (km2) Grain Crops 27.56 16.20 27.12 23.76 19.28 13.61 29.93 29.90 Tobacco 0.38 0 0 2.57 3.00 11.23 8.84 0.60 Vegetables 15.78 8.59 4.27 5.74 3.17 9.06 21.81 8.24 Others 10.90 8.80 10.59 12.45 9.29 4.46 18.22 9.83 Forestry (km2) Commercial forestry 216.86 72.45 105.03 84.12 134.20 174.56 119.13 225.61 Ecological forestry 192.70 64.38 93.33 74.75 119.25 155.11 105.86 200.48 Fishery (km2) Fish and prawn 0.10 0.03 0.05 0.04 0.06 0.08 0.05 0.10 Livestock (103 head) Pigs 41.78 28.85 56.64 46.26 27.35 15.05 55.80 55.21 Cattle 0.35 0.10 0.27 0.60 0.02 0.47 0.50 0.67 Sheep 10.15 19.56 14.32 22.41 16.38 16.20 43.74 24.90 Poultry 77.93 36.28 76.90 39.04 27.50 29.36 122.22 53.06 Industry (RMB 104) Electric power 28.90 0 0.53 0 2.26 0.07 0.16 0.13 Chemical 643.43 0 0 0 0 49.50 0 41.11 Cement 0 0 34.37 0 0 0 0 0 Coal 0 0 1.62 0 0 0 0 0 Electronic 3.17 0 0 0 0 0 0 0 Food 1.99 177.66 0 0 0.95 0 2.17 0.88 Others 0 1.82 0 0 0 0 0 1.20 164 (4) Annual targets of the economic activities under Scenario 4 Subarea 1 2 3 4 5 6 7 8 Agriculture (km ) Grain Crops 27.39 14.83 27.04 23.45 17.81 12.70 29.54 29.84 Tobacco 0.37 0 0 2.22 2.66 10.22 7.42 0.60 Vegetables 15.29 7.88 4.20 5.33 2.91 8.95 15.35 7.97 Others 10.38 6.72 9.57 11.94 7.91 3.07 17.12 9.21 Forestry (km2) Commercial forestry 162.79 54.38 78.84 63.14 100.74 131.03 89.42 169.36 Ecological forestry 138.63 46.31 67.14 53.77 85.79 111.59 76.15 144.22 Fishery (km2) Fish and prawn 0.08 0.03 0.04 0.03 0.05 0.06 0.04 0.08 Livestock (103 head) Pigs 41.59 27.51 56.22 43.22 25.73 13.03 54.98 55.14 Cattle 0.33 0.10 0.26 0.54 0.01 0.45 0.47 0.58 Sheep 9.55 13.79 10.09 18.71 12.25 15.30 30.88 17.46 Poultry 71.16 33.24 69.93 37.75 25.54 25.68 80.07 51.60 Industry (RMB 104) Electric power 20.91 0 0.45 0 1.86 0.06 0.14 0.11 Chemical 587.60 0 0 0 0 45.20 0 37.54 Cement 0 0 27.35 0 0 0 0 0 Coal 0 0 1.48 0 0 0 0 0 Electronic 2.65 0 0 0 0 0 0 0 Food 1.93 162.32 0 0 0.75 0 1.72 0.80 Others 0 1.71 0 0 0 0 0 0.96 165 Appendix B - ITSP-WQM model Solutions to Decision Variables under Scenario 1 (1) Agricultural activities causing an over generation of pollution (km ) Incoming Subarea water quality Grain crops Tobacco Vegetable Others EI [8.17,27.23] [0.11,0.37] [4.44,15.78] [2.96,9.85] 1 II 0 0 0 0 I 0 0 0 0 III 8.09 0 [1.24,4.27] [2.56,8.54] II [0,24.81] 0 0 0 1 0 0 0 0 III [4.90,16.33] [0.70,2.33] [0.80,3.17] [1.96,6.53] II 0 0 0 0 1 0 0 0 0 III [8.74,29.14] [1.8,6.0] [2.67,8.90] [4.81,16.03] II 0 0 0 0 1 0 0 0 0 166 (2) Fish farming activities causing an over generation of pollution (km2) Subarea Incoming water quality Fish and prawn • 167 (3) Livestock husbandry causing an over generation of pollution (103 head) Incoming Subarea water quality Pigs Cattle Sheep Poultry III 12.42 0.09 2.69 19.32 1 II 0 [0,0.31] 0 0 I 0 0 0 0 m 16.74 0.07 1.76 18.89 II 0 [0,0.24] 0 0 I 0 0 0 0 III 7.23 0 2.43 7.07 II 0 0 0 0 I 0 0 0 0 III 16.25 0.13 5.40 11.37 II 0 [0, 0.45] 0 0 I 0 0 0 0 168 (4) Industrial activities causing an over generation of pollution (RMB 104) Incoming Subarea water quality Electric power Chemical Cement Coal Electronic Food Others III 0 [265.88, 531.76] 0 0 0 0.93 0 1 II 0 117.69 0 0 0 0 0 I 0 0 0 0 0 0 0 III 0 0 0 0 0 0 0 3 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 III 0 0 0 0 0 0.28 0 5 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 III 0 0 0 0 0 0.64 0 7 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 169 Appendix C - ITSP-WQM model Solutions to Decision Variables under Scenario 2 (1) Agricultural activities causing an over generation of pollution (km2) Incoming Subarea water quality Grain crops Tobacco Vegetable Others III 8.17 0.11 4.44 2.96 1 II 0 0 0 0 I 0 0 0 0 [8.01,26.96] [0, 22.02] 0 III 4.90 0.70 0.80 1.96 II 0 0 0 0 I 0 0 0 0 III 8.74 1.80 2.67 4.81 II 0 0 0 0 I 0 0 0 0 170 (2) Fish farming activities causing an over generation of pollution (km2) Subarea Incoming water quality Fish and prawn 171 (3) Livestock husbandry causing an over generation of pollution (103 head) Incoming Subarea water quality Pigs Cattle Sheep Poultry in 12.42 0.09 2.69 19.32 1 II 0 0 0 0 I 0 0 0 0 in 16.74 0 1.76 18.89 II 0 0 0 0 I 0 0 0 0 III 7.23 0 2.43 7.07 II 0 0 0 0 I 0 0 0 0 III 16.25 0 5.40 11.37 II 0 0 0 0 I 0 0 0 0 172 (4) Industrial activities causing an over generation of pollution (RMB 104) Incoming water Subarea quality Electric power Chemical Cement Coal Electronic Food Others HI 0 265.88 0 0 0 0.93 0 1 n 0 143.26 0 0 0 0 0 i 0 0 0 0 0 0 0 III 0 992.18 0 0 0 0 0 3 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 III 0 0 0 0 0 0.28 0 5 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 m 0 0 0 0 0 0.64 0 7 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 173 Appendix D - ITSP-WQM model Solutions to Decision Variables under Scenario 3 (1) Agricultural activities causing an over generation of pollution (km2) Incoming Subarea water quality Grain crops Tobacco Vegetable Others in 10.89 0.15 5.92 3.94 1 II 0 0 0 0 I 0 0 0 0 m [10.78,27.12] 0 1.65 3.42 II [0,49.60] 0 0 0 I 0 0 0 0 m 6.53 0.93 1.06 2.61 II 0 0 0 0 I 0 0 0 0 in 11.66 2.40 3.56 6.41 n o 0 0 0 i o 0 0 0 174 (2) Fish farming activities causing an over generation of pollution (km2) Subarea Incoming water quality Fish and prawn m 0.02 175 (3) Livestock husbandry causing an over generation of pollution (103 head) Incoming Subarea water quality Pigs Cattle Sheep Poultry in 20.71 0.16 4.48 32.20 1 n 0 0 4.48 32.20 i 0 0 0 0 m 27.90 0.12 2.93 31.49 n 0 [0, 3.29] [0, 53.36] 0 i 0 0 0 0 12.05 € 27.08 18.95 176 (4) Industrial activities causing an over generation of pollution (RMB 104) Incoming water Subarea quality Electric power Chemical Cement Coal Electronic Food Others 319.06 0 0 1.12 0 319.06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.34 0 0 0 0 0 0 0 0 0 0 0 0.77 0 0 0 0 0 0 0 0 0 177 Appendix E - ITSP-WQM model Solutions to Decision Variables under Scenario 4 (1) Agricultural activities causing an over generation of pollution (km2) Incoming Subarea water quality Grain crops Tobacco Vegetable Others m 9.59 0.13 5.35 3.63 1 n 0 0 0 0 I 0 0 0 0 in [9.46,27.04] 0 1.47 3.35 II [0, 27.04] 0 0 0 I 0 0 0 0 ffl 6.23 0.93 1.02 2.77 II 0 0 0 0 I 0 0 0 0 in 10.34 2.60 5.37 5.99 n 0 0 0 0 i 0 0 0 0 178 (2) Fish farming activities causing an over generation of pollution (km2) Subarea Incoming water quality Fish and prawn ffl 0.03 179 (3) Livestock husbandry causing an over generation of pollution (103 head) Incoming Subarea water quality Pigs Cattle Sheep Poultry m 14.56 0 3.34 24.91 i n 0 0 0 0 i 0 0 0 0 HI 19.68 0.05 3.53 24.48 n 0 0 [0, 80.54] 0 i 0 0 0 0 m 9.01 0 4.29 8.94 II 0 0 0 0 I 0 0 0 0 in 19.24 [0, 0.93] 10.81 28.02 II 0 0 0 0 I 0 0 0 0 180 (4) Industrial activities causing an over generation of pollution (RMB 104) Incoming water Subarea quality Electric power Chemical Cement Coal Electronic Food Others III 0 293.80 0 0 0 0.96 0 1 II 0 293.80 0 0 0 0 0 I 0 0 0 0 0 0 0 III 0 0 0 0 0 0 0 3 II 0 0 0 0 0 0 0 I 0 0 0 0 1<|B10_ III 0 0 0 0 0 0.38 0 5 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 III 0 0 0 0 0 0.86 0 7 n 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 181 Appendix F - ITSCCP-WQM model Solutions to Decision Variables (1) Agricultural activities causing an over generation of pollution (km2) Incoming Subarea water quality Grain crops Tobacco Vegetable Others IH [8.20,27.23] [0.11,0.37] [4.44, 15.78] [2.96,9.85] 1 H 0 0 0 0 1 0 0 0 0 m 8.09 0 [1.24,4.27] [2.56,8.54] n 0 0 0 0 i 0 0 0 0 m 4.90 [0.70,3.00] [0.80,3.17] [1.96,6.53] n 0 0 0 0 i 0 0 0 0 m [8.74,15.51] [1.80,6.34] [2.67,21.81] [4.81,16.03] D 0 0 0 0 1 0 0 0 0 182 (2) Fish farming activities causing an over generation of pollution (km2) Subarea Incoming water quality Fish and prawn ffl [0,0.02] 183 (3) Livestock husbandry causing an over generation of pollution (103 head) Incoming Subarea water quality Pigs Cattle Sheep Poultry in 12.42 [0.09, 0.20] 2.69 [0,19.32] 1 n 0 0 0 0 i 0 0 0 0 m 16.74 0.07 [0,1.76] [0,18.89] n 0 0 0 0 I 0 0 0 0 m 7.23 0 2.43 [0, 7.07] II 0 0 0 0 I 0 0 0 0 HI 16.25 [0.13,0.45] 5.40 [0,11.37] II 0 0 0 0 I 0 0 0 0 184 (4) Industrial causing an over generation of pollution (RMB 104) Incoming water Subarea quality Electric power Chemical Cement Coal Electronic Food Others III 0 265.88 0 0 0 [0.93,1.87] 0 1 II 0 [84.58,101.71] 0 0 0 0 0 I 0 0 0 0 0 0 0 III 0 0 0 0 0 0 0 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 III 0 0 0 0 0 [0.28,1.10] 0 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 III 0 0 0 0 0 [0.64,2.51] 0 II 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 185