MULTIOB JECTNE WATER QUALITY MANAGEMENT

PLANNING FOR THE LAKE ERHAI WATERSHED

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 Systems Engineering

by

S haoming Wu

Facul ty of Engineering

University of Regina

Regina, Saskatchewan, Canada

August, 1997

O Copyright 1997: Shaoming Wu

395 Wellington Street 395, rue Wellington OttawaON KIAON4 Ottawa ON K1A ON4 Canada Canada

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The author retains ownership of the L'auteur conserve la propneté du copyight in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thése ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation.

The Lake Erhai Watershed is located in Southwestern China with an area of around

2,500 km2. There exist a number of human activities, such as agriculture, industrial

productions, tourism, forestry, net-cage fish culture and lime/brick productions. Lake

Erhai, with its freshwater resources, has been playing a vital role in the local socio-

economic development. However, the watershed is now confronted by many environmenta1

problems, especially the degradation of the lake water quality due to the discharge of

human-made contaminants. The purpose of this research is to provide a plan for sustainable

developrnent of the Lake Erhai Watershed with a specid emphasis on the lake water

quality protection.

As a large-scale regional water quality management system, the Lake Erhai

Watershed is associated with multiobjective, uncertain, dynamic and interactive features.

There has been no study for the region which simultaneously considered al1 these complex

features. From a methodology point of view, the existing approaches for multiobjective

programming under uncertainty are limited by a number of difficulties. Consequently, a

hybrid inexact-fuzzy multiobjective programming (IFMOLP) method is proposed and

applied to the project for the Lake Erhai Watershed.

The IFMOLP is developed by coupling inexact programming and fuzzy programming

methodologies within a general framework. A two-phase solution process is used to

achieve Pareto optima, and an interactive approach is suggested to ensure the desired

compromise is obtained.

* a

and their interrelationships being considered in the modeling formulation. The decision

variables represent the planning for these activities in different spatial locations (seven

subareas) over the planning time horizon (two periods). The mode1 constraints include

relationships between the decision variables and the related system conditions. The general

objective is to achieve desired compromise between environmental, resources and

economic considerations.

The IFMOLP mode1 for the Lake Erhai Watershed is solved under several scenarios

with different tradeoffs between conflicting objectives. The modeling results suggest that

the agricultural activities should generally be maintained at existing levels. Food

processing, tobacco and tourism industries should be promoted. In cornparison,

development for many other industries, as well as and limehrick production, has to be

limited or restricted. Also, it is suggested that the net-cage fish culture be phased out of the

Iake.

This planning study provides a scientific base for the formulation of

policies/strategies in regional socio-economic development and environmental protection.

The IFMOLP improves upon the previous multiobjective programming methods w ith

advantages in data availability, solution algorithm, and result interpretation. It allows

uncertainties and decision-makers' aspirations to be effectively communicated to the

modeling process. The generated inexact solutions and alternatives are favored by the local

authorities due to their increased flexibility and applicability in detemining the final

schemes. The IFMOLP is proved to be an effective tool for environmental systems

planning.

1 would like to express my sincere gratitude to my supervisor, Dr. Gordon Huang.

He introduced me into some very interesting areas of research, and constantly offered

insightful advice and kind encouragement throughout my graduate work. The knowledge

and expertise I l emt from him would be an invaluable asset for my future career.

1 would also Iike to thank Dr. Maynard Chen, Dr. G. Fuller, Dr. P.

Tontiwachwuthikul and Dr. Mingyuan Chen for their constructive comments and

suggestions which resulted in an improved thesis.

Dr. G. Fuller, Dr. T. Viraraghavan and Dr. S. Sharrna provided me with excellent

instruction and kind help during the period of my study to which 1 am so much indebted.

1 am grateful to the Faculty of Graduate Studies and the Faculty of Engineering of

the University of Regina for the financial assistance. Thanks are extended to the United

Nations Environment Programme and the Natural Sciences and Engineering research

Council of Canada for their support to my research projects.

Thanks are also due to a number of organizations in China for their effort in

providing the information required for this research. The Environmental Science Center

of Peking University, Yunnan Environmental Protection Bureau, Yunnan Provincial

Research Institute of Environmental Science, Dali Environmentai Protection Bureau and

Dali Research Institute of Environmentai were very supportive ail the time.

Finally, my appreciation goes to my friends whose help, encouragement and

friendship were very important for the completion of my graduate work at the University

of Regina.

TABLE OF CONTENTS

ABSTRACT

ACKNOWLEDGEMENTS

LIST OF TABLES

LIST OF RGURES

CHAPTER 1. INTRODUCTION

1.1. BACKGROUND

1.2. STATEMENT OF PROBLEMS

1.3. RATIONALES

1.4. OBJECTIVES

1.5. STUDY SCOPE

CHAPTER 2. SYSTEM DESCRIPTION AND CHARACTERIZATiON

2.1. THE STUDY AREA

2.2. ENVIRONMENTAL PROBLEMS

2.3. WATER RESOURCES AND QUA= OF LAKE ERHAI

2.3.1. Water Balance in Lake Erhai

2.3.2. Lake Water Quality

2.4. POLLUTION SOURCES

2.4.1. Point Poiiution Sources

2.4.2. Non-point Source Pollution

2.5. SYSTEM FEATURES

2.5.1. Multiobjective Feature

2.5.2. Uncertain Feature

2.5.3. Dynamic Feaîure

2.5.4. Interactive Relationships Between S ystem Components

2.6, SUMMARY

CHAPTER 3. LITERATURE REVIEW 50

3.1. MATHEMATICAL PROG-G APPROACHES FOR DEALING

WïïH MULTIPLE OBJECTIVES AND UNCERTAINTIES 50

3.1.1. Fuzzy Multiobjective Decision-Making 50

3.1.2. Stochastic Programrning with Multiple Objective Functions 54

3.2. REGIONAL WATER QUALITY MANAGEMENT PLANNING THROUGH

APPLICATION OF MATHEMATICAL PROGRAMMING 56 .

3.3. SUMMARY 59

CHAPTER 4. OPTIMIZATION APPROACH

4.1. INTRODUCTION

4.2. INEXACT LINEAR PROGRAMMING

4.2.1. Definitions

4.2.2. Solution Algorithm

4.3. FUZZY MIN-OPERATOR APPROACH TO MULTIOBJECTIVE

PROBLEMS

4.3.1. Fuzzy Syrnmetrical Model

4.3.2. Fuzzy Approach with Min-Operator

4.4. INE:XACT-FUZZY MULTIOBJECTIVE LlNEAR PROGRAMMING

4.4.1. Inexact Multiobjective Programming Model

4.4.2. Fuzzy Transformation

4.4.3. ILP Transformation

4.4.4. IFMOLP Submodels

4.4.5. Pareto Optimum

4.4.6. Solution Sequence

4.4.7. Interactive Approach

4.5. SUMMARY

CHAPTER 5. IFMOLP MODEL FOR THE LAKE ERHAI WATERSHED

5.1. MODEL IDENTIFICATION

5.2. MODEL FORMULATION

CHAPTER 6. MODEL INPUTS AND OUTPUTS

6.1. INPUT DATA

6.1.1. Data Acquisition

6.1 2 . Input Parameters for A* and Matrices

6.1.3. Input Parameters for ~'Vector

6.2. MODEL SOLUTIONS

6.2.1. Generation of Decision Alternatives

6.2.2. IFMOLP Solutions

6.2.3. Contribution Stnictures

CHAPTER 7. XNTERPRETATION AND DISCUSSION

7.1. RESULTS INTERF'RETATION

7.1.1. Solutions

7.1.2. Contribution S t n i w s

7.2. COMPARISONS BETWEEN DIFFERENT SCENARIOS

7.3. SUGGESTIONS FOR IMPLEMENTATION

C m 8. CONCLUSIONS

8.1. SUMMARY

8.2. RECOMMENDATION FOR FUTURE RESEARCH

REFERENCES

APPENDICES

Appendix A Input Parameters for A* and C? Matxices in the IFMOLP Model 175

Appendix B Input Parameters for B* Vector in the IFMOLP Mode1 183

Appendix C Detailed lFMOLP Solutions for Scenario 1 193

Appendix D Detailed IFMOLP Solutions for Scenario 2 202

AppendUr E Detailed IFMOLP Solutions for Scenario 3

Appendix F Detaild IFMOLP Solutions for Scenano 4

LIST OF TABLES

Table 2.1 . Table 2.2.

Table 2.3.

Table 2.4.

Table 2.5.

Table 2.6.

Table 2.7.

Table 2.8.

Table 2.9.

Table 2.10.

Table 2.1 1.

Table 2.1 2.

Table 4.1.

GeneraI characteristics of Lake Erhai 11

Existing patterns of human activities 16

Precipitation under different frequencies in the Lake Erhai Watershed 20

Temporal variations of inflow to Lake Erhai

Statistics of hydrological data during dry and wet seasons

Water budget of Lake Erhai

Results of water quality assessrnent for Lake Erhai

Industrial wastewater generated in the Dali Municipality

Pollutants discharged h m the Yunnan Chernical Fuber Plant

Pollutants generated by M i n Paper Mill

Amounts of residentiai wastewater generated in the Lake

Erhai Watershed

Amounts of solid waste generated in the ]Lake Erhai Watershed

Payoff table for IFMOLP problem

LIST OF FIGURES

Figure 1.1.

Figure 2.1.

Figure 2.2.

Figure 2.3.

Figure 2.4.

Figure 2.5.

Figure 2.6.

Figure 2.7.

Figure 4.1.

Figure 4.2.

Figures 6.1 .

Figure 6.2.

A GIS map of the Lake Erhai Watershed 2

Major townships in the Lake Erhai Watershed 13

Geographical location of the Lake Erhai Watershed 15

Distribution of nitrogen and phosphonis loadings ,27

Eutrophication in Lake Erhai from 1985 to 1994 28

Degree of erosion in the Lake Erhai Watershed 41

Interactive relaîionships between enviionmental, resources and

economic objectives 46

Interactive relaîionship between diffenmt systern activities 47

Decomposition of a minimized objective function 79

Framework for the interactive IFMOLP approach 85

Graphical presentation of the comparative results of the iFMOLS

(1) Econornic objective 114

(2) SoiI loss protection objective 115

(3) Forest cover objective 116

(4) Nitrogen Ioss control objective 117

(5) Phosphorus loss control objective I l 8

(6) COD discharge control objective 119

Graphical presentation of the IFMOLP solutions for scenario 4

(1) Paddy faniland

(2) Dry farmland

vii

Vegetable familand

Textile industry

Chernical fiber indusïry

Paper mil1

Food processing

Cernent manufacturing

Leather industry

Tobacco industry

Net-cage fish culture

Tourism industry

Fomt cover

Brick production

Lime production

Figures 6.3. Contribution structures for scenario 4

(1) Economic objective

(2) Soi1 loss protection objective

(3) Nitrogen loss control objective

(4) Phosphorus loss control objective

(5) COD discharge control objective

CHAPTER 1. INTRODUCTION

1.1. BACKGROUND

Lake Erhai is loçated in Yunnan Plateau of Southwestern China with an m a of 250

km2. This freshwater lake plays a vital mle in Local econornic development with its

resources used for water supply, agricultural irrigation, fishery, tourism and navigation.

The study m a , Lake Erhai Watershed, has a total area of 2,566 km2, and possesses

extensive scenic and cultural resources with a mild clirnate. A GIS rnap of the watenhed

is pnxented in Figure 1.1, which was produced using PC A R C m O .

The total population in the area is around 704,000 with 22 ethnic minorities. There

is a variety of econornic activities around the lake, including agriculturaVindustria1

prduction, net-cage fish culture, fo~iestry, tourism and limebrick production. However,

the social and economic development in the watershed has been accompanied by

increasing environmental concerns. Cunently, many environmental problems, such as

water pollution, soi1 erosion and ecological deterioration exist within the watershed

system. Among them, the most pressing one is the degradation of the lake water quality

It is îherefore proposai that assessment of current environmental conditions be

carried out and that environmental implications of on-going and planned socio-economic

development activities be thoroughïy studied. Further, environmental planning for the

watershed should be undertaken using systerns analysis approaches to incorporate a

variety of impact factos within a general framework. Thus, a project entitled "Diagnostic

Study for Socio-Economic and Environmental Problems in the Lake Erhai Watershed"

was initiated and supporteci by the United Nations Environment Programme (UNEP). The

project consists of the following three major components:

* 'Diagnostic analysis of socio-economic and environmental problems in the Lake

Erhai Watershed;

Feasibility study on environmental management and pollution control measures;

Decision support system for integrated environmental management and planning.

As a major part of the required decision support system, this thesis entitled

"Multiobjective Water Quality Management Planning for Lake Erhai Watershed" is

dedicated to provide decisionmalcers with the planning for a nuniber of human activities.

As required by the UNEP and the local environmental protection agencies (EPA), this

planning should focus on the foilowing aims: (a) keep harmonization between the

environment and the economy on the basis of preserving and improving water quality in

the Lake Erhai; (b) effectively reflect interactive relationships between economic

development and environmental protection; (c) provide a quantitative bais for

adjusting/just.ying the existhg environmental management activities; (e) generate

planning schemes with applicability, suitability, flexibility and usability.

1.2. STATEMENT OF PROBLEMS

Water quality management planning is in essence a multiobjective decision-making

issue since it should cover a number of aspects related to economic development,

environmental impact, resources conservation and even political consideration. A sound

planning practice would provide feasible alternatives to accomplish water quality

standards with reasonable allocation of waste loadings h m pollution sources to

receiving waters under limited levels of econornic development. Impacts of uncertainty

are also significant in most water quality management problem. The random character of

natwal processes governing water resowces, the estimation errors in parameters of water

quality models and the vagueness of planning objectives and constraints are all possible

sources of uncertainty (Beck, 1987). As weii, most of the human activities are not only

related to each other but are also responsible for pollution problems. Any change in one

activity rnay lead to a series of consequences to the others and the reiated environmental

components. The complicated interactive relationships between system factors in regional

water quality systerns often create difficulties to management practices. It is also

necessary to consider the dynamic feature of the study system since temporal vadations

exist for most of the hurnan activities dong with socio-economic developrnent.

The Lake Erhai Watershed can be considenxi as a large-scale regional water quality

management systern typically with the multiobjective, uncertain, interactive and dynamic

features. This necessitates the application of a systematic approach for integrated

environmental planning. This means that, in the planning process, ail related system

activities should be considered as a general entity. The system optirnization should be

able to effectively reflect uncertainties and complexities of the study system and rnake

tradeoffs or compromises between interests from dflerent groups of stakeholders and

managers. Thus, a hybnd inexact-fuzzy multiobjective programming approach (IFMOLP)

for solving reai-world decision-making problerns is proposed and applied to the project

for the Lake Erfiai Watershed. The practical applicability and effectiveness of the

proposed approach are examined in this study.

1.3. RATIONALES

Most of the previous mdtiobjective decision making studies applied fuzzy and

stochastic approaches to deai with uncertainties. However, shortcomings in data

availability, solution algorithms, computational requirements and result interpretation

have generally limited their practical application. There has been a few studies applying

conventional rnultiobjective optimization techniques to water quality planning. Some

authors used stochastic approaches to handle uncertainties in optirnization models.

However, there has been no study of regionai water quality management using

multiobjective programniing that can deai with uncertainties.

There has been no environmental planning study for the Lake Erhai Watershed that

comprehensively deah with various environmental, socio-economic and resource factors.

Although some pollution control schemes, policies and regdations were proposed by

local authorities, they were not detaikd enough and need to be justified from a system

point of view (DEPB, 1994, 1995; Liao et al., 1993). Therefore, there is a demand for

effective environmental planning to ensure sustainable regional development. The

development of an inexact multiobjective programhg mode1 and iîs application will

help to more effectively reflect muhiobjective, uncertain, dynamic and interactive

fanues of the study system.

1.4. OBJECTIVES

This research is expected to achieve the following objectives:

To propose a system analysis approach which is capable of solving practical

decision-making problems related to a number of human activities with the

objective of niaximizing environmental and economic benefits. A hybrid inexact-

fuzzy approach for multiobjective mathematical progrannming under uncertainty

(IFM0I.P) would be developed. It is expected to be able to effectively reflect the

complexities of an environmental management system and provide the desired

compromise between different objectives.

To apply the proposai IFMOLP approach to the study of water quality management

planning for the Lake Erhai Watershed. The multiobjective, uncertain, dynamic and

interactive features of the study system will be effectively reflected in the

optimization model.'The results will provide reasonable alternatives for sustainable

management of local environmental and economic authorities, with the main

objective of protecting water quality in Lake Mai.

A cornputer-based planning system with user-friendly interface WU be developed to

assist local users to conduct programming analysis based on updated information in

the future. Thus, decision-rnakers can dynamically adjust planning schemes for the

future periods according to changed system conditions.

This study WU be the first application of inexact multiobjective programming that

can effectively deal with uncertainties to regional water quality management. The

knowledge gained in the study would provide valuable support for succeeding researches

and applications.

This study wilI also be an initial atternpt to extend inexact rnathematical

programming (IMP) methodologies to multiobjective decision-making issues. The

developed hybrid ItFMOLP approach wili have significant advantage in handling

uncertainties associated with real-world decision-making problems. The successful

application of the method to this study demonstrates that the IFMOLP can be an effective

and efficient tool for large-scale environmental planning. As an effective decision-

support system, the proposed IFMOLP cm also be applied to other engineering research

areas.

This study will be a pioneer exercise in integrated quantitative environmental

planning in China. Specific to the study area, scienaific bases are provided to the local

environmental management authorities for their justifyingladjusting the existing pattern

of human aceivities, fonnulating related local policies/regulations regardkg

environmental management and pollution control and producing long-terni planning of

the region's economic development and environmental management activities.

15. STUDY SCOPE

The scopes of this study involve the following considerations:

Many sectors, including agriculture, tourism, forest, net-cage fishery production,

industry, Stone excavation, in-lake navigation, in-lake fkhing, limekiln/brickkiln

and water supply/demand are considered in this study. Their interactive

relationships are reflected through formulation and application of an inexact-fuzzy

multiobjective bear programdg (IFMOLP) model.

To reflect intemgional and spatial considerations in the planning study, the

wamhed is* to be divided into seven subareas with different environmental,

economic and resource characteristics correspondhg to ecological, hydrological,

and administrative zones specified by the local authorities and experts. The details

of the seven subareas are depicted in Figure 1.1.

The tourism industry is concentrated in subarea 2 with two major separate sections

for sightseeing. Thus, subarea 2 is further divided into subarea 2-1 and subarea 2-2

for tourism industry.

The study tirne horizon is 14 years (1997 to 2010), which is further divided into two

planning periods (1997 - 2000 and 2001 - 2010). Over the 14-year planning

horizon, it is assumed that regional development would lead to a series of impacts

on environmental, resource, socioeconomic and biophysical sectors in the

watershed and affect different system activities.

The cost/benefit values in the IFMOLP modeling study are expressed in present

value dollars. They are escalated to reflect anticipated conditions and then

discounteci to generate present value ternis for the objective function.

CHAPTER 2.

SYSTEM DESCRIPTION AND CHARACTERIZATION

2.1, THE STUDY AREA

The study area, Lake Erhai Watershed, is located in the central part of Dali

Prefecture, Yunnan Province in southwestern China Lake Erhai, part of the

Lanchangjiang River system, is a freshwater lake with a surface area of 250 to 257 km2

and avolume of 2.9 to 3.0 x 10' d. Its drainage watershed covers 2,565 km? There are a

total of 117 aibutary rivers and streams to the lake. There is only one natural outlet, Xier

River. The area is locaîed in wami subtropical climate zone. The annual mean

temperature in the area is 1 6S°C, and annual precipitation is 1,W2 mm.

nie average precipitation on the lake surface is 0.26 biUion m3, with an average

annual evapomtion of 0.302 billion m3. Table 2.1 shows general characteristics of Lake

Erhai (average from 1 952 to 1 988).

The land in the watershed consists of high mountains, lowland hills, valley flatland,

riverbeds, and lakes. Its structure is composed of 70% mountain, 20% flat land, and 10%

water bodies. The existing land use can be classified hto familand (14.5%), forest

(44.7%), abandoned grassland (20.3%), human habitat (2.7), transportation (OS), water

body (9.5%), and barren land (1.7%). The watershed is fdled with waterways

Table 2.1. General characteristics of Lake Erhai

-- -- -. - -

Water level Lake area Lake volume Average Inflow Outflow Length of

water depth lake shore

(ml (km2) (m3) (ml (m3) (m3) (km)

and rich in surface and groundwater resources including geothermal springs. As a

nationaliy designated region for tourism, the area is endowed with many beautiful scenic

sites as weli as unique histofical and cultural properties.

The watershed extends to the jurisdictions of Dali City and Eqwan, Binchun and

Yangbi counties in Dali Bai Ethnic Autonomous Prefecture. The population in the ara is

about 704,000, and only 25.5% of the total are non-agriculhual. The average growth rate

of the population between 1950's and 1990's is about 2.15% annually. There are 22

ethnic minorities living in the watershed, which is also the primary habitat for the ethnic

Bai. The major townships within each subarea are s h o w in Figure 2.1.

The study area's gross domestic product (GDP) arnounted to Y1,511 million RMB

(present value, $1 CDN = YS.9 RMB) in 1990, accounting for 52.4% of Dali Prefecture's

total GDP (~2,882 million RMB). The GDP per capita was 41,341 RMB. The local

economy has experienced rapid growth since the early 1980's. Although the overall

economic structue of the area is weii balanced between primary, secondaxy and tertiary

sectors, there are great spatial variations. Regional specialization exists in the primary

sector whik the development is diversified in the siudy area. For example, more grain

production and livestock husbandry can be found around Dali City and Binchuan, more

daky land can be found in Eryuan, and Yangbi has more forest cover. The secondary

sector, concentrated in Dali City, is rnainly composed of light industries, such as tobacco

Urban Water

\ #

'-? =

i i,

**. i Fi- 2.1. Major townships in the Lake Erhai Watershed i

1 B.-

-'',@.-'

processing, food processing, textile, and pulp and paper industry. The terthy sector is

being increasingly developed mainly based on tourism and commerce as the. area is

situated at the key junction linking Kunming (provincial capital) and the western part of

the province (Figure 2.2).

With respect to the human activities considered for planning, the seven subareas

have quite varying levels in their development. Table 2.2 gives the existing pattern of

the hurnan activities in each subarea

2.2. ENVIRONMENTAL PROBLEMS

With the rapid population increase and economic development, the environmentai

issues around the Lake Erfiai have becorne increasingly problematic. Five major

environmental problems are identified in the Lake Erhai Wateished:

Decline of the water level in Lake Erhai caused by increased discharge of lake water

for hydropower generation has led to deterioration of lake water quality, increased

soil erosion of river beds and fadands, and the decline of groundwater levels that

affect lake shore cornrnunities which directly use groundwater for domestic

purposeS.

v - - . -. ..-. .-- 1

\

I QI334 \

I

1

I

1

l

t CHINA : 1

1 1 KOREA

I r \ \ - - - 1 4 ------q \ ---- 4-,,,,,,,,,-A----- \

EP l I \ \ \

H TAN 1

Dh >Jnming BANGLMESH; YUNNAN

t j MYANMAR u o s ' )#cc

-t---

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- - - - CMlXHllA

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t l VlETHAV 4

---- Dali Pref - . Railway

Figure 2.2. Geographical location of the Lake Erhai watershed

15

( 1 ) Existing land use patterns of agricultural activities (km2)

1.Paddyfarm 16.2 34.2 9.6 2.8 24.0 10.8 91.8

2. Dry farm 22.2 43.8 18.6 7.2 33.0 3 1.2 215.0

3. Vegetable 0.12 1.8 1.4 1.2 0.60 0.60 2.3

Sum 38.52 79.8 29.6 11.2 57.6 42.6 309.1

(2) Existing production output of industriai activities (Y 10,00O/yr)

1 . Textile

2. Fiber

3. Paper

4. Food

5. Cernent

6. Leather

7. Tobacco

Sum

(3) Existing area for net-cage fishery production levels (m2)

(4) Existing tourist flow ( 1 0,000person-day/yr)

Sub-area 1 2- 1 2-2 3 4 5 6 7

81 60 243 36 81 - - -

(5) Existing forest cover (km2)

(6) Existing brick production levels (10,OOOpcs/yr)

(7) Existing lime production levels (tlyr)

Significant structural changes of the aquatic population in the lake are evident, due

to the decline of the water level and related changes in the lake ecosystem. This

would increase the possibility of extinction for the lake's native species.

The lake water quaiity is gradudiy changing ftom submesotrophic to mesouophic

due to the increased nutnent discharges (nitrides and phosphides) fiom crop

farming, livestock husbandry, fish cuitme and other activities related to non-point

source pollution.

Deforestation in the watershed coupled with increased soi1 erosion has accelerated

the Pace of the sedime!ntation process in the lake.

The sçenic resources, biodiversity and endangered species in the watershed a~

poorly pmtected due to a lack of proper management measm.

2.3, WATER RESOURCES AND QUALITY OF LAKE ERHAi

2.3.1. Water Balance in Lake Erhai

(a) Water Supply and Demand

Average annual precipitation in the Lake Ehai Watemhed is 1,048 mm with about

85% of annual rainfall coming between June and October. The disaribution of

precipitation varies spatialiy in the area. Table 2.3 shows precipitation under different

frequencies in the Lake Erhai Watershed.

The average annual inflow to the lake is about 8.02 x 10h3. The maximum inflow

is 18.8 x 10' m3 while minimum inflow is only 1.84 x 108 m3. Precipitation in the West

(subareas 1, 2 and 3) is 25 to 30% higher than that in the east (subarea 6). Also,

precipitation in the north (subarea 7,1200 mm) is higher than thaî in the south (subareas

4 and 5, 700 mm). Thus, distribution of wmr resources is not weil balanced in the

watershed area. In ternis of temporal variation, inflow to the lake between July and

October accounts for 80% of annual total, while inflow fiom November to July is usually

less than 20% of the total (Table 2.4) There exists a hydrological cycle for every three

years in the watmhed. For exarnple, a dry period appeared duicing 1981 to 1984 when

annual M o w to the lake was only about 4.65 x 108 m3 (58% annual average). The years

from 1961 to 1974 consisted of a long period with plenty of water supplies, in which

average annual inflow to the lake was 76 x 10' m3 (Table 2.5).

The average annual outfiow from Lake Erhai was abnit 8.16 x 108 m3. The

maximum outflow is 18.18 x 10' m3 while the minimum is 4.15 x log m3. Water

resources in the Lake Erhai Watershed have been fully exploited and utilized. Its

utilization ratio reaches 90.7%. Amoinits of water withdrawal from Lake Erhai per year

8 3 8 3 were 7 .O x 10 m for hydropower generation, 1.3 x 10 m for agriculîural irrigation, 0.4

x IO* m3 for industrial uses, 0.13 x 108 m3 for residential uses, and 0.5 x 108 m3 for

Binchuan County (extemal system).

Table 2.3. Precipitations under different frequencies in the Lake Erhai Watershed (mm)

Frequency East South West North Cangshan

Table 2.4. Temporal variations of inflow to Lake Erhai (%)

F* Year Jan Feb Mar Apr May June Iuly Aug Sep Oct Nov Dec July - Oct

* "F' means frequency.

Water resources in the watershed area have been over developed. Totally, around

9.33 x IO* m3 of warer was used evety year, exceeding the average inflow of 8.02 x 108

m3. The deficit of water balance has kept widening with increasing demand for water

resources. A number of water resources projects have been completed for infrastnicture

improvement and agriculture development such as the storage of water resources in the

upper reach, pumping of water to higher lands, and water delivery to extemal systems.

@) Consequent Problems

The over discharge of the lake water resulted in reduced lake water level. The

average water level in Lake Mai decreased by 1.92 rn h m the 1950s and 1980s (Table

2.6). The water surface area of Lake Erhai was about 255 km2 with a capacity of over 2.9

billion m3 in the 1970s. Since the eady 1980s. the watex surface m a has decreased to 236

to 246 km2 with a capacity of about 2.49 billion m3. Consequently, the ecological

conditions of the lake and its watershed have been deteriorating.

In the last ten years, in addition to power genemion, the amount of water fox

industnal and residential uses has also increased yearly. Power generation and

agxicultural irrigation consume the majority of the lake water, up to 0.7 billion m3 and

0.13 billion m3 respectively. Over use of the warer resomes accelerared the conflicts

between supply and demand.

2.3.2. Lake Water Quality

There are twelve environmental monitoring stations at three sections of Lake Erhai.

Table 2.7 shows results of water quality assessrnent for the lake h m 1991 to 1995. In

1995, water qualiîy as expressed by pH, DO, Total-P, Total-N, and Cu was below the

required standards. Organic pollution was niainly from COD, BOD, ammonia-niirogen,

and Total-P.

The assessrnent indicaies that the water quality of Lake Erhai is generally better

than the other water bodies in the watershed. However, concentrations of nitrogen and

phosphorus exceded the standards due to non-point source pollutant emission from a

number of hurnan activities, resulting in lake eutrophication problems (Figure 2.3 and

2.4). In Fa11 1996, the water quatity of the lake was seriously detenorated because of the

development of blue-green algae. Concentsuions of t o t W and total-N at eight of the

monitoring stations were 0.01 - 0. 05 and 0.44 - 0.703 rn& respectively. The lake

transparency was 1 .O - 2.8. Dissolveci oxygen in some sections was as low as 2.6 mg/L. In

November 1996 (winter), the lake water qualiey was st i l l in a poor condition, with a low

concentration of dissolved oxygen, reaching the lowest at 1.7 mg/'. Results of

comprehensive assessrnent indicate that water qudity level at most sections was grade III

with some of them reacbing grade N (PRCEPA, 1988). The number of algae was 51 1 to

2100 per llter with the dominant species king blue-green algae. Presently, almost the

entire lake is nearly in a state of eutrophication.

From domestic wask in the unsttni region P-N t 12 t /d I%) From animal husbandry

N f 449tI8(43.2%) D-N 9.1 t/r(ld%) in n0-m P243t /r(433%) P-P 9z.6 t/ r(f 3%) Ei 14226 t / 8(65#)

From animal husbandry in western N 144*/443.294)

P 234 t / r ( l32w

P-N 753 r/.(bS%)

P-N 3389 t / 447%) P-N S a 1 t/ r[O.t%)

n-N sa t/r@S%) P-P 1126.St/i(16.3W

P-P 3146 t/i(lU%)

P-N 33.11 / d O J % )

P N 279St / &4%) D-N 25 t/r(OA'Yr)

D-N 242 c/aOAY.)

- From animal htubandry in southtrn N 370 t/dlI%)

P s9.8t/r(t l%)

Fmm Dom* W e in Eastern region N 1684 t /*(49W

P 473 t / r(6.394)

Fmm animal hasbandry in castern N 245 t/ 47.3%)

P 39.6t/47.3)

Figure 2.3. Distribution of Nitmgen and Phosphorus Loadings

rncso-tmphiaition 1-1 digr>-trophication

Figure 2.4. Eutrophication in Lake Erhai from 1985 to 1994

There were many factors related to the lake eutrophication, such as water level,

water temperature, sunshine, and increased nutrient concentrations. When al l these

factors tend to be adverse, lake euû-ophication would occur. It indicates that the lake's

water quality is at a aitical state. In order to pmvent occurrence of further eutrophication

in the funire, conuol of point and non-point source pollutant emissions to the lake by

management measures would be necessary.

2.4. POLLUTION SOURCES

2.4.1. Point Pollution Sources

ïhere are around 3 1 ,111 industrial enterprises in Dali frefecture under different

owners, such as governments, pnvate companies, and foreign investors. Of hem, 81 have

been considered to be significantly environment-related. Most of the enterprises are

located in Dali, with the oîheirs scattemi in Heqing, Yunlong, Xianyun, Midu and

Jiançhuan.

Table 2.8 shows industrial wasfewater generated in the Dali City. There are 557

industrial enterprises in the Dali City. Sixty-five of them discharge industrial wastewater

with an average amount of 5.89 tjd.

Table 2.8. Industrial wastewater generated in the Dali Municipality

Total Industrial

Year sewage sewage COD (t/yr) As (kglyr) Al (kglyr) Phenol Cyanide Petroleum

(10,ooO Vyr) (1 0,000 tfyr) (kg/yr) (WY r) WY

(a) Poilution from Pulp/Paper and Chemical Fiber Industries

In the study ma, Dali Pulp/Paper Mill, Erbin Pulp/Paper Mill and Yunnan

Chemical Fiber Plant discharge the greatest amounts of wastewater (71.6%). The main

materials used for pulp production in the Dali Pulp/Paper Mill are Yunnan Pine,

eucalyptus and used carciboard. This plant produces 30,000 t of pdp per year, consumes

19,000 m3/d water, and discharge 17,000 m3/d wastewater. Thus, each tonne of pulp

produn produces 250 m3 of wastewater. Amoms of COD, BOD and SS discharged from

pulp/paper production processes are 41, 10 and 8 t/d, respectively. All wastewater from

the Dali Paper Mill is currently dkcharged into Xier River without any treatment.

Yunnan Chemical Fiber Plant is located in the center of Dali City. The factory was

built in 1965. The factory produces 5,000 tfyr of viscose fiber. The water needed for this

plant is obtained fiom Xier River with a consumption rate of 12,000 m3/d. Amount of

wastewater diichargd from the plant is 8,000 t/d, which means 600 tomes of water is

used for producing each tonne of product. Table 2.9 shows amounts of pollutants

discharged h m the Yunnan Chemical Fiber Plant into the Xier River.

The Yunnan Chemical Fiber Plant consumes a great amount of water. Its

wastewater contains high concentration of COD and BOD. The plant has no wastewater

treatment faciiity. The wastewater is discharged directly into Xier River without

treatment .

Erbii Paper Mill is near Xier River. It uses rice straw, Chinese Alpine and used

gwinysacks as its cmde matenals. Its consumption of rice straw and gunnysacks are 3,900

and 1,100 t/yr, respectively. Amount of wastewater discharged from this plant is 8,800

t/d. Table 2.10 shows the details of pollutants generated by this industry. The water

consumption for each tonne of produa is 1,200 m3. There is a great amount of SS in the

wastewater since the straw contains silicon dioxide. The wastewater is discharged into

Xier River without any treatment.

The above three plants contribute to the majority of hi& pollutant-concentration

wastewater emission (without any treatment), and cause water pollution problems in the

watershed. Also, since the wastewater contains allcalinity and SS (with high

concentrations), corrosion problem to power generation equipment exists.

(b) Wastewater from Rural Enterprises

Rural enterprises are main components for economic development in the region,

including farrning, construction, zransportation, food and service sector. Other related

industrial activities are ore smelt, construction material, silicon tile, Chinese herbs and

leather. A large nurnber of rural enterprises, especialiy those related to resources

exploitation, usually are developed at the expense of environmental deterioration, such as

landscape degradation and discharging wastewater.

S i c e rural enterprises are scattered in different locations with small production

levels, their wastewaters are hard to manage. Thus, the wastewater, through runoff and

rainstorm, will flow into rivers and finally into Lake Erhai. The total amount of

wastewater discharged by rurai enterprises is cumntly estimated at 1 15,600 t/y.

(c) Residential Wastewater

Table 2.1 1 shows amounts of residential wastewater generated in the Lake mai

Watershed. This type of wastewater is usually related to population. Total amount of

wastewater discharged is about 16 million t/yr with a COD emission rate of about

260,000 t/yr. A large arnount of wastewater to the Lake Erhai Watemhed is h m sewage

pipes dong two banks of Xier River. However, wastewater fiom a number of mal

villages and Fengyi Town is discharged directly by nearby ditches to Bo10 River and Lake

Erhai.

(d) Solid Waste

The generation rate of solid waste in the study area is 0.99 kg/personday.

Municipal solid waste (MSW) generation has been increasing at a rate of 10% per year.

Table 2.12 shows the amounrs of solid waste generated in the study system. The total

amount of solid waste generaîed in 1994 was 97,282 tonnes, including 413 tonnes of

hazardous solid waste, 65,068 tonnes of non-hazardous waste, 31,801 tonnes of other

waste (such as coal ashes). Common masures for dealing with solid waste in the study

m a are composting and landfill. Composting sites in many villages are near

Table 2.1 1. Arnounts of residential wastewater generated in the Lake Erhai Watershed

Parameter Population type 90 91 92 93 94

Residential wastewater

emission rate

(m3lperson-day)

COD discharged

(kg/person-day)

Residential wastewater

( 1 0 , ~ Vyr)

COD emission from

residentiai wastewater

( 1 o,ooo kgfyr)

non-agriculture

agriculture

tourists

non-agricul ture

agriculture

tourists

non-agricul ture

agriculture

tourists

total

total

Table 2.12. Amounts of solid waste generated in the Lake Erhai Watershed (tonnes)

Area 1995 1997 2000 2005 2010

Xiaguan 47,500 57,500 76,500 1 12,300 165,000

DaliTown 4,900 5,900 7,900 1 1,600 17,100

Feng y i 4,300 5,200 6,900 10,200 15,000

Xizhou 1,900 2,500 3,100 4,500 6,700

Total 58,600 70,900 94,400 138,600 203,800

groundwater table with potential water pollution problems. There is generally no

collection and reuse of industrial waste in the area. The discardeci waste without any

treatment is eventually rushed away by moff into the lake.

2.4.2. Non-point Source Poliution

(a) Sources

Non-point pollution sources are major contributors to the lake pollution problem It

was estimateci that 5,000 to 7,000 tonnes of nitrogen, and 5,000 to 5,500 tonnes of

phosphorous are dischargesi into the lake per year. Soi1 l o s fiom a@cultural land and

other hurnan activities is another problem related to water quality in the lake.

The non-point pollution sources in the Lake Erhai Watershed can be divided into 5

categories:

in-lake net cage culture,

soi1 erosion,

viiiage wastes.

Specifically, the following factors are found to be attributable to non-point source

pollution problems:

soii and nutrients runoff due to destruction of forest and vegetation;

soi1 and nuaien& runoff due to excessive reclamation on hiUy areas and grasslands;

soi1 and nutrients runoff due to reclamation of waste lands and excessive use of steep

siopes;

nutrients and pesticides runoff due to excessive uses of &&ers and pesticides;

increased poliution loads due to diicharge of sewage from villages and towns;

increased poliution loads due to garbage and solid waste generation fÎom villages and

towns;

direct water pollution h m aquaculture and livestock husbandry;

water pollution caused by oil, wastewater and solid waste ernissions b m tourist

vessek;

soil and nutrients losses due to rainfaii or rctinstorm;

soil and nutnents losses due to landslide.

(b) Geographic Characteristics

The non-point pollution sources are located in four geographical areas:

(1) The Northern Region

The majority of lowland in the north is cultivated. This region contains Miju River,

Luoshi River and several springs, which are dl connected to Lake Mai . The rivers

account for 50% of total runoff and nitrogen/phosphonrs losses into the lake. Nutrients

corne not only from field runoff, but also silt leaching. Deforestation and cultivation in

the watershed have increased soil erosion and acœlerated sedimentation rate in the lake.

It was estimated that about 30% of lands in the lake watershed suffer fkom soil erosion

with an estirnateci annual soil loss of several million tonnes (Figure 2.5).

(2) The Western Region

The majority of l o w h d in the watershed, located in the West of Lake Exhai and the

lower reaches of the eighteen streams from the Cangshan Mountains, is cultivated or used

for other economic purposes. Non-point source pollutants are mainly fiom crop famiing,

livestwk husbandry and village waste which release nutrients, toxic compounds,

pesticides and herbicides into the lake. This area also contributes a significant amount of

the silt which is eventually deposited to the lake bottom. Eighteen s t e m and a large

volume of overland runoff flow into the lake from this region (Figure 2.5).

4S03taaa

Figure 2.5. Degree of erosion in the Lake Erhai Watershed

(3) The Southeastern Region

The southeastem region contains the Boluo River and other small mm, and is

also affected by the Xier River's back flow. As well, there is a large urban area with

significant amount of urban runoffs. The major outfiow river for the watershed Xier

River, is contaniinaîed by industriaYresidentia1 wastes &orn this areas. Boluo River

brings nuîrients from agicultural lands and silt from eroded soils into the lake.

(4) Lake Erhai and Net-Cage Fish Culture

Net-cage fish culture is one of the largest poliution sources for the lake. There are a

large number of small-scale net-cages in different parts of the lake. They conîribute to the

nutrient loading In the lake primarily by feeding and fecal matenais from fish. Sewage

and leaked oii fmm in-lake vessels represent another type of non-point sources.

2.5. SYS'iEM FEATURES

2.5.1. Multiobjective Feature

Objectives h m environmental, economic and resources aspects exist

simultaneously in the regional water quality management problem These objectives have

potentials of lirriiting or promoting each other. In this study, the essential goal is to find a

solution to the water quality management problems in Lake Erhai and sustainhg a local

economy. A number of system factors related directly or indireçtly to the goal should be

considered. They may include econornic retum, water pollution control, soi1 erosion

reduction and forest resources protection. In this regard, the study problem is how to find

a satisfactory compromise between interests fiom different stakeholders and managers in

order to niaximize overall benefits of the entire system

2 5.2. Uncertain F e a t u ~

Decisions in water quality management are ofbn made on the basis of imprecise

information. Goals and constraints may not be defined precisely due to ilidefineci and

subjective requirements based on human judgements or preferences. Many analysts get

used to using the mean value or middle value to represent imprecise data. However,

information loss resulting from the approximations would substantially reduce the

significance of optirnizaîion analysis and lead to a higher risk of making decision

rnistakes. For this study, there is uncertainty associated with rnost of the available

information about system components, and even the relationships between some

components are vague. This makes the system more complicated and hard to be

effectively analyzed quantitatively. For example, it is hard to obtain a detenninistic value

of loading capacity for tourists in a tourism site. Only sorne uncertain information can be

obtained to represent it. Consequently, the ernployrnent of systems analysis methods that

can effectively reflect uncertainties is important for generating reliable and realistic

planning alternatives.

For the planning time horizon of 14 years, social, economic, legislative and

resources conditions will vary with tirne. Refletion of this temporal variation

characteristic in the systems analysis models would be important for generating effective

and realistic environmental planning alternatives. Tbus, developrnent of dynarnic

optimization for the study problem is desired for effedve environmenial management

and planning.

Due to the possibiity of continuous changes in system components dong with tirne,

it is suggested that the environrnental planning study should lead to a %al-tirne" decision

support systern. This means that the research results should be composed of not ody a set

of nmi decision alternatives but also a controliable management system such as a

cornputer software package. Decision-makes cm then input updated information for the

future periods to the planning mode1 and generate the correspondhg solutions with the

software. Thus, new planning alternatives can be obtained through interpretation of the

solutions. This "real-tirne" characteristic is beneficial for improving effdveness of the

environmen ta1 planning study .

2.5.4. Interactive Relationships Between Systern Components

For each tennporal/spatial unit with given environmental, resource and econornic

conditions, there exist interactions and confiicts between different system activities and

between diffexent system constraints/objectives.

(a) Relationships between environmental, resource and economic objectives

Figure 2.6 shows interactive relationships between environmental, resowce and

economic objectives. It is indicated that economic activities are generally responsible for

water pollution in the Lake Erhai. However, economic activities would also generate

revenues which can be partty used as capital/operating costs for pollution abatement.

On the other hand, there are limited natural resowces and poUutant loading capacity

in the watershed, which implies the necessity for their effective use. Therefore,

environmental planning wili help to desigdplan a variety of system activities under these

limited "allowances" for pollutant emission and resources consumption in order to realize

sustainable socio-economic development with satisfied environmenial and e source

objectives and rnaximized benefit for the global system.

(b) Relationships between different system activities

Figure 2.7 shows interactive relationships between different system activities. It is

indicated that most of the activities are interrelated to each other. Any change in one

subsystem may lead to a series of consequences to and responses fiom the others.

improvement of

& 4

I planning of a variety of system activities under limited "allowance" for environmentai contamination and resources consumption 1 sustainable socio-economic development with satisfied environ- mental & resources objectives and maximized global system benefit

limited pollutant . loading capacity

Figure 2.6. Interactive relationships between environmen tal, resources and economic objectives

limi ted resources

polhtants emission

'I

economic benefits

water pollution in Lake Erhai

I t i

-+ capital for pollution management and control

Therefore, in planning of such a system, individual or independent consideration of one

or severai subsysterns would not be able to completely reflect the gened system

characteristics. This means thai even good planning for one or several sectors may not be

good for the entire system if some related factors/subsystems are neglected. Therefore.

employment of systems analysis methods for environmental planning would be essential

for integrated reflection of the cornplex system characteristics.

2.6. SUMMARY

The Lake Erhai Watershed is a large-scale water resources system. Human activities

around the lake are quite diversifmi with the rich natural resources. Together with

population expansion, the local economy has gained significant growth with a weU-

balanced structure. But the development level differs fkom specific regions. Currently,

some environmental problerns pose obstacles for the existing human activities and the

further socio-econodc developrnent. The pressing problems are mainly related to the

detenoration of the lake wa!er quality, involving the soil erosion, point and non-point

source pollution, deforestation and ecological deterioration.

Cornplexity of the study system is thoroughly analyzed as the basis of

environmental management planning. Generally, water quality in Lake Erhai is related to

a number of environrnental, resource and economic acîivities/objectives in different

temporal/ spatial uni&. There are also interactions between these activities/objectîves.

Tlius, a simple decision process by direct analysis/assessment or expert consultation

would not sufficiently reflect the complex system characteristics. Therefore, the

development of suitable systems analysis approaches to integrate a variety of system

components (objectives, constraints, and activities) within a general modeling hmework

would be necessary for this study. The systerns analysis should be able to effectively

reflect interactive, multiobjective, dynamic and uncertain features of the study system Its

outputs would be interpreted to generate desired and realistic planning alternatives for a

number of human activities as weli as related environmental management Strategies and

policies.

CHAPTER 3. LITERATURE REVIEW

3.1. MATHEMATICAL PROGRAMMING APPROACHES FOR DEALING

WITH MULTIPLE OBJECTIVES AND UNCERTAINTIES

3.1.1. Fuzzy Multiobjective Decision-making

(a) Classification of fuzzy approaches

Classification of fuzzy mathematical programming @MF') methods has been

discussed based on the type of uncertain information (Zirnmermann,l985; Leung, 1988;

Luhandjula, 1989; FedrizW, Kacp~zyk and Verdegay, 1991; Inuiguchi, Ichihashi and

Tanaka, 1990; Lai and Hwang, 1992, 1994). In the works by Lai and Hwang (1992,

1994), fuzzy multiobjective prografnming (FMOP) pxoblem were distinguished from

possibilistic multiobjective programming (PMOP) pmblems. The FMOP problems are

associated with fûzzy input data which should be modeled by subjective preference-based

membership functions. On the other hand, the PMOP problems are associated with

imprecise data that should be mode1ed by possibility distributions. Possibility

distributions are an analogue of probability distributions and can be either subjective or

objective. Considering d l possible problems and existing approaches, this systematical

classification appears more appropriate than those in the other works.

Conventional multiobjective programming techniques are generally classifiai into

three categories: generating techniques, methods with pnor articulation of preferences

and interactive approaches (with progressive articulation of preferences) (Goicoechea, et

al., 1982; Hwang and Masud, 1979). Al1 the existing fuzzy rnultiobjective prograrnming

approaches fa11 in the later two categories, Le., the information about decision-rnaker's

(DM'S) preferences is required either before or during solution processes.

@) Fuzzy multiobjective pmgrarnming (FMûP) approaches

A major FMOP technique with pior articulation of preferences is fuzzy goal

prograrnming (FGP). The FGP methods include general FGP approach, preemptive and

weighted additive FGP, interpofative membership function, preference structure and

nesteù priority problems. Fuzzy set theory is applied to goal programhg with the

advantage of ailowing for vague aspirations. The DM'S linguistic statements can be

quantified by eliciting membership functions carrying the preference concept. To solve a

fuzzy goal programming problem with m fuzzy goals, NarasUnhan (1980) first proposed

2" crisp goal prograrnming sub-problems. Hannan (1981) cornbined these 2" sub-

problems into a single conventional problem. On the other hand, Yang et al. (1 991) used

Zinuilennann's fuzzy programming model (Zimniell~lsulxl, 1978) to solve fuzzy goal

programming problems. In many decision problem, some goals are so important that

unless these goals are reached, the DMs would not consider the achievements of other

goals. The fuzzy goal programming with a priority structure for ordering goals is called

preemptive FGP. Tiwari, Dhannar and Rao's preemptive model can be used to solve a

fuzzy goal programming problem with k priority levels where each level xnay include rrq,

goals (Tiwari et al., 1986). The preemptive model must be formed and solved

sequentialty since each subsequent stage needs optimality information from previous

stage. To improve the solution efficiency, a weighted additive model was introduced to

aggregate priorities of the considered (fuzzy) goals. Weights or prionties among

goals/objectives need to be determined as the initial step of the solution process to elicit

the relative importance. Decision-makers @Ms) rnay provide either crisp weights or

(vaguely) linguistic weights. There are several approaches to obtain cRsp weights

(Zeleny, 1973; Lai and Hwang, 1994a; Narasimhan, 1 982), while Narashhan (1 98 1) also

us& membership functions to mode1 linguisticffizzy priorities. Jnterpolated mernbership

functions are piecewise linear functions constructeci by sorne specific objective values

decided by the DMs. FGP problems with interpolated membership functions have been

solved by Hannan (1981a), huiguchi et al. (1990), and Yang et al. (1991). For a goal

programming (GP) problem, many different sets of subjective aspiration levels codd be

assignai by different tearns of experts. To solve this problem, Rubin and Narasimhan

(1984) proposed a nested priority concept so that îhe relative importance of goals depends

on the solution under consideration. Thus, the DMs may reevaluate the relative

importance of goals in light of the satisfaction levels achieved In addition to the FGP, the

global criterion concept was also used to solve rnultiobejctive linear programming

(MOLP) problems with fuzzy constraints by using Zimmermann's min-operator @mg,

1983,1984).

There are quite a number of interactive fuzzy MOP rnethods reported in literature.

Werner's algorithm solves a MOLP problem with fuzzy objective and fuzzy available

resources (Werners, 1987a, 1987b). Lai and Hwang's interactive expert decision-making

support systern provides interation-orienteci, adaptive and dynamic leaming feanires by

considering ai l possibilities of a specific domain of MOP problems which are integrated

in a logical order (1994a). Leung (1987) extended the preemptive fuzzy goal

programmhg approach to developing an interactive procedure for solving a hierarchical

fuzzy objective problem Fabian et al. (1 987) extended the flexible prograrnming concept

to solve a nonlinear MOP problem with no feasible solution. Sasaki et al. (1991)

proposed an interactive approach combining FGP and the generalized upper bound

structure to solve a fuzzy multiple objective 0-1 LP problern where goals and available

resources are fuzzy. Baptistella and Ollero (1980) used gradient projection method, fuzzy

algorithm. and linguistic conmller concepts to develop three solution procedures for a

fuzzy MOP problern.

(c) PossibWc Muhiobjective Programming Approaches

Approaches for solving PMOP problems &O n e 4 either "a prior aaicdation" or

"progmsive articulation" of preference information. There are some typical methods for

the former. Tanaka and Asai (1984% 1984b) assumed a MOLP problem wiîh imprecise

input data having symmetric triangular possibility distributions, then obtained a nonlinear

single objective progranunhg problem by using the max-min operator. Lai and Hwang

(Lai, 1991; Lai and Hwang, 199%) handled imprecise profit (rnax) objectives with

triangular possibility distributions by maximizing the rnost possible value, mininiizing

risk of obtaining lower profit and maximiz'ig possibilîties of obtaining higher profit. The

imprecise constraints were treated with Ramik and Rimanek's fuzzy ranking concept

(1989). Negi (1989) applied Dubois and M e ' s exceedance and strict exceedance indices

(1988) to deal with imprecise objectives and constraints modeled by triangular or

trapezoidal possibility distributions. Luhandjula (1987) proposed the concept of a-

possible feasib'ity and B-possible efficiency. An a-possible feasible and f%-possible

efficient compromise solution can then be obtained by solving auxiliary cnsp MOP

problem denved by use of the extension pMciple and a and p-level cuts Li and Lee

(1990a, 1 WOb) solved a multiobjective de Novo programming problem with imprecise

input data by extendmg Carlsson and Korhonen's, and Verdegay's concepts (Carlsson

and Korhonen, 1986 Verdegay, 1984) to obtain an auxiliary crisp MOP problem.

Wierzchon (1987). extended Dubois and Prade's, and Orlovsky's concepts of degrees of

interaction and inclusion (Dubois and Prade, 1987; Orlovsky, 1978) to solve a PMOP

problern.

For interactive mthods, Sakawa and Yano (1990) introduced the concept of M-a-

Pareto optimal solutions to obtaùi a crisp MOP problem which can be soIved by their

min-rnax approach. The "FIlP" method proposed by Slowinski (1986, 1990) used

optimistic and pessimistic cornparison indices to handle the irnprecision of PMOP

problerns and to obtain a misp muitiobjective kear Wtional programniing problem

which was M e r solved by Choo and Atkln's interactive approach (Choo and A t h ,

1980). With the assumption of imprecise aspiration levels, Rommelf'anger (1989) treated

irnprecise objectives as imprecise constraints, and handled a l l impn!cise constraints with

Rarnik and Rimanek's fuzzy ranking concept (1 989).

3.1.2. S tochastic P r o g r h g with Multiple Objective Functions

A stochastic programming problem with muItiple objective functions can be solved

in the following two rnanners: replace the problem by an equivalent crisp mdtiobjective

programming problem which can be solved by various deterministic niultiobjective

programming methods or reduce it to a single-objective stochastic programming problem

which cm be easily solved.

Stancu-Mimasian (1978) considered a multiple criteria stochastic programming

problem where the elements of vectors are stochastic va~iables with known (joint)

probability distribution. He proposed to reduce it to "Chebyshev" problem (with single

objective) which c m be solved îhrough minimum-risk approach (Tigan and Stancu-

Minasian, 1983). Contini (1968) and Chobot (1973) considered applying a goal

programming approach to sochastic cases. Stancu-Minasian and Tigan (1988) extended

the stochastic goal programmjng to a linear fractional problem. The btility function

method proposed by Neumann-Morgenstern (1953) cm be used to transforrn a stochastic

muitiobjective programming problern to a single-objective one. The method was shown

to be usefui in solving group decision-making problems (Bereanu, 1976; Ciobanu, 1976).

Stancu-Minasian (1984) also considered a more general case of minimum-risk problem in

which the probabilities that the values of linear objective funciions exceed some levels of

performance are maximized. The same author provided a discussion on obtaining

efficient solutions for stochastic mdtiobjective prograrnming problems (Stancu-

Minasian, 1990).

Some interactive rnethods have been proposed for solving stochastic multiobjective

programmllig problem. n i e PROTRADE (Probabiiistic Tradeoff Development) method

(Goicoechea et al., 1982) can be a stochastic analog to the detenninistic STEM method

(Benayoun, 1971). In the iterative process for efficient solution, the DMs may modw the

initial conditions according to an already attained objective function value and the

comsponding probability of reaching it. Teghem (1983) proposed another interactive

stochastic method, named STRAIVGE (STRAtegy for Nuclear Generation of Electricity),

which uses pararneaic analysis to provide detailed information on a large set of efficient

solutions. Leclercq (1982) considered a multiobjective problem where the coefficients are

randorn variabbs and some of the constraints contain random variables. The solution

aigorithm consists of a series of alternaiion between cornputaiional and decisional stages.

Marcotte and Soland (1986) provided an interactive branch and bound algorithm for

stochastic multicritena optimization. Urli and Nadeau (1990) formulated a general

rnultiobjective linear prograx-mhg model for the situation when decision-makers

possessed only incomplete information about the stochastic parameters. The algorithm

contained a number of mudes for the transformation of stochastic objectives and

constraints in order to obtain a detemiinistic equivalent multiobjective hear

programming formulation which can be solved by an interactive method.

3.2. REGIONAL WATER QUALITY MANAGEMENT PLANNING

THROUGH APPLICATION OF MATHEMATICAL PROGRAMMING

The pioneer attempt to apply mathematical programmhg techniques to regional

water quality problems was done by Deininger (1965). In that work, a linear

programming (LP) model was constnicted using various approximations of differential

equations of DO (dissolved oxygen) river profile. Locks et al. (1967) presented two LP

least-cost models to determine the desired level of wastewater treatment to meer the given

DO criteria. The two appmacbes differed from each other in fomuiating constraints.

Nonlinear progmnmhg (NLP) models to tackle similar DO tasks were used among

others by Hwang et al. (1 973) and Bayer (1 974). Herbay et al. (1 983) applied the MINOS

NLP package under the condition that the flow and operation of mannent plants are

seasonally variable. Rossman (1989) presented a method to design seasonal discharge

problem that limit the risk of standard violations in any year. Dynamic pmgramming

(DP) was applied first for a hypothetical river water quality management problem by

Dysart (1969). Futagami (1970) applied a least-cost DP model under BOD constraints for

optimal sewage system planning for the Yodo River basin in Japan. One of the classical

and best docuniented least-cost DP applications was made by Newsome (1972) for the

Trent River in the UK. A similar application was p~sented for the Neckar River in

Gerrnany by Hahn and Cernbrowiîz (1 981).

A stochastic LP approach was applied by Lohani and Saleemi (1982) to the Hsintien

River in Taiwan. The stochastic entities included parameters of the DO model,

streamflow, waste flow and effluent BOD concentration. Bum and Lence (1992)

proposeci a refreshing LP approach for a DO problem to hclude uncertainty by

considering multiple design scenarios. A stochastic programrning (SP) least-cost

approach to determine wastewater matment efficiencies was presented by EUis (1987). A

stochastic DP least-cost mode1 was developed by Cardwell and Ellis (1993) and applied

to the Schuykill River in Pennsylvania. Somlyody (1986) developed an eu~ophication

management model for Lake Balaton (Hungary). The rnethod incorporated a stochastic

and hear load response relation obtained frm a dynamic phosphorus mode1 via Monte

Carlo simulations.

The applicability of fuzzy set and possibility theories for the representation of

imprecise information in water quality management problems was investigated by Julien

(1994). Imprecise parameters in water quality decision-making can be represented by

possibility distributions defining maximum achievable probabilities. The corresponding

possibilistic programming problem is viewed as an alternative to the stochastic one where

the parameten are modeled as fuzzy variables instead of random variables. The

possibilistic problem can be solved through a succession of classical linear programfning

rnoâels. The resulting possibility distributions of the objective value provide a

possib'itic assessrnent of the risk based on possibility levels.

There have been a few applications of multiobjective programming in water quality

management ~por ted in fiteram. Monarchi et al. (1973) applied a sequential

rnultiobjective prograrnming solving technique (SEMOPS) to a hypothetical case. Neely

et al. (1975) introduced goal prograrnming to a problem of selecting a projet ~ielated to

public water supply where they considered both economic and environmental objectives

represented by ten goals. Haimes (1977) appiied the Surrogate Worth Tradeoff (SWT)

~flethod to the Mawee River Basin in the US to plan the use of water and related land

resources. Sakawa et al, (1977, 1978, 1979, 1980) developed an interactive nonlinear

dtiobjective optirnization approach and applied it to severai river water quality

planning problems in Japan. Bishop et al. (1 977) and Lohani and Adulbhan (1979) also

reporteci their applications of goal programming to water quality management problerns.

Steuer and Wood (1986) used a river basin water quaiity planning problem to

demonstrate the implementability of an augrnented weighted Tchebycheff procedure for

solving multiobjective mix 0-1 integer prograrnming problems. Lai et al. (1994)

illustrated their TOPSIS (Technique for Order preference by Similarity to Ideal Solution)

with the case study for the Bow River Valley water quality management project.

33. SUMMARY

It has k e n realized in the past several decades that classical mathematical

prograrnming techniques are insuffiCient in reflecting many real-world situations,

particularly in long-terni planning problerns. The nature of practical problems necessitates

the consideration of bot. multiple objectives and uncertainties in decision-making

analysis. The development and application of multiobjective mathematical prograrnrning

so far cm be quite hitful. At the sarne tirne, researchers attempted to couple the various

kinds of uncertainty into the programrning models. Most of the existing approaches for

multiobjective programming under uncertainty stem h m fuzzy mathematical

programming and stochastic mathematical programming.

Limitations in data availability, information precision, solution algorithrns and

computational requirements may mate considerable difficufty in the practical application

of stochastic and fuzzy MOP approaches. Stochastic approaches require information

sufficiently precise to define different scenarios with associated subjective probabities.

This strict data requirement has been the major obstacle to its practical application. Fuzzy

set and possibility theories were developed based on the contention that uncertainty due

to irnprecision is not adequately modeled by probability theory. But there is still debate

over the need of possibilistic measures for reflecting the uncertainties. Methodological

questions c o n c e d g the definition of possibiiity distributions pose problerns for the

adoption of the fuzzy approach, although possibility theory offers the most meanulgful

interpretation of mernbership degrees for decision-making (Julien, 1 994). As well, most

of the stochastic and fuzzy MOP methods lead to large and complicated intermediate

models in their solution algorithms, which are computationally onerous to solve.

Furthennore, the b z y and stochastic models with their crisp solution generated from

uncertain parameters can not be justified on interp~tation of the results.

As reviewed by the literature survey, only a few previous works on regional water

quality planning targeted either the uncertain or multiobjective nature of the study

systems. Probability theory seem to be the only approach applied to represent

uncertainties existing in water quality management problems. Furthennore, there has been

na repoaed research considering sirnultaneously both uncertain and multiobjective

features of the regional system. This may be mainly due to the complexity of regional

water quality system on one hand and the lack of effective and efficient modeling tools on

the other hand. Nevertheles, this review indicates the necessity to incorporate the

uncertainty and multiobjective features within a general framework Consequently,

attempts to propose and apply effective methodologies for multiobjective optimization

under uncertainty to regional water quality management problems would be a

contribution to environmental systems engineering.

CHAPTER 4. OPTIMIZAITON APPROACH

4-1. INTRODUCTION

Multiobjective pmgramming (MOP) under uncertahty, as evidenced in the

fiterature nwiew, ha gained great interest in the past decade due to the fact thai

detenninistic and single objective optimizaîion methods are far fiom sufficient for

practical problem-solving. A number of luiear programmhg (LP) methods and their

improvements have been proposed to address the rnultiobjective and uncertain features.

Generally, niany researchen attempted to make their methods capable of dealing with

real-world uncertainties by investigating a variety of circumstances associated with

system parameters. As weli, interactive approaches were emphasized since aggregated

functions of multiple objectives cannot be explicitly identified through numerical

analysis.

In the fuzzy/stochastic MOLP, uncertainties are normally presented as rnembership

funciions or probabilistic distributions. In rnany practical situations, however, this type of

information may hardly be hown, with only two bounds of the mlated variations king

specified as intervals. Although Urli and Nadeau (1990) proposed a generd methodology

named "MOSLP with Incomplete Information" aimed to tackle the abve situation,

significant ~ c u l t i e s in its application to practical problerns still exist due to the

complicated solution processes. In fact, most of the solution algorithrns of

fuzzy/stochastic approaches may lead to complicated intemediate subrnodels (e.g.

nonlinear or piecewise-linear submodeb). These factors, associated with the limitations

regarding computational requirement and results interpretation, have limited their

practical application, especially for large-scale problems. Consequently, development of a

more effective and applicable approach for rnultiobjective decision-making under

uncertainty would be desirable.

One of the objectives of thls study is to develop a hybrid inexact-fuzzy

multiobjective linear programming @FMOLP) approach by coupling inexact linear

programming (XP) and fuzzy linear programming (FLP) methods for solving real world

decision-niaking problems. The W was developed as the basic algorithm of inexact

mathematical prograrnming (Huang, 1994) which is effective for optimization under

incomplete unceitainty (e.g. information with known fluctuation intervals but unknown

probabilistic or possibilistic distributions). The method has been successiùily applied to a

variety of management and planning problems (Huang, 1996; Huang et al., 1996; Chang,

1995; Yeh, 1996). Zimmermann (1978) proposed two fuzzy programming approaches by

using agpgate operators, "min" operator and "product" operator, to solve multiple

objective pmblems, The method with the "product" operator results in a nonlinear

subrnodel which is difficult to solve. The min-opexatm is frequently used to measure

compensation between objectives due tu the ease of computation (Li and Lee, 1990;

Luhandjula, 1982). In the IFMOLP, a l l the uncertain system parameters are handled as

inexact intervals by applying the ILP algorithm The fuzzy approach using min-operator

is employed for converthg a multiobjective problem to a single objective one. A two-

phase procedure is used to obtain a nondominateci solution. An interactive approach is

proposed fbr conveniently incorporating indispensable intervention from decision-makers

during the IFMOLP modeling process.

43. INEXACT LINEAR PROGRAMMING

Let x denote a closed and bounded set of real numbers. An inexact number x* is

defined as an interval with hown upper and lower boimds but unknown distribution

information for x:

where x- and x+ are the lower and upper bounds of x*. respectively. When x- = x*, x*

becornes a deterrninistic number.

For x*, we defke ~ip(x9 as follows:

sign(x3 =1, if xt20 ,

-1, i fx *<o .

Tts absolute value 1x1' is definecl as foilows:

lxlf = xiT ifxf 2 0,

Thus we have: ixr = x-, if x* 2 O,

- x', if x* c O;

ixT = x', if 3 z O, and

4.2.2. Solution Algorithm

An inexact linear program can be expressed as follows:

min f * fi=c X , (4.4.a)

f ml where A* E { % ' J ~ , B* E {%*) mxl, E {%*) xi E {R ) , and %' denote a set of

inexact numbers.

An interactive solution algorithm was developed to solve the above problern

through analyzing the detailed mode1 characteristics and the relationships between

parameters and variables and between objective and constraints. According to the

algorithm proposed by Huang et al. (1994), a solution for model (4.4) can be obtained

through a two step method, where a submodel correspondhg to f' for the objective to be

mininiized is fvst formulated/solved, and then the relevant submodel correspondhg to f +

can be formulaîed/solved based on the generated solution for f'.

For n inexact coefficients cjf (j = 1, 2, ... , n) in the objective function of model

(4.4), if kl of them are positive, and k2 are negative, let the former kl coefficients be

positive, i.e. c t 2 O (j = 1,2, ... , kt), and the latter k2 coefficients be negative, i.e. ci' < O

(j = kl+l, k1+2, ... , n), where ki + k2 = n (situations when the two bounds of cjf have

different signs are not considered). Thus, we can deveIop the following ILP solution

algonthm.

For mode1 (4.4), the ILP submodel corresponding to f-, which provides the first step

of the solution process when the objective is to be mininiized, c m be formulated as

foilows (assuming that b? > O):

The ILP submodel corresponding to f+, which provides the second step of the

solution process based on solutions h m submodel(4.5), xGl (j = 1,2, ... , kl) and xj,

(j = kl+l, k2+2, ... , n), can be formulated as foliows (assuming that b: > 0):

min f+ = 2 cj+ xj. + 2 cj+ xi,

When the objective is to be maxirnized, the submodel corresponding to f + would be

f h t fonnulated and solved. Submodels (4.5) and (4.6) are ordinary LP problems with

single objective iùnctiom. Thenfore, solutions f-qtl, xiqt (j = 1,2, ... , kl) and xj+, (j =

ki+l, k1+2 ... , n) can be obtained by solving submodel(4.5), whereas f +,,,,tl, xj*sr (j = 1,

2, ... , kl) and xj'op. (j = k l + l , k1+2, ... , n) cm be obtained h m (4.6). Ths, we cm have

* final solution set with ffvl = [f-,tl, f +qti] and xj + = [xj,, ~ { ~ t l .

4.3. FUZZY MIN-OPERATOR APPROACH TO MULTIOB JECTIVE

PROBLEMS

Behan and Zadeh (1 970) suggested a "symrnetrical model" for decision rnaking in

a fuzzy enviromnent that has served as a point of departure for many authors in h y

decision theory. They consider a situation of decision making under uncertainty, in which

the objective function as well as constraint(s) are fuzzy. The fuzzy objective function is

characterized by its rnembership function and so are the constraints. Since we want to

sat is fy (optimîze) the objective function as weU as the constraînts, a decision in a fuzzy

environment is defineci in analogy to non-fbzzy enviromnents as the selection of activities

which sirnultaneously satisb objective function(s) and constraints. According to the

above definition and assurning that the constraints are "non-interactive", the logical "and"

corresponds to the interseaion. The "decision" in a fuzzy environment can therefore be

viewed as the intersection of fuzzy constraints and fuzzy objective function(s). The

relationship between comtraints and objective fünctions in a fuzzy environment is

therefore fully symmetric, that is, there is no longer difference between the former and the

later.

4.3.2. Fuzzy Agproach with Min-Operator

Based on the "symmetrical model", Zimmermann (1 978) pmposed a fûzzy approach

with min-operator to solve the deterministic multiobjective linear prograrnming problem

as follows:

min fk=CkX, k = l , 2 ,... ,p,

max fi = CIX, 1 =p+l, p72, ... , q,

X ~ O ,

wherex~ {%)'xl, Cke { % } l ~ ~ ~ ~ { % } l ~ ~ i € {%}ln

The membership functions for the objectives are defined as:

p(fÙ = (fp - f u / ( f p - fi'-3, k = l , 2 ,..., p,

p(f1) = ( f, - fP)/(fi(+ - ffi, l=p+l,p+2 ,... ,q,

where

f,<-, = aspiration level for kth minimization objective function,

ft", = Serior limit for kîh minimization objective function,

fy) = aspiration level for [th maximization objective function,

fv = inferïor Iunit for ith maximization objective function.

If the min-operaîor (h) is used, the multiobjective model (4.7) cm be transformed to

a singleabjective model as follows:

where h is defined as:

The aspiration level and inferior lhnit consist of the fuzzy goal of an objective

function. A fuzzy goal means an objective which can be characterized as a fuzzy set in an

appropriaîe space. Specificdy, letting X = {x) be a given set of alternatives, a fuzzy goal - G in X would be identifieci with a given fuzzy set G in X. The detemination of fuzzy

goals (ft<), fp), ff? and fi(-3 for objective fuactims in mode1 (4.9) is an interactive

process for any practical problern. Concepts of "individual optima" and "worst justifiable

solution" are generally used before any modification resulting fiom interactions with

decision-rmike~s. Any further modified fûzzy goals should normally fall within the range

specified by the above two bounds. The "individual optima" are obtained by solving the

problem with each of the objective functions in (4.7.a) and (4.7.b) subject to the

constraints in (4.7.c) and (4.7.d). The "wmst justifiable solution" is the worst value of one

objective funciion computed with each set of optimai solutions to decision variables for

di other objectives obtained in seeking "individual optima*'. A convenient way of

finding the "individual optima" and "worst justifiable solution" is to construct the payoff

table for a multiobjective problem (Benayoun et al., 197 1).

4.4. INEXACT-FUZZY MULTIOBJECTIVE LINEAIR PROGRAMMING

4.4.1. Inexact Multiobjective Prograrnming Mode1

A general MOLP problem with inexact parameters can be formuiated as follows:

min fk* = c**, k= 1'2, ... ,p, (4.1 1 .a)

mut f? = ~ 1 % 1 = p+l, pt2, ... , q, (4.1 1 .b)

rt . A?X*S~:, i = l9 2, ... , m., (4.1 1 .c)

where X' E {s*)~, ~ k * E {%*}'*, C: E {%*)lx, A: E (w*} and 9tf denotes a set of

inexact numbers.

When all parameters in model (4.11) are hown as intelvals without distribution

information, this is an inexact MOLP (IMOLP) problem. When any of the parameters is

assigned with mernbership funaion, the model becomes a hybrid inexact-fuzzy MOLP

(IFMOLP) problem In this study, the fuzzy min-operator approach and the ILP algorithm

are jointly used for converting an uncertain multiobjective problem into a deterministic

single-objective formulation. Thus, linear rnembership functions are assigned to fuzzy

goals of system objectives, while coefficients in objective functiom and constraints' left-

hand side, and right-hand side constraint values are ail handled as inexact intemals.

4.4.2. Fuzzy Transformation

A min-operator lif as an inexact nurnber is introduced to ihe model (4.1 1) which

would then be transforrned to:

max A*,

s.t. f;(X?sf,(+>-ll'(f,'*'-f,<-?,k=1,2 ..., p.

fi* or", 2 fi'-' + ??(fi('+' - f/-)), 1 = p+l, p+2, ... , q,

A~T S b?, i = 1,2 ,... , m,

x* 2 O,

os A*!s1,

where

fL-) = aspiration level for kth nnmaiization objective function,

f p ) = inferior M t for kîh minimization objeciive function,

fi'+' = aspidon level for lth maximization objective function,

f,(-, = infenor iimit for ith maximization objective function,

and h is defined as:

The initial fuzzy goals prior to interaction with DM can be detennined in a manner

similar to the detenninistic model. However, the process would be more complicated

since a l l the parameters in mode1 (4.12) present as inexact nurnbers. It is necessary to

detail the procedure of cornputing each "individual optima" and "worst justifiable

solution" for an IFMOLP pmblem.

[Step 11 Solve q single-objective subrnodels (Le. p maxirnizaticn and q-p

minimization problems). Eacb of them has its objective function being k m (4.1 l.a) or

(4.1 1 .b), subject to constraints (4.1 1 .c) and (4.1 1 .d).

[Step 21 Obtaining the solution for each of the above submodels as foilows:

x*) = {xi*), XÎ*), . .. , x,*)}, Q k, for maxUlluation objectives, and

fio = (XII(< xPo, ... , xtqr)}, V 1, for minimization objectives.

f,' m4"1 = (fc (xf<'?, fz pl), O*. f: (x*)), fq @@+')), S.. 9 f t (x'@)},

where xiQ> c xN3, and xg4 c xNW). '][1im, q inexact function values are obtained for

each objective.

[Step 41 Fiially, "individual optima" and "worst justifiable solution" for each

objective cm be obtained as follows:

(i) For each of the p rninimized objectives,

aspiration level (fi-)) = min {f;(xf("3 1 w = 1.2, ... , p. p+l , ... , q} , k = 1,2, ... , p;

inferior linrit (fn = max (fi(xqW9 1 w = 1,2, ... , p. p+1, ... , q), k = l ,2, ... . p;

(ii) For each of the q-p maWnized objectives,

aspiraiion level (fi'+) = max {f;(xqw3 1 w = l,2, ... , p, pl, ... , q), 1 = pl, p+2, ... , q.

inferior linrit (ff*)) = min 1 w = 1,2, ... , p. p+1, ... , q} , 1 = p+1, p-t-2, - ... , q.

Each individual problem can be solved by the inexact linear programming method

with its solution presented as inexact nunibers. Table 4.1 depicts a Srpical payoff table for

the IFMOLP, where the "individual optima" and "worst justifiable solution" for each

objective are obtained in the 1s t c o l m .

4.4.3. UP Transformation

Due to the rnultiobjective feature of the problem, interactive relationships between

mode1 parameters and decision vaxiables might become much more complicated

compared with single-objective problem. This would bring about difficulties in

transforming mode1 (4.12) to detenninistic forms. To tum this around, several techniques

are proposed to ensure applicability and reliabiity of the proposed method.

Table 4.1. Payoff table for IFMOLP problem

Original objective functions:

Individual optima: Pm

Individual optima solutions:

xIfw

x:w

Pay-off solutions: min fIî(x)

..O

min ft(X)

.m.

min 1 3 )

... rnax fr *(X)

a..

min f m

... ... min fl* min f< min ft ... ... max f,,' max 4' min fs

f ( ~ ) ... f:(Xl) ... fii(&) [min*.max]

... ... .. . ... ... [min*, max]

f,'O(,,) ... f:(Xl) ... fi((&) [min*. max]

S.. ..a a.. ... ... [min*, max]

x ... f;(x, > ... f;(X,J [min*. max 1

... f$&) ... f ) [min, mm*]

... ... ... ... [min, rnax*] ... fl*(X,,) ... fi*(&)* ... fi*(&) [min, max*]

I.. *.* ... ... .. [min, mm*]

f ) ... f:(X,) ... ft&)* [min, max*]

* mpresents optimal solutions

(a) Separation of fuzzy operator

Given a specific bound of li' in mode1 (4.12). it may not function consistently for ail

objective functions. For example, h* corresponds to both ft(x3 in (4.12.b) and f l ( ~ 3 in

(4.12.c), while fi(x3 and f:(X3 correspond to different consuaint structures (Huang,

1996). An approach to mitigate this problem is to introduce two separated operators hif

and k2*, where kt is for (4.lZ.b) while for (4.12.c). Thus, we have:

max hi*+hzf,

s.t. fZ(x3 S f p - hlf(fp) - fp) , k = l , 2 ,..., p,

fm 2 fi(-) + k2*(ff,) - ff-3, I=p+l,2 ,... ,q,

A ~ X * s b:, i = 1,2 ,... ,m,

xf r O,

where kt and are defined respectively as:

hl* = min cr(fk9, k = l , 2 ,..., p, (4.15.a)

and, &* = min p(fi7, f=p+l, 2, ... ,q. (4.15.b)

When ai i fk+(x? and f i ( ~ f ) [or fL(X3 and f:(X3] correspond to a consistent

bound for hi, only one operator is needed This will happen only when all objective

functions are to be either maximized or rninirnized and al1 coefficients for each decision

variable in al1 objective functions have the sanie sign (positive or negative).

(b) Decomposition of objective funcaons

For a single objective ILP problem, the distribution of bound values (upper or lower

bound) for the constraints' left-hand side coefficients corresponds to the signs of

coefficients in the system objective. This algorithm is applicable to multiobjective

problerns only when all objective functions have the same sign dishibution for their

coefficients, which may seldorn occur in practice. Consequently, a sign decomposition

method (SID) is proposed for solving the above problem For an objective function (max

or min) with both positive and negative coefficients, it can be ûamfonned to two

decomposed sub-objectives, with one of them k i n g maximized and the other minimized.

Thus, all coefficients in the decomposed sub-objective functions become positive,

enabling application of the ILP algorithm. For t coefficients in objective function (4.11 .a),

assume that fk of them be positive, and the remaining be negative. Let the former tk

coefficients be positive, i.e. c r i 2 O for s = 1,2, ... ,k, and the latter t - ti, coefficients be

negative, i.e. c z c O for s = ti, + 1,4; + 2 ... , t Thus, (4.1 1.a) cm be specined as folIows:

Objective function (4.16) can be decomposed into two sets of sub-objectives:

and

Thus, we would obtain 2p sub-objectives based on (4.11.a) if a l l minimization

objectives need to be decomposed. Obviously, ali coefficients for boih (4.17.3 and

(417.b) are positive.

Similarly, objective funcrion (4.1 l.b) cm also be decomposed into two other sets of .

sub-objectives. Thus, mode1 (4.11) can be transforrned to:

max f,: = CA:, 1 = p+l, p+2, ... , q, (4.18.c) sa1

The objectives (4.18.a) to (4.18.d) can be simplified to:

min frk= c*, h'=1,2 ,... ,q, (4.1 9.a)

max f . ? = ~ y . t = 4 4 , q+2, ... , 2q, (4.1 9.b)

where

{fkl'l* ~fn') E {fk'),

{fiz'}. {fil*} E {f?),

{ c d } {c~*J* S = 1,2, ... , fkr

(*hf) tS {cki)7 s = k + 1,tk+2, ... ,t,

{cl:} E {CA, s = l * 2 ,... ,tl,

{-cl:) E (CF), s=t1+ 1, tl+2 *... , t.

Genemlly, the above model contains îq objectives with ail the5 coefficients being

positive. The number of decomposed sub-objectives wiU become less than 2q when all

coefficients for any individual objective function in (4.11 .a) or (4.1 1 .b) have the same

' sign. Thus, the interative relationships among model parametes and variables can then

be defined.

(c) Fuzzy goals for decomposed sub-objectives

Fuzzy goals for the decomposed sub-objdves in model (4.18) cm be specified by

using decision variable values at the points of "individual optima" and "worst justifiable

solution" as shown in Table 4.1. This meîhod can help ensure that solutions for model

(4.1 8) conespond to the original systern objectives defined in model (4.1 1).

For example, assume that the k-th minimization objective function fk* in model

(4.12) hm both positive and negative signs for its coefficients, and that its "individual

optima" and "wom justifiable solution" correspond to & and &, respectively. The f:

cm îhen be decomposed into two sub-objectives: min f$ and max f ~ * (both with

positive coefficients), Each sub-objective function can have two values comsponding to

Xk and XI. These two values will then serve as ''aspiration level" and 'inferior limit*' of

fuzzy goals for QI* and fizf in the final IFMOLP submodels (Figure 4.1).

4.4.4. IFMOLP Submodels

With the above transformation processes, two submodels for solving the IFMOLP

problem defined in mode1 (4.11) can be obtained as foliows:

and

Submodel (4.21) can also be first solved in the solution process. The specific

sequence can be deternilned by an integrated analysis and a comparison of relative

pnonties for different system objectives. With the above two submodels, solutions for ai i

decision variables (X&J can be obtained. Solutions for the objective function values (fk*

and f13 cm be obtained by using mode1 (4.1 1) and the generated x5qt values.

4.4.5. Pareto Optimum

The fuzzy approach with min-operator is used to aggregate multiple objective

functions in the IFMOLP algorithm. Yager (1978) indicated that the biggest disadvantage

of using the operator is îhat "It does not guarantee a nondominauxi solution and it is

completely non-cornpensatory. The i.esults obtallied by the 'min' operator represents the

worst situation and cannot be compensated by other mernbers which may be very good."

This problem can be solved by using an "arithrnetical average" aggregate operator instead

of "min" operator. An individual operator is applied to each objective function while

rnaximizhg the arithmetic suni of a i i the operators as a transformeci objective fwiction.

Obviously, interactions among the objectives/constraints would be affected when

pursuhg the nondominated solution with separated operators. Low performance

objectives may be given very low h values compared to high performance ones. Some

constraints may be over-satisfied while some poorIy satisfied. One potential hprovement

upon the above would be to use a two-phase approach (Lee and Li, 1993). A unique

operator will be used in the first phase in which a solution for h is obtained. In the second

phase, independent operators are used to solve the rnodel again with more constraints on

each h @y using the h value obtained in the first phase). Guu and Wu (1997) proved thai

an efficient solution can be found through this approach. Thus, a nondominated solution

would be ultimately obtained while the compromise among the objectives can be

guaranteed due to the restriction by unique h.

For applying the two-phase approach to an IPMOLP problem, submodels (4.20) and

(4.21) should be solved as the first phase. Two submodels for the second phase are then

as follows:

and

2 ch' X; 2 fr- + &-(fii - fi;), e l

The two-phase IFMOLP approach is recommended for application since iîs

gemrated so~uîion c m be both compensatory and efficient with limited hcrease in

cornputational requirement.

4.4.6. Solution Sequence

Based on the inexact mathematical prograrnrning theory, the submodel

conesponding to the preferred bound of the system objective would be first solved for a

single objective problem. in ILP, the submodel correspondhg to the upper bound of the

objective function should be first solved when the objective is to be maximized and vice

versa. For the IFMOLP submodels, however, hi and b" (or hi+ and &) exist

simultaneously in each of the two submodels [i.e. submodels (4.20) and (4.21)] while the

upper bound of an operator corresponds to the prefemd bound(s) of the original objective

function(s) and the lower bound of the operator to the anti-preferred bound(s). Thus, the

sequence for solving them would be dependent on relative priorities for the four sets of

the decomposed sub-objectives. Obviously, submodel(4.20) should be solved first if ali

decomposed sub-objectives are to be maximized, while mode1 (4.21) would be solved

fht if they are to be mhimized. When both "min" and "max" exist for the sub-

objectives, the safest approach is to have both submodels be first solved altemaiely. The

final result can then be obtained by cornparison of the two solutions. Another approach to

reduce computational requirernent is to examine which objective is dominant in the

problem if the minirnized objectives are more significant, submodel (4.21) would be

solved h t . Interaction with decision-makers will be helpfiil for M e r justification of

the significance.

4.4.7. Interactive Approach

The IFMOLP would be an interactive approach for solving real-world

multiobjective problems. Solution fiom each iterative computation shodd be presented to

decision-&rs for their feedback The following aspects should be emphasized by the

decision-fnakers when evaluating the resuIts: (i) the satisfiability of the system objectives

83

and made-offs between them; (ii) the satisfiability of the mode1 consmaints related to

possible system failure; (iii) the uncertain level of the solutions (highly uncertain

solutions may be of limited use for decisionmaking).

Based on decision-makers' degree of satisfaction with the results, modification of

the IFMOLP can be undertaken through M e r interaction with the decision-makers and

the related stakeholders. Parameters for modification may include: (i) fuzzy goals of the

objective fuaciions; (ii) inexact vahes of the consîraints' right-hand sides. If solution for

an objective function is below expectation, the "inferior limit" for its fuzzy goal can be

increased. By analyzing intemlationships among the objectives/constraints and the

associated risks, the decision-makers may also relax/tighten the constraints or add new

ones. These operations may be helpfiil for finally obtaining desirable results. Figure 4.2

sumrnarizes a fiamework for the interactive lFMOLP approach.

During the interactive process, some other activities can also be undertaken for

further improvement. For example, the decomposed sub-objective functions could be re-

composed after submodels (4.20) and (4.21) are solved, The results would be useful for

more indepth evaluation in combination with projected conditions. Another important

activity in the interactive anaiysis would be to assess the consequences muited fiom

using diffemt operators (x* values) for minimization and mvllmization objective

hctions. For minimized and maximized objective functions. the difference between hi'

and b* would indicate different "satisfaction levels" of their fUzzy goals. If the obtained

compromise between the two sets of objectives is not satisfactory, it can be adjusted

Formulation of initial IMOLP mode1

I + Construction of payoff table

Individual optimal solutions and fùzzy goals

Decomposition of objective functions. * 4

Fuzzy goals of decomposed objective functions

Formulation of the IFMOLP submodels

Modification of fuzzy goals, inexact constraints, andlor other parameters

Interaction with decision-makers s Solutions of IFMOLP submodels through

the two-phase approach

Satisfactory? v 4

t)

Results interpretation

I

Figure 4.2. Framework for the interactive lFMOLP approach

either by modifying their f u z y goals or adding restrictions on A..' values before M e r

computation.

4.5. SUMMARY

A hybrid inexact-fuzzy approach was proposed for solvhg rnultiobjective linear

prograrnming problems under uncertainty. The method is a signifiant development based

on the existing single objective inexact programrning methods. It also irnproves upon the

previous multiobjective progtamming methods with advantages in data availability,

solution algorithm and result interpretation. Multiobjective and uncertain features of a

complicated study system are tackled jointly within an integrated optimization

framework. The rnethoâ inherits advantages of the inexact programming methods and

altows system uncertainties and decision-makers' aspirations to be effectively

communicated into programming process. A two-phase solution process for Pareto

optimum is recommencied for irnpmved pfactical effectiveness and applicability. The

inexact solutions can provide decision-makers with a flexible decision space. The

interactive approaches can assure that the desired compromise wiil ultimately be found,

while the required intemention for decision-malcers is straightforward and expiicit. Also,

the approach has a relatively low computational requirement due to the simplicity of its

detenninïstic submodels.

CHAPTER 5.

IFMOLP MODEL FOR THE LAKE ERHAI WATERSHED

5.1. MODEL IDENTIFICATION

in the application of optimization approach to the Lake Erhai Watershed ma, the

whole tirne horizon and the interactions between different systern components should be

considered as an inîegrated system. The planning for the study system was broken up into

two temporal stages (1997 to 2000 and 2001 to 2010). Spatially, the entire watershed is

divided into seven subareas based on the consideration of the administrative convenience

and the detailed system conditions in different zones. The temporal and spatial

considerations would serve as the bases for the model construction.

The decision variables represent various activities in diffemt spatial locations over

the two planning periods, as weli as dynamic characteristics of activities

(developrnent/expansion decisions) correspondhg to variations of environmental,

economic a d o r resources conditions. The objective is to achieve the desiiced planning

for different system activities with the consideration of environmentai/economic

tradeoffs. The constraints include aii relationships between decision variables and a

variety of system conditions. These were ail described into inexact mathematical

expressions. Thus, the M O L P model for the study problem can be stnictured as

follows:

maximize (or mininiize):

economic objective,

forest cover objective,

soi1 l o s objective,

water quality objectives:

- nitrogen loss objective,

- phosphorous loss objective,

- COD discharge objective,

subject to:

land avaiiability constraints,

agricultural production constraints,

forest-related activity constraints,

industrial activity constrâints,

tourism-related activity constraints,

net-cage fish culture constraints,

limefbrick production constraints,

water dernand/supply constraints,

soi1 loss constraints,

water quality constraints,

technical constraints.

Decision variables for the above mode1 include activities in the two penods and

seven subareas as follows:

Primary industry:

- paddy farm ara,

- dry paddy farrn area,

- vegetable farrn area.

Secondary industry:

- output value of textile industry,

- output value of chernical fiber industry,

- output value of cigarette industry,

- output value of cernent industry,

- output value of pulplpaper industry,

- output value of leather indusay.

Tertiary industry and others:

- tourist flow,

- forest coverage,

- area for net-cage fish culture,

- brick production,

- lime production.

5.2. MODEL FORMULATION

The detailed formulation of the IFMOLP mode1 for water quality planning in the

Lake Erhai watershed is presented as follows.

(a) Objective Functions

(1) Economic objective:

(net benefit fkom secondary industry)

(net benefit fkom net-cage culture)

(net benefit fiom tourism)

- i: i: O N Y ~ ( F C ~ (maintenance cost for forest)

(cost for forest coverage expansion)

+ ( N Y ~ ( B B ~ BR@* (net benefit from brick production)

+ (NYd(I&? LM&*. (net benefit fiom lime production)

(2) Forest cover objective:

(sum of total forest cover)

(3) Soit loss conirol objective:

3 7 2

niin f3 = Ç C ( N Y ~ ( ~ ) ( A s ~ ~ ~ A G ~ ~ * (soil ~OSS from agicultural land)

(soil loss fiom forest land)

(soil loss fiom brick production)

+ ~ k ) ( u i r ) ~ ~ ~ k * - (soi1 loss fiorn lime production) j=l k=l

(4) Nitrogen loss control objective:

(N loss via agricultural ninoff)

(NY~W W k * (FI loss from net-cage fish culture)

(5) Phosphorous loss control objective:

(P loss from net-cage fish culture)

(6) COD discharge control objective:

7 7 2

min f6 = (NY~@C~L)IN~~* (COD discharge from sewndary industry) i=l j=l k=l

(b) Constraints

(1) Soi1 loss from agricultural activities:

(2) Nitrogen loss fÎom agricultural activities:

(3) Phosphorous loss h m agrïcultural activities:

(4) Dissolved nitrogen loss via agricultural runoff:

(5) Dissolved phosphorous loss via agricultural moff:

(6) COD Discharge fiom industriai activities:

(7) Poliutants from net-cage fish culture:

k= 1.2; (total waste discharge)

k= l,2; (total N discharge)

(8) Land for tourist activities:

(9) Soil loss from brick production:

k = l ,2. (total P discharge)

(10) Soii loss from lime production:

(1 1) Total soi1 loss:

(12) Totd dissolved nitmgen loss:

(1 3) Total dissolved phosphorous 105s:

(14) Total COD discharge:

(16) Land use for agriculture:

(17) Land use for agriculture and forest:

(1 8) Forest coverage expansion:

(19) Constraints for secondary industry:

Control for net-cage fish culture:

(21) Control for brick production:

(22) Control for lime production:

(23) Technical constraints :

AG$ 2 O, i= l ,2 ,3 ; j = 1 , 2 ,..., 7; k = l,2;

mi$* 2 O, i=1 ,2 ,..., 7; j = 1 , 2 ,..., 7; k = 1,2;

f i 20 , j = 1,2, ... ,7; k = l,2;

'IRjk' 2 O, j =1,2-1,2-2,3, ..., 7; k=l ,2 ;

PRJ: 20, j = 1,2, ... ,7; k=l ,S;

BR$* 2 O, j =1,2, ... $7; k=l ,2 ;

LMrf 2 0 , j=1,2, ... ,7; k= l,2,

where:

AB^#* = net benefit fiom agricultural ~ t i v i t y i in sub-area j during period k

(y 1 0,0O0/km2/ y);

AG$ = land area for agricultural activity i in sub-arwi j during period k (km2);

AGCi = lower lirnit of land area for agricultwal activity i (km2);

AN = nitrogen content of soil (%);

AP = phosphorus content of soi1 (%);

AS~~I' = soi1 loss from agricultural i in sub-area j during pend k (r/km2 CS) [l year = 2

CS (cropping season)];

B B L ~ = net benefit from brick production during period k (Y 10,000/10,000 pcs);

BR$ = brick production in sub-area j during pend k (10,000 pcs/yr);

BRCk = lower limît of brick production d h g period k (10,000 pcs/yr);

B S ~ = soil loss fmm brick production in sub-area j (t/i0,000 pcs);

CAF~* = maximum allowable land area for agriculture and forest in sub-area j during

period k (&);

C A G ~ ~ = maximum aUowable land area for agriculture in sub-area j during period k

(km2);

cmjk* = maximum aliowable ~trogen loss from agricuitural aaivities in sub-area j

during period k (kg&);

CAP; = maximum allowable phosphorous loss from agriculhd activities in sub-area j

d u ~ g period k (kg/yr);

CAS; = maximum allowable soil loss from agricultural activities in sub-ma j duMg

period k (t/yr);

CBR = maximum allowable brick production level during pend 1 (10,000 pcslyr);

CBS** = maximum ailowable soii loss h m brick production in sub-ma j during period

k (Vyr);

CBT: = maximum allowable total soi1 loss from brick production during period k (t/yr);

cm%* = maximum allowable total COD discharge in sub-ma j during period k (kg,@);

CIC**= maximum allowable COD discharge from industrial activities in sub-ma j

d u ~ g period k (kg&);

ai = maximum allowable production level for industry i (Y10,O);

CLM = maximum allowable lime production level during period 1 (tfyr);

= maximum allowable soil loss from lime production in sub-a.a j during pend k

Wyr);

CLT~' = maximum allowable total soi1 loss fkom fime production during period k (m);

(2%; = maximum allowable nitrogen loss in sub-area j during period k (kg&);

cmk*= maximum allowable niîmgen loss from netcage fish c u l t u ~ during period k

(kglyr);

C N P ~ = maximum allowable phosphoms loss from net-cage culture d d g period

k (kg/yr);

CNRikf = maximum allowable dissolved nitrogen loss k m agricultural iwioff in sub-

area j during period k (kg/yr);

CNT = maximum allowable area for net-cage nSh culture during period 1 (m2);

C N W ~ = maximum allowable amount of waste discharge from net-cage culture during

period k (kg@);

CPG = maximum allowable phosphorous loss in sub-area j during period k (kglyr);

CPR**= maximum aliowable dissolved phosphorous loss fiom agriculturai runoff in

sub-ma j during pend k (kg@);

CS^* = maximum aüowable soi1 loss from sub-area j durhg peiod k (t/yr);

CILfk* = maximum allowable land area for tourist activity in sub-area j' durhg period k

ml>;

CW&* = water supply during period k (1,000 m3);

FC~* = maintenance cost for forest during period k (Y 1 0,000/km2 yr);

102

FE' = expansion cost for forest coverage (~10,000/km~);

= forest coverage in sub-area j during penod k (km2);

FS* = soil loss from forest land (tons/km2 yr);

i = syrnbol for the primary and secondary industries (for primary industry: i = 1 for

paddy farm, 2 for dry farm and 3 for vegetable farm; for secondary indusiry: i = 1

for textile, 2 for chernical fiber, 3 for papa mill, 4 for food processing, 5 for

cernent, 6 for leather, and 7 for tobacco industries);

1 = COD discharge from industry i during period k (kg/Y 10,000);

INij: = output value of industry i in sub-area j during period k (~10,000&);

J = symbol for subareas related tourist activities, j' = 1,2-1,2-2,3,4;

k = symbol for periods, k = 1,2;

LB? = net benefit from lime production during period k (XlO,Oûû/t);

LM,f = level of lime production in sub-area j dining period k (tlyr);

W C k = lower limit of lime production level during period k (t/yr);

= soil loss from lime production in sub-area j (t/t);

103

NB; = net bene& h m net-cage fish culture d u ~ g penod k (~10,000/m~/~r);

= nitrogen discharge h m net-cage fish culture (kg/m2/yr);

= phosphorous discharge from net-cage fish culture (kg/m2/yr);

= net-cage c u l ~ r e area in sub-area j d u ~ g period k (m2);

= lower limit of area for net-cage culture duMg period k (m3);

= waste discharge h m net-cage culture (kg/m2&r);

= number of years for period k (yr), where NY = 4, and a = 10;

= runoff from agricultural land in sub-area j (cm);

= dissolved nitrogen content of agriculturai runoff (mg/m3);

= dissolved phosphorous content of agriculturai runoff (mg/m?;

= net benefit h m tourist industq during period k (Y10,000/10,~ person-day);

= COD discharge f%om tourkt activities (kg/10,000 personday);

= land area for tourist activities in sub-ma j' (h2/10,000 person-day);

= nitrogen discharge Erom tourist activities (kg/10,000 person-day);

= phosphorous discharge from tourist ativities (kg/10,000 person-day);

104

Tl$%* = tourist flow in sub-area j' during period k (10,000 person-day/y);

W A ~ = water demand for agricultural activity i (1,000 m3/km2);

WB* = water demand for brick production (1,000 m3/10,000 pcs);

WIk* = water demand for indusaial activity i during period k (1.000 m3fi 10,ûûû);

WT~* = water demand for tourist activities during period k (1,000 m3/10,000 person-

day).

CHAPTER 6. MODEL INPUTS AND OUTPUTS

6.1. INPUT DATA

6.1.1. Data Acquisition

Data investigation, verification and analysis require substantial effort for the

success of such a large-scale study. Generally, the data required for the IFMOLP model

cm be classified into rhm groups: economic parameters, physical parameters and control

parameters. Neither the analysts/decision-makers nor the public interest groups have a

complete set of adequately p-e data Sources of the three groups of data are briefed as

follows :

(a) Econornic parameters

The economic parameters include benefit and cost coefficients used in the model.

The estimated values are mainly h m the predictions based on historicai information

provided by local authorities. Discount rates for the planning horizon are considered

based on the official data from the related govemmental agencies. There exist obvious

uncertainties with the economic parameters due to a nurnber of factors such as data

insufficiency, prediction error and linear assumptions. Ii is relatively easier to estirnate an

interval for the variation of an uncertain parameter than to specify its probability or

possibility distribution. Thus, intemal numbers with two extreme values could be used

for reflecting uncertainties associated with a number of modeling pararneters.

(b) Physical parameters

The required parameters representing the physical characteristics of the Lake m a i

Watershed mainly relate to environmental impact and resource consumption. These

parameters are mainly from the subsysrems of hydrology, water quality, soi1 erosion and

nutrient transport which serve as important bases for the environmental planning. A

number of technicd documents from local authorities are also used. The available

information does not allow the determination of the physicd parameters either precisely

or with a detailed probability or possibility distribution. As a resuit, interval values are

used for rnany physical parameters as inputs for the IFMOLP model.

(c) Control pararneters

The control parameters include two groups: îhe right hand side constraints of

resources availability and the fuzzy goals for the multiple objectives. Their determination

requires interactions with decision-maken and substantial efforts to convert human

judgement to numerical presentation.

Constraint values

These pararneters represent rhe expected restrahts considering environmental

impact and resources availability. Standards and regdations related to water quaIity and

other environmental criteria would be the bases for the detemûnation of the constraints.

Due to mdtiobjective feature of the study system, these parameten rnight be adjusted

during the IFMOLP solution process to obtain a satisfactory compromise.

Communication with decision-rnakers is necessary before any constraint values are

adjusted. Considering the imperfect howledge of the study system, a tolerance interval is

used for each constraint.

Fuzzy goals

The fuzzy goals in the IFMOLP model, as described in Chapter 4, will serve as

controlling parameters to balance between multiple objectives. Thus, determination of the

fuzzy goals is critical for effective application of the IFMOLP. Any modificaiion of the

fuzzy goals should be based on a series of interactions witti decision-makers. Also, any

updated outcornes should be presented to the DMs for further evaluation until a

satisfactory compromise is reached.

6.1.2. Input Parameters For A* and @ Matrices

The input parameters for A" and C* matrices in IFMOLP model (4.1 1) include the

foliowing 26 aspects:

(1) net benefits fiom agricultural activities (~10,000/km~/yr),

paddyfarm,

dry fm*

vegetable farm;

(2) net benefit fiom net-cage culture (Y 10,0OO/rn~/~r);

(3) net benefit fiom tourism industry ('M 10,000/10,000 personday);

(4) maintenance cost of forest (~10,000/km2/yr);

(5) expansion cost of forest coverage (Y 10,000/km2);

(6) net benefit from brick production (~10,000/10,000 pcs);

(7) net benefit from lime production (~10,0ûû/t);

(8) soi1 loss fmm agricultural land (t/krn2 CS),

paddy farm,

rn vegetable fm

(9) nitrogen/phosphorus content o f soil (a);

(10) nitmgen in run-off fiow h m agriculturai activities (kg/km2);

(1 1) phosphorous in run-off flow fiom agricultural activities (kg/km2);

(12) soii loss from forest land (t/kd yr);

(1 3) soil loss from brick production (VI 0,000 pcs);

(14) soil loss from lime production (t/t);

(15) COD discharge from industrial activities (kg(v10,OOO);

(1 6) niuogen discharge fiom net-cage fish culture (kg/m2/yr);

(17) phosphorous discharge fiom net-cage fish culture (kglm2/yr);

(18) waste discharge h m net-cage fish culture (kg/m2/yr);

(19) COD discharge from tourist activities (kg/10,000 personday);

(20) land area required for tourist activities (km2/ 10,000 personday);

(21) nitrogen discharge h m tourist activities (kg/10,000 person-day);

(22) phosphorous discharge fiom tourist activities (kgl10,000 personday);

(23) water demand for agricultural activities (1 ,a00 m3/lm2);

(24) water demand for brick production (1,000 rn3/10,000 pcs);

(25) water demand for industrial adVities (1,000 m3/M10,000);

(26) water demand for tourist activities (1,000 m3/ 1 0,000 personday).

The detailed data for the above parameters are provided in Appendix A.

6 i .3. Input Parameters for B* Vemr

nie input parameters for B* vecta in IFMOLP mode1 (4.1 1) include the following

17 aspects:

(1) soi1 loss fiom agicultural land (t/yr);

(2) nitrogen loss k m agricultural land (km);

(3) phosphorous loss from agricultural land (kg/yr);

(4) dissolved nitrogen loss with runoff h m agricultural land (kglyr);

(5) dissolved phosphorous loss with runoff h m agricultural land (kglyr);

(6) COD discharge from industrial activities (t/yr);

(7) waste from net-cage culture ( k m ) ;

(8) land area for tomist activity (km2);

(9) soil loss from brick production (t/yr);

(10) soil loss from lime production (t/yr);

(1 1) total soi1 loss (t/yr);

(12) total dissolved nitrogen discharge (t/yr);

(1 3) total dissolved phosphorous discharge (t/yr);

(14) total COD discharge (t/yr);

(1 5) water demanà (1,000 m3/y.r);

(16) land for agricultural activities (km2);

(17) land for agicultural activities and forest coverage (km2).

The data values finaliy used for generating compromise solutions are provided in

Appendix B.

6.2.MODEL SOLUTIONS

6.2.1. Generation of Decision Alternatives

One of the major attributes of the proposed two-phase IFMOLP approach is its

abifity to generate as many Pareto optimum solutions with their associated tradeoffs as

rnight be needed by the DMs. This cm be achieved by simply adjusting fuzzy go& of the

objectives with limited computational effort. For the study problern under consideration.

generation and presentation of multiple solution scenarios with varied environmental-

economic tradeoffb would be invaluable for finding an optimal or near optimal decision

alternative for practical implementation.

Four scenarios with different environrnental~conornic tradeoffs are generated for

environmental management in the study area.

Scenario 1 is believed to be an aitemative with desired balance between

environmental and econornic objectives.

Scenario 2 corresponds to situations when industrial developrnent is emphasized.

Scenario 3 emphasizes industrial water pollution control at the cost of significantly

reduced economic retum within the watershed system.

Scenario 4 is generated based on Scenario 1, with the consideration of terminating

net-cage fish culture in Lake Erhai.

Scenario 1 is generated first and recognized as an adequate compromise by the

DMs. Based on this, scenarios 2 and 3 are generated and expected to provide the DMs

with a more flexible decision space. Scenario 2 may lead &O increased economic rehm as

well as increased risk of water pollution in the lake. This scenario corresponds to a

relatively optirnistic environmental management strategy. Scenario 3 is a relatively

consewative strategy. More recently, the local environmental management authority

began to consider texmination of net-cage fish due to the increasing eutrophication of the

lake. Thus, Scenario 4 is prepared based on scenario 1 with the net-cage fish culture

sector being eliniinated fiom plannùig consideration. The interpretation of the results in

the following chapters will focus on scenarios 4 since it will most likely be recommended

for practical implernentation. The comparative results of objective function values under

different scenarios rn presented graphically in Figures 6.1 (1) - (6).

The optirnization results are also compared with a scenario under the assumption

that ail the considered activities in each subarea would maintain the existing levels in the

plamhg horizon.

6-2.2. IFMOLP Solutions

The IFMOLP solutions for objective functions and decision variables under ail the

four scenarios are given in tabular form (Appendices C - F), while the graphieal

presentation is also provided for Scenario 4 as the eventually recommended decision

6E+06 -

The top and the bottom of shaded area correspond to the upper and Iower bounds of solution, respectively

Scenario

( O corresponds to existing conditions; 1,2 and 3 for IFMOLP scenarios 1,2 and 3, respectively)

Figure 6.1. Comparative results of IFMOLP - (1) Economic objective

The top and the bottom of shaded area correspond to the upper and lower bounds of solution, respectively

Scenario

( O corresponds to existing conditions; 1,2 and 3 for IFMOLP scen~os 1,2 and 3, respectively)

Figure 6.1. Comparative results of IFMOLP - (2) Soi1 loss protection objective

115

The top and the bottom of shaded area correspond to the upper and Iowa bounds of solution, respectively

Scenario

( O corresponds to existing conditions; 1,2 and 3 for IFMOLP scenados 1.2 and 3, respectively)

Figure 6.1. Comparative results of IFMOLP - (5) Phosphorous loss control objective

alternative (Figures 6.2 (1) - (15)). The planning for each activity in each subarea at each

stage is aiso comparecl with its existing level.

6.2.3. Contribution Structures

In addition to direct solutions frorn the IFMOLP model, contributions to systern

objectives by each activity in the two planning periods under scenario 4 are quantifieci

and presented in cornparison with the present conditions to M e r clarify environmental-

economic chmcteristics of the generated traâeoffs (Figures 6.3 (1) - (5)).

Net- Toufism Lime/ûrick

i -2% Agriculture

Industries

59.796 Existing pattern

Industries 57.1-68.4%

Planning period 1

Industries 67.5-71.4%

Planning period 2

Figure 6.3. Contribution structure - (1) Economic return

Agriwlture

Existing pattern 92*0%

90.&90.7% Planning period 1

Agriculture 90.5-90.9%

Planing period 2

Figure 6.3. Contribution structure - (2) Soi1 loss

Tourism 0.3% Agriculture

1.7%

Net-cage fishery 98.0%

Existing Pattern

83483.9%

Planning period 1

Tourism

Planning period 2

Figure 6.3. Contribution structure - (3 ) Nitrogen loss

99.0% Existing Pattern

Planning period 1

4

Planning period 2

Figure 6.3. Contribution structure - (4) Phosphorus loss

139

Tounsm 2.5%

97.5%

Existing Pattern

97.0-972% Planning period 1

95.6-96.4%

Planning period 2

Figure 6.3. Contribution structure - ( 5 ) COD discharge

140

CHAPTER 7. INTERPRETATION AND DISCUSSION

7.1, RESULTS ANALYSIS

7.1.1. Solutions

The mode1 solutions provide planning pattern for each activity in each subarea at

each planning tem. Various system conditions and the DMs' requirements are

incorporated within the lFMOLP mode1 Solutions for many activities are presented as

intervals, which reflect the impact fiom the input uncertainties.

(a) Agricultural activities

(1) Paddy farm

For subareas 1 to 6, the paddy farmland areas in period 1 should be reduced slightly

from existing levels, while limitai expansion would be expected in period 2. The

reduction in penod 1 can be justified by the consideration of non-point source (NPS)

poilution conîrol. In penod 2, some other sources for NPS poilution are to be limited. The

expansion of paddy farmland rnight then become possible since it is given some extra

environmental capacity. For example, Subarea 5 has a relatively high grain production

level. Cwrently, there exist many lime kilns and brick kilns in that area which occupy

agricultural lands and contribute significantly to NPS poilution in the Lake Erhai.

Consequently, paddy fam development m y be limited in period 1. However, the

agriculture may be expanded in period 2 when the lime kilns and brick kilns are reduced

or restricted in the future.

The solutions for Subarea 7 is somewhat different. This subarea, located in the

upper reach of the lake, contributes the highest proportion of NPS pollutant loading to the

lake through its activities for agricultural production and net-cage fish culture. The

subama dominates the entire watershed in the net-cage fish culture sector, which is to be

eliminated by the local environmental authorities, This would be the main reason that this

subarea is allowed to have a higher expansion potential in period 1. The possible

reduction in period 2 is the result of the general NPS pollution restriction for the entire

watershed.

Generaliy, yield of grain production in the study system is s ac i en t (or more than

enough) for supplying rice product to local residents. Paddy farm's nce product does not

generate high econornic retum (compared with other land use activities, such as vegetable

farms or tourism-related activities). At the same time, it has a higher non-point source

pollution potential. Consequently, its further development wîU be generally Limited fiom

both environmental and economic points of view.

Expansion of dry farm for agricultural production is normaüy of conflict with forest

coverage, since the related land reclamation rnay potentially reduce forest coverage (or

opportunities for f m s t coverage expansion). Dry farm is also responsible for NPS

pollution problems in the lake. Its planning profle for the watershed is similar to that for

the paddy fm, and further expansion would be limited. Same as the paddy farmland,

limited expansion for the dry farm in subarea 7 is also feasible due to the cut of net-cage

fish culture,

(3) Vegetable farm

Demands for vegetables will be increased continuously as tourism industries are

developed and people's living standards are irnproved in the watershed area. Vegetable

products bring higher econornic retums. Therefore, the related policy would be to

significantly expand vegetable farms. However, dernands for vegetables are not infinite.

If the development is over a critical level, low economic efficiency rnay be generated.

GeneraUy, the IFMOP solution indicates that vegetable farms should be expanded

with flexible increments. The detafieci production levels need to be determined following

practical market analysis.

(4) summary

Agriculture is a traditional industry in the watershed. The majority of the population

in the region are farmers. Agricultural activities currently produœ l e s than 1/5 of total

economic return in the watershed area. At the same t h e , they generate significant non-

point source water pollution problems. Since agriculture has b e n developed to a rnatured

level and the related management and engineering measwscan only partly mitigate the

non-point source pollution problem, agricultural activities and the related poilution

problerns may not fluctuate with tirne so significantly as other human activities (e.g.

tourism and industries). In this regard, the major agricultural activities (paddy and dry

farm) would be limited below the existing levels, while allowing expansion to vegetable

farrning, since the latter occupies a smaller portion of the total farmland generates a

higher rate of econornic retum.

(b) Industrial activities

(1) Textile indusûy

Textile industries are located in subarea 2 @ali Town) and subarea 4 (Xiaguan

City). This typ of industry may generate high econornic efficiency due to the convenience

of obtaining cmde materials within the watershed area. However, significant organic

pollution problems exist with the industry. Thus, when wastewater matment facilities are

not available (or not effective enough) for controhg their pollution problems at the

present stage, m e r development would be restricted. in the second period when more

advanced industrial production and poiiution control technologies are avaiiable, potential

expansion/development for them may be considered. The modeling solution is consistent

with the above consideration.

(2) Chernical fiber industry

Chernical fiber industry in the study ma generates a high econoniic retum.

However, it produces very serious pollution pmblems, with the emitted pollutants king

hard to remove. The IFMOLP modeling suggests that this type of industry would be

continuously restricted. Fial temination in the future should be considered.

(3) PulpPaper industry

Two pulp/paper mills exist in subarea 4 (Xiaguan City), including Dali Paper Mill

and Erbin Paper Production Plant. This type of industry generates high economic

efficiencies for the study systern. However, both factones are currently using backward

technologies for their production and pollution control processes which lead to serious

impacts on water quality in Xier River. Therefore, their production would be reduced or

maintaird at the current level if the existing technologies are not improved.

Another alternative for controllhg pollution from the pulp/paper industries is to

move the pulp production part, which has the highest pollution contribution, to the

extemai systems. Thus, only paper production part, which has relatively low pollution

potential and higher economic efficiency, will be kept within the waiershed area. This

option, as shown in the modeling solution, would lead to allowance for long-tenn

expansion for the industry's production level.

(4) Food processing industry

Demands for food, both in temis of quantity and variqty will increase continuously

with the development of the tourism industry and the improvement of people's living

standards in the watershed area. The food processing factones are scattered in aimost the

entire watershed. The IFMOLP solution indicates that ail the existing food processing

productions wouId be expanded, especially for those in urban areas (e-g. Xiquan and

Dali). This industrial sector has high economic efficiencies with its wastewater king

relatively easy to handle by direcdy discharge to municipal sewage systems.

(5) Cernent industry

Cernent rnanufacturing is mainly in subarea 5, while subarea 7 has some as weil. It

brings high economic efficiency at the cost of landscape degradation, which has

detrimental impacts on tourism, land resources, agriculture and forestry. This industry

also leads to increasing soii erosion to the lake. Therefore, its development in the near

future would be dependent on the availability of improved land excavation and cernent

production technologies. The IFMOLP modeling solutions propose to have a flexible

production level for this industry in period 1, and to consider its potential expansion in

pend 2. The future expansion should be concentrated in subarea 5.

(6) Leather industry

The leather industry in the study system generates high economic efficiency.

However, it also produces very serious poliution problems with the emitted wastewater

containhg not only organic poilutants but dso heavy metals which are poisonous and

hard to remove. Ctmently, the leather industry in the study area is quite smaU in scale. It

is thus recommended that this industry be lirriited or eliminated.

(7) Tobacco Industry

The tobacco industry takes a dominant role in the local economy. It brings the

highest econornic retum among al i econornic activities, but has relatively less poiiution

impact on the lake. Thus, M e r developrnent of this industry should be encourageci as

long as effective wastewater treatment faciiities are avaüable.

Genedly, for industrial activities, it is recommended that tobacco i d food

processing industries would be promoted continuously in the planning horizon. The

tobacco industry is a major contributor to regional economy with relatively low pollution

potentiai. The food processing industry is needed for supporthg tourism development

and for satisfjing increasing dernands h m the local residents.

For the other industries, careful consideration of their existence and development

should be undertaken. These include pulp/paper, chernical fiber, Ieather, textile and

cernent industries. Although these industries may also contribute to the local economy,

they are directly mponsible to organiç pollution in Xier River. Among them, pulp,

chernical fiber and leather production will generate a large amount of poiiutants with high

COD concentrations. Therefore, results h m the IFMOLP suggest that production for

these sectors be significantly reduced or termina. An alternative for this is to move

these industries to external systerns that have higher environmental supporting capacity.

For textile, paper and cernent industries, the IFMOLP solutions recommend that

their status would be flexible from the short-terrn management point of view. Since the

study system is now under demanding environmental conditions, a conservative strategy

may be desired. Thus, the scales of these activities would be kept at or below the existing

levels. Any decision for further developrnent should be made with careîül consideration.

At the sarne tirne, development of hi&-tech industries with low or no pollution potentials

would be encouraged.

(c) Other sectors

(1) Net-cage fïsh culture

Zn-lake net-cage fish culture is the major contributor to non-point source nimgen

and phosphoms pollution in Lake Erhai It dso has a low economic efficiency, and thus

cannot be justifieci h m either an environmental or econornic point of view.

Consequently, it is recomniended thaî this type of activity should be tednated at the

present stage. Enforcement of this policy is under consideration by local authorities. An

alternative for this type of activity is to develop fishery ponds out of the lake.

The study watershed has plenty of tourism resources. The tourist industry would be

promoted continuously according to the IFMOLP outputs. This is attributable to its

advantage of low pollution potential and hi@ economic efficiency. However, the related

tourist fiow is not only related to human efforts of improving scenic spots and the service

sector, but also a number of external factors. This nieans that there exists an upper Iimit

for potentîal tourist flow. Spatially, subareas 5 to 7 possess limited tourism resources, and

thus have ïittle potential for tourism development.

(3) Forest coverage

An increase in forest cover will enhance soi1 conservation and may bring better

environmental quality in the lake. However, expansion of forest coverage requires high

capital and maintenance costs with low direct economic retum. The IFMOLP resuks

148

indicate that, in period 1, forest would be slightly expanded for improving Lake Erhai's

water quality to a desired level. In period 2, forest coverage level would he maintained

considerhg the relatively high expansion investment.

Spatially, more expansion of forest coverage may be demanded for the lake's upper

reach (Le. Subarea 7) which is the largest sub-wateished for the study region and

contributes the rnost to non-point source poliution in the lake.

(4) Lime and brick production

Lime and brick production activities scatter throughout the watershed area. These

activities have low econornic efficiencies. At the sarne tirne, they generate a number of

impacts on other environmental and resource sectors. The major source of fuel used for

lime and brick productions is forest since there is a shortage of coal and other energy

resources in the study area. Consequently, forest cover is being reduced resulting in

increased soi1 loss and decreased biodiversity. Unelciln and brickkiln use lirnestone and

some special clays as their mde materïals. Excavation of the meria ls rnay lead to

impacts on landscape and problems of soi1 erosion. During their operating processes, the

limekiln and brickkiln also generate residues. These residues are normally disposed on

the surrounding land. The residue disposal sites wïii then becorne unsuitable for

agriculture.

Therwfre, the IFMOLP solutions suggest that, at the present stage, lime and brick

productions would be maintained under their existing levels. From a long-term planning

point of view, the two activities would be restxicted or eliminated when appropriate

technologies/substitutes are developed or lime/brick acquisition h m extemal systems

becomes possible and econornical.

7.1.2. Contribution Structures

(a) Econornic Objective

The economic benefit within the study scope cornes c m n t l y from agriculture,

industries, net-cage fish culhue, todsrn and lime/brick production. Among them, the

industrial activities contribute the most (59.7%) while the remaining is mostly obtained

fiom agriculture (26.4%) and tourism (1 0.9%). The net-cage fish culture and lime/brick

production only have slight contributions, accounting for 1.7% and 1.2%, respectively.

The planning profile does not have a significant change in p e n d 1 even when net-

cage fish culture is tenninated. However, the proportion conttibuted by industrial

activities will get some increase (highest to -71%) in period 2, whiie that by @culture

will be lower. This can be weiï explained by the pxeceding discussions related to

agricuitural and industrial activities. The agriculture, as suggested by the IFMOLP

solution, would mostly be rnaintained around or under the existing level. On the other

hand, some industrial ativities, such as food processing, tobacco, textile and cernent

might get considerable growth due to the improved economic-environmental efficiencies.

The low efficiencies associateci with net-cage fish culture and ihe/brick productions are

welï reflected in the modehg results. Thus, tennination and/or resaiction of these sectors

are suggested.

(b) Soi1 loss

Agricultural land is the main source of soil loss for the watershed. At present and

throughout the planning horizon, around 90% of soil loss to the lake comes h m

agricultwal farms. Forest land contributes 7.5% of the current total soil loss. This portion

would be siigbtly increasing with the expansion of forest cover dong with time. The

lime/brick production results in about 0.4% of total soil loss, but as a point source it has a

much higher intensity.

(c) Nitrogen and phosphorus losses

Mently, net-cage fish culture is the dominant contributor to nitrogen and phosphoms

poilution problems. Once the policy of terrninating net-cage fish culture is implemented,

the level of nitrogen and phosphorus contamination in the lake wouId be much reduced,

In the two planning periods, the loss of the two pollutants will be mainly îrom agriculture

and tourism with the agriculture generally contributhg more. In period 1, agriculture

would produce - 84% of total nitrogen loss and -59% total phosphoms los. However,

with the expected development of tourism industry in period 2, increased contribution

h m tourism activities will be experienced.

(d) COD discharge

The COD discharge cornes from industriai production and tourism industry. The

former contributes the majority of the pollution, and the latter about 2.5%. With the

implernentation of poliution control policies and the p i a ~ e d development, the tourism

industry will conîribute a higher COD discharge. Even though, the COD pollution

problem is stiil dominated by the indusirial activities. Any consideration for COD

reduction should focus on the related industrial activities.

7.2. COMPARISONS BETWEEN DIFFERENT SCENARIOS

(a) Economic objective

Arnong the four scenarios, scenario 2 corresponds to situations when industrial

development is emphasized, which may lead to increased economic rem. The upper

bound of economic return under this scenario is a bit higher than that for the others, with

its lower bound king much lower. Examination of the detailed planning schemes

indicates that chernical fiber and pulpfpaper industries wiU be promoted under this

scenario. Both of the two industries contribute the most to organic pollution problem in

the watershed area although they b ~ g significant economic benefit. Thus, this scenario

may lead to increased water pollution nsks. Econornicaüy, it also needs more investment

for water pollution abatement. Generally, this scenario corresponds to a relatively

optimistic environmental management strategy.

Scenarios 1 and 4 provide a balance between environmental and economic

objectives, with scenario 4 containhg constraints of restricting net-cage fish culture in the

lake. Their economic retums are not significantly lower than that for scenario 2, while

much higher environmental efficiencies cm be obtained. These scenarios are suitable for

the existing system and its potential developrnent in the future.

Scenario 3 emphasizes industrial water pollution control with the cost of

significantly reduced economic retum within the watershed system. This corresponds to

an extremely conservative strategy. Thus, industries with high econornic efficiencies but

serious pollution problems will be limited or resnicted Ieading to relatively low risk of

organic pollution problems:

(b) Objetives for controlling nitmgen, phosphorus and soil losses

For the study watershed, industrial activities do not significantly contribute to non-

point source nitrogen, phosphorus and soil losses. 'Ihe main contributors are agriculture

and netcage fish culture. For agriculture, non-point source poilutant losses are due to

land erosion of soil and unused nutrients from feaiLizer and manure. For net-cage fish

culture, nitrogen and phosphoms are mainly from nutrients that are thrown into the net-

cages but not consumeci by fish, as well as fish excreta High nitrogen and phosphorus

concentrations can lead to eutrophication of the lake. Moreover, niîmgen, in the form of

nitrates can contaminate water and make it unsafe for drinking.

Similar levels of nitrogen, phosphoms and soil losses were found for most of the

scenarios, except scenario 3 in which industrial development is limited whiie agriculture

could be potentially promoted as a compensation for a balanced economy. Thus,

expanded cropping area for agriculture under this scenario would lead to more nitrogen,

phosphoms and soil losses.

(c) Forest cover objective

The IFMOP solution indicates that the scenarïo 2 corresponds to the lowek forest

coverage, followed by scenarios 1, 3 and 4. This scenario encourages continuous

development of industries. Thus, forest coverage would be afTected by (i) provision of

crude materials for pulp production, (ii) forest loss due to soi1 excavaiion for cernent

industries and stone excavation for construction and craft-producing purposes.

Solutions for scenario 2 also has high fluctuation ranges. Thus, forest coverage may

be IIliLintained or increased through (i) adjusting related industrial structures (e.g. move

stone excavation and pulp production to extemal systems), (ii) irnporting crude materials

(eg. pulp and rnarble stone) fiom extemal systems, or (iii) enhancing management for

industries with serious impacts.

(ci) COD emission control objective

Scenario 2 corresponds to the largest amount of COD generation in the watershed

ma, since a numbez of high COD-ernission industries (e.g. chernical fiber, pulp/paper

and leather) would be pmmoted under this scenario. Consequently, effective pollution

control measures need to be undertaken if this scenario is adopted. The COD generation

under scenario 3 is of the lowest value, since this scenario has the highest resmction on

industrial poliutant ernission.

The fou. scenarios correspond to different objective fbnction values, which

represent decisions regarding environmental/economic tradeoffs. The IFMOLP results

present the obvious conflict between environmental and economic objectives. For the

watershed area, a significant growth of industriai output wiU cause very high increase in

COD discharge. The t e h a î i o n of net-cage fish culture may significantly reduce the

potential of lake eutrophication. The conflict between multiple objectives, as a typical

complex feature of environmental system, is weU reflected in the IFMOLP solution

process. Generally, planning for lower econornic benefits may help to ensure that water

quality standards are met (based on the cost of reduced income frorn economic activities)

but as planning aims toward higher econornic benefits (especialiy for benefits from

industrial activities) the AiabiXity of achieving water quality objectives m a y become

dependent upon how pollution problems are controiîed (i.e. the risk of substandard water

may be potentially inclieased). In other words, planning for lower economic r e m

represents a conservative strategy while that for higher retum represents an optirnistic

strategy. Thus, the inexact IFMOLP solutions allow detailed interpretation of the tradeoff

between environmental puilution risks and economic objectives. This would be usefui for

not only planning future system adVities, but also adjusting(just@ing the existing

activities in the study system

7.3. SUGGESTIONS FOR IMPLEMENTATION

This study offers scientifc basis for fomulating policies and strategies of

environmental management in the lake w atershed. Interp~tation of the environmental

planning results can be used for govemrnental authonties related to the lake water quality

management as a policy-support for initiating new enviromenid regulations or adjusting

existing measures. Detailed schemes for environment-related activities can be designed

based on the modeling solutions. As to implementation of the planning results. some

suggestions are provided as foliows..

(a) Decision making under uncertainty

The design for considered activities could be adjustable since the generated

IFMOLP solutions contain many uncertain elements presented as intenrals. This brings

flexibility for decision-makers to adjust the detailed designs based on projected applicable

conditions with updated information. Generally, stability and safety with satisfied

environmental-economic efficiencies fkom the entire system point of view WU be

paranteeci as long as the implemented schemes do not fluctuate out of the IFMOLP

solution intervals. However, final determination of specific schemes would require

M e r interaction with stakeholders and decision-rnakers.

(b) Real-time planning

For the planning time horizon of 14 years, social, economic, legislative and

resources conditions will vary. Therefore, refletion of this temporal variation

characteristic in the systerns analysis mode1 would be important for generating effective

and realistic environmental planning alternatives. Thus, it is required that the planning

scheme should be updated at any time when any systern condition changes significantly.

This research provides not only the presentation of planning alternatives, but also a user-

friendly cornputer system as a "real time" planning tool to meet the above requirement.

By renewing information for mode1 inputs based on changed conditions, updated

planning schernes for subsequent period c m be obtained conveniently by local users who

are able to run the provided rnodeling software.

CHAPTER 8. CONCLUSIONS

8.1. SUMMARY

A study of water quality management planning for the Lake Ekhai Watershed,

China, is conducted as a sub-project of the UNEF's "Diagnostic Study for Socio-

Econornic and Environmental Problerns in the Lake Erhai Watershed". The proposed

Inexact Fuzzy Muhiobjective Linear Prograrnrning methoci is effective in dealing with

problems of rnultiobjective decision-making under uncertainty. The mode1 has been

applied to the case study in the Lake Erhai Watershed, where a number of environmental,

resources and economic factors are considered. The IFMOLP modeling results provide

bases for the formulation of policies/strategies regarding regional socio-econornic

development and environmental protection. Four scenarios correspondhg to different

envYonmentaleconomic tradeoffs are studied. Among hem, the one considered by

decision-makers to be a compromise between environmentai and economic objectives is

recommended for implementation.

For different activities in the study system? it is well ~cognized that maintainimg an

acceptable standard of water quality in Lake Erhai is of the highest priority. This means

that economic development should not be based on the cost of lake water contamination.

Among the considered activities, tourisrn industry should be promoted for its low

poilution potential and hi@ economic efficiency. Since agriculture has been developed to

a rnatured ievel, and the related management and engineering measures can only partly

mitigate the non-point source pollution problem, it is suggested that most of agricultural

activities should be maintained at existing levels. For industrial activities, tobacco and

food processing industries should be promoted due to their sound compromise between

econornic and environmental objectives. Careful consideration for the existence and

development of the other indusûies should be made regarding their specific pollution

impacts.

The IFMOLP is a significant progress upon inexact mathemaîical prograndng.

The methoci inherits advantages of inexact programrning methods, and aliows system

uncertainties and decision-maken' aspirations to be effectively communicated into the

programrning process. The inexact solutions provide decision-makers with a flexible

decision space, and are useful for further risk analysis. Management alternatives can be

generated by adjusting the decision variable values within their solution intervals

according to projected planning situations. They are flexible in reflecting potential system

condition variations caused by the existence of input uncertainties. This advantage is

favored by decision-makers due to the increased flexibility and applicability for

detennining the final decision schemes.

The IFMOLP also irnpmves upon the previous multiobjective programming

methods with advantages in data availability, solution algonthm, and results

interpretation. Multiobjective, uncemin and interactive features of a variety of system

components are tackled jointly within an integrated optimization framework The

approach also has relatively low computational requirements due to simplicity of its

deterministic submodels. As weil, the proposed interactive two-phase IFMOLP solution

process would guarantee that the non-dominated compromise solution be obtained.

8.2. RECOMMENDATION FOR FUTURE RESEARCH

In this study, the IFMOLP hybridizes the inexact programming and fuzzy approach

to fom an integrated approach to deal with multiobjective bear prograrnming problems

under uncertainty. Even though its advantages have been demonstrated through this real

case study, many research niches exist for furcher extending the methodology. For

instance, a series of inexact-fûzzy multiobjective prograrnming (IFMOP) methods based

on inexact integer prograrnming, dynamic propaniming and quadratic programming can

be potentialiy developed. In addition, there are rnany possibilities of incorporating various

multiobjective programming approaches within the inexact programrning framework to

provide more effective decision supports methodologies.

Inexact mathematical programri.ting methods are currently capable of dealing with

linear and quadratic relationships for decision variables in objectives hct ions and

constraints. In reality, regional water quaLity management systems are very complicated

with intricate relationships and interactions between system components. Thus,

development of inexact nonlhear programmîng methods and relevant solution algorithms

would help to extend applicable ranges of the inexact multiobjective programming

rnerhods and their applications.

Geographical information system (GIS) would provide a convenient tool for

database management, results presentation and pst-optirnirnality analysis. The GIS may

also function as user-interfaces for integrated modeling computation and results

presentation.

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APPENDIX A

INPUT PARAMETERS FOR A* and Cf MATRICES

APPENDIX A -- INPUT PARAMETERS FOR A* and Cf MATRICES

(1) Net benefits from agridturai activities (~10,000/km~/yr)

a) Paddy fam

Sub-area lower bound upper bound lower bound upper bound

Sub-area lower bound upper bound lower bound upper bound

Sub-are lower bound upper bound lower bound upper bound

(2) Net benefit from net-box fishery (Y 1 0,000/m2/yr)

lower bound: 0.010 upper bund: 0.012

(3) Net benefit from tourism industiy ( X 1 0,000/10,000 personday)

lower bound: 34.6 upper bound: 51.9

(4) Maintenance cost of forest (Y 1 0,000/km2/yr)

lower bound: 0.1 1 upper bound: 0.12

(5) Expansion cost of forest coverage (~10,00o/km~)

lower bound: 33.3 upper bound: 36.8

(6) Net benefit from brick production (X 10,000/10,~pcs)

lower bound: 0.10 upper bound 0.12

(7) Net benefit from lime production (~l0,OQOlt)

lower bound: 0.014 upper bound: 0.016

(8) Soil loss from agMultural land (r/lon2/crop)

a) Paddy fm

Sub-ma lower bound upper bound lower bound upper bomd

b) Dry farm

Sub-ma lower bound upper bound lower bound upper b m d

c) Vegetable farm

Sub-area lower bound upper bound lower bound upper bound

(9) NitrogenfPhosphorus content of soi1 (%)

nitrogen content of soil 0.25%

phosphoms content of soi1 O. 10%

(10) Nitrogen in rm-off flow for agricuitural activities (kgbm2)

Subarea 1 2 3 4 5 6 7

lowerbound 30.0 30.0 30.0 13.7 13.7 9.4 1.35

upperbound 36.6 36.6 36.6 16.7 16.7 11.4 1.65

(11) Phosphorous in run-off flow for agricultural activities (kg/km2)

Subarea 1 2 3 4 5 6 7

lower bound 1.9 1.9 1.9 0.855 0.855 0.333 0.09

upper bound 2.3 2.3 2.3 1 .O5 1 .O5 0,407 0.1 1

lower bound: 90 upper bound: 110

(13) Soi1 loss from brkk production (tf10,ûûûpcs)

Subarea 1 2 3 4 5 6 7 -- - - - - -

lowerbund 0.24 0.24 0.24 0.24 O. 17 0.24 0.24

upper bound 0.32 0.32 0.32 0.32 0.23 0.32 0.32

(14) Soi1 loss from lime production (t/t) -- - - - - -

Subarea 1 2 3 4 5 6 7

lower bound 0.021 0.021 0.021 0.021 0.015 0.021 0.021

upperbound 0.029 0.029 0.029 0.029 0.021 0.029 0.029

(15) COD discharge from industrial activities (kg/ulO,ûûû)

Activity lower bound upper bound lower bound upper bound

-- - -- -

lower bound: 12.8 upper bound: 14.2

(17) Phosphorous discharge from net-box fishery production (kg/m2/yr)

lower bound: 2.14 upper bound: 2.36

(18) Waste discharge from net-box fishery production (kglm2/yr)

lower bound: 427.5 upper bound: 472.5

(19) COD discharge from tourist activities (kgl10,ûûûperson-&y)

lower bound: 850 upper bound: 1150

(20) Land area required for tourist activitia (lan2/10,000person-day)

- - ---

lower bound 0.689 0.102 0.377 0.286 0.507 - - -

upper bound 0.932 0.138 0.512 0.388 0.685 - - -

(21) Nitrogen discharge from tourist activities (kg/lO,OOOperson-day)

lower bound: 4.05 upper bound: 4.95

(22) Phosphorous discharge from tourist activities (kg/lO,OOOperson-day)

lower bound: 0.9 upper bound: 1.1

lower bound 720 576 768

upper bound 10800 864 1152

(24) Water demand for brick production (1 .0OOm~/l0,000pcs) - - --

lower bound: 0.01 6 upper bound: 0.024

(25) Water demand for industriel activities (1 ,000rn3/vl~,~)

Activity lower bound uppez bound Iower bound upper bound

(26) Water demand for tourist activities (1 ,000m3/10,000penon-day)

k= 1 k = 2

lower bound: 1.2 1 .O8

upper bound: 1.8 1.62

APPENDIX B

INPUT PARAMETERS FOR B* VECTOR

APPENDIX B -- INPUT PARAMETERS FOR Bf VECTOR

(1) Soi1 loss from land area for agricultural activities (t/yr)

Sub-area lower bound upper bound lower bound upper bound

(2) Nitrogen loss from land area for agricuitural activities (kglyr)

Sub-area lower bound upper bound lower bound upper b o d

(3) Phosphorous loss from land area for agricultural activities (kglyr)

Sub-ma lower bound upper bound lower bound upper bound

(4) Dissolved nitrogen loss with run-off from agriculture land area (kglyr)

Sub-area lower bound upper bound lower bound upper bound

(5) Dissolved phosphorous loss with run-off from agriculture land area (kg/yr)

Sub-area lower bound upper bound lower bound upper bound

(6) COD discharge from industrial activities (kglyr)

Sub-area lower b o d upper bound lower bound upper bound

(7) Discharge from nets fishery activity (kg/yr)

--

Discharge lower bound upper bound lower bound upper bound

Total waste O

Nitrogen O

Phosphorous O

(8) Land area for tourist activity (km2)

Sub-area lower bound upper bound lower bound upper bound

(9) Soi1 loss from brick production (tonslyr)

Sub-area lower bound upper bound lower bound upper bound

(10) Soi1 loss from lime production (tonslyr)

Sub-area lower bound upper bound lower bound upper bound

1 6.58 8.90 6.58 8.90

2 408.0 552.0 408.0 552.0

3 - - - - 4 - - - - 5 734.4 993.6 734.4 993.6

6 102.0 138.0 102.0 138.0

7 148.5 200.9 148.5 200.9

sum 1399 1893 1 120 1515

(11) Total soi1 loss (tonsfyr)

Sub-area lower bound upper bound lower bound upper bound

(12) Total dissolved nitrogen discharge (kglyr)

Sub-area lower bound upper bound lower bound upper bound

(13) Total dissolved phosphorous charge (kgly r)

Sub-area lower bound upper bound lower bound upper bound

(14) Total COD discharge (kglyr)

Sub-area lower bound upper bound lower bound upper bound

(13 Water demand (1,00Om~/~r)

lower bound upper bound lower bound upper bound

(16) Land use for agricultural activities (km2)

Sub-area lower bound upper bound lower bound upper bound

(17) Land use for agricultural activities and forest coverage (km2)

Sub-area lower bound upper bound lower bound upper bound

APPENDIX C

DETAILED IFMOLP SOLUTIONS FOR SCENARIO 1

APPENDIX C

DETAILED IFMOLP SOLUTIONS FOR SCENAIUO 1

Solution to Obiective Functions

Objective function Lower bound Upper bound

Ekonomic benefit (mm fi), ~10,000 3,418,614 4,816,598

Forest coverage (mu fi), k d 1,712 1,875

Soi1 loss (min f3), ton 12,311,270 13,377,654

Nitrogen discharge (min f4), kg 7,838,750 10,067,193

Phosphourous discharge (min fs), kg 1,29 1,956 1,657,567

COD discharge (min fs), kg 25 1 ,129,094 348,8 14,667

Solution to Decision Variables

Land use of agriculturai activities (km2)

1. Paddy farrn

Sub-area lower bound upper bound lower bound upper bound

2. Dry farxn

Sub-area lower bound upper bound lower bound upper bound

3. Vegetable farm

Sub-area lower bound upper bound lower bound upper bound

Production output of industrial activities (~10,00O/yr)

1. Textile industry

Sub-area lower bound upper bound . lower bound upper bound

2.Chemical fibre

--- pp

Sub-area lower bound upper bound lower bound upper bound

3. Paper miU

k=l k = 2

Sub-area Iower bound upper bound lower bound upper bound

4. Food processing

Sub-area lower bound upper bound lower bound upper bound

5. Cernent manufacturing

Sub-area lower bound upper bound lower bound upper bound

Sub-area lower bound upper bound lower bound upper bound

7. Tobacco industry

Sub-ma lower bound upper bound lower bound upper bound

Area for net-fishery activity (mZ)

Sub-area lower bound upper bound lower bound upper bound

Tourist flow (lO,OOOpersonday/yr)

Sub-ma lower bound upper bound lower bound upper bound

Forest coverege (km2)

Sub-area lower bound upper bound lower bound upper bound

Brick production (10,000pcslyr)

Sub-ma lower bound upper bound lower bound upper bound

Lime production (tlyr)

Sub-area lower bound upper bound lower bound upper bound

APPENDIX D

DETAILED IFMOLP SOLUTIONS FOR SCENARIO 2

APPENDIX D

DETAILED IFMOLP SOLUTIONS FOR SCENARIO 2

Solution to Obiective Functions

Objective function Lower bound Upper bound

Economic benefit (max fi), ~10,000 2,705,668 4,9 1 9,809

Forest coverag (mm fi), km2 1,628 1,888

Soi1 loss (min f3), ton 12,260,659 13 ,203,804

Nitrogen discharge (min f4), kg 7,831,882 10,065,635

Phosphourous discharge (min fs), kg 1,290,374 1,657,467

COD discharge (min f6), kg 300,251,063 508,12S,4û4

Solution to Decision Variables

Land use of agricultural aetinties (km2)

1. Paddy farm

Sub-axea lowa bound upper bound lower bound Upper bound

2. Dry fam

Sub-ma lower bound upper bound lower bound Upper bound

3. Vegetable farrn

Sub-ma lower bound upper bound lower bound Upper bound

Production output of industrial activities (u10,OOOIyr)

1. Textile industry

Sub-area lower bound upper bound lower bound Upper bound

2.Chemicd fibre

k=l k = 2

Sub-area lower bound upper bond lower bound Upper bound

3. Paper mil1

- -- --

Sub-area lower bound upper bound lower bound Upper bound

4. Food processing

Sub-ma lower bound upper bound lower bound Upper bound

5. Cernent manufacturing

Sub-area lower bound upper bound lower bound upper bound

Sub-area lower bound upper bound lower bound upper bound

1 - - - -

7. Tobacco industry

k = 1 k = 2

Sub-area lower bound upper bound lower bound upper bound

Ares for netashery activity (m2)

Sub-area Lower bound upper bound lower bound upper bound

Tourist flow (10,OOOperson-daylyr)

Sub-ana lower bound upper bound lower bound upper bound

Forest coverage (km2)

-

Sub-area lower bound upper bound lower bound upper bound

Brick production (10,00Opcs/yr)

Sub-area Lower bound upper bound lower bound upper bound

Lime production (tfyr)

Sub-ma Lowex bound upper bound lower bound upper bound

APPENDIX E

DETAILED IFMOLP SOLUTIONS FOR SCENARIO 3

APPENDIX E

DETNLED IFMOLP SOLUTIONS FOR SCENAIUO 3

Solution to Obiective Functions

Objective funciion Lower bound Upper bound

Economic benefit (rnax fi), %10,000 3,971,87 1 4,607,238

Forest coverage (max fz), 1,777 1,851

Soi1 loss (min f3), ton 12,352,197 13$39,298

Nitrogen discharge (min f4), kg 7,839,121 10,232,818

Phosphourous discharge (min fs), kg 1,292,029 1,685,182

COD discharge (min f6), kg 201,733,123 273,640,375

Solution to Decision Variables

Land use of agricuitural adivities (km2)

1. Paddy farm

Sub-area Lower bound upper bound Iower bound upper bound

2. Dry f m

Sub-ma h w e r bound upper bound lower bound upper bound

3. Vegetable farm

-

Sub-area Lawer bound upper bound lower bound upper bound

Production output of industrial activities (wl0,000/yr)

Sub-ana Lower bound upper bound lower bound Upper bound

2.Chemical fibre

Sub-area Lower bound upper bound Iower bound Upper bound

Sub-area Lower bound upper bound lower bound Upper bound

4. Food processing

Sub-area lower bound Upper bound lower bound Upper bound

5. Cernent manufacturing

- -

Sub-area lower bound upper bound lower bound upper bound

Sub-area lower bound upper bound lower bound upper bound

7. Tobacco indusuy

- -

Sub-area lower bound upper bound lower bound upper bound

Area for net-fisheq activity (m2)

Sub-area lower bound upper bound lower bound upper bound

Tourist flow (10,000person-daylyr)

Sub-area lower bound upper bound lower bound upper bound

Forest coverage (km2)

Sub-ma lower bound upper bound lower bound upper bound

Brick production (10,000pcslyr)

Sub-area Lower bound upper bound lower bound upper bound

Lime production (tlyr)

Sub-area b w e r bound upper bound lower bound upper bound

APPENDIX F

DETAILED IFMOLP SOLUTIONS FOR SCENARIO 4

APPENDIX F

DETAILED IFMOLP SOLUTIONS FOR SCENARIO 4

Solution to Obiective Functions

Objective hction Lower bound Upper bound --

Econornic benefit ( m a ~ fi), Y 10,000 3,226,386 4,525,270

Forest coverage (max fd, km2 1,712 1,846

Soi1 loss (min f3), ton 12,223,905 12,836,430

Nitrogen discharge (min f4), kg 199,935 249,345

Phosphoumus discharge (min f5), kg 18,301 22,7 14

COD diicharge (min fs), kg 200,932,837 3 19,772,304

Solution to Decision Variables

Land use of agricuitural activities (km2)

1. Paddy fâtm

Sub-area lower bound upper bound lower bound upper bound

2. Dry fam

Sub-area Iower bound upper bound lower bound upper bound

3. Vegetable farm

Sub-area lower bound upper bound lower bound upper bound

Production output of industrial activities (~10,0001yr)

1. Textile indusîry

Sub-area lower bound upper bound lower bound upper bound

2.Chemical fibre

Sub-area lower bound upper bound lower bound upper bound

3. Paper miil

Sub-area Lower bound upper bound lower bound upper bound

4. Food processing

Sub-area lower bound upper bound lower bound upper bound

- - -- -

Sub-area Lower bound upper bomd Io wer bound upper bound

6 Leather indusûy

Sub-area lower bound upper bound lower bound upper bound

7. Tobacco industry

Sub-area lower bound upper bound lower bound upper bound

Ares for net-fishery activity (m2)

-

Sub-area lower bound upper bound lower bound upper bound

Tourist flow (10,000person-daylyr)

Sub-area lower bound upper bound lower bound upper bound

Forest coverage (km2)

Sub-area lower bound upper bound lower bound upper bound

Brick production (10,00Opcs/yr)

- -

Sub-area lower bound upper bound lower bound upper bound

Lime production (t/yr)

Sub-area lower bound upper bound lower bound Upper bound

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