MULTIOB JECTNE WATER QUALITY MANAGEMENT PLANNING … · 2005. 2. 2. · As a large-scale regional...
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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---
""'
- - - - CMlXHllA
1
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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