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Multicriterion modeling of wastewatermanagement : a comparison of techniques
7. Point Value Used in Discordance Matrix Determination . . . 53
8. Type of Outranking as a Function of Concordanceand Discordance Levels 58
9. Payoff Matrix 61
10. Concordance Matrix 76
11. Discordance Matrix 77
12. ELECTRE I Results 79
13. Characteristic Makeup of the Seven Cases forSensitivity Analysis of ELECTRE II Application 84
14. Ranking of Alternatives Using ELECTRE II forthe Seven Different Cases 87
15. Binary Incidence Matrix Obtained Using SlicingParameter Value of 0.9 90
16. Results of Q-analysis 93
17. Ranking of Alternatives Using MCQA-I Techniques 95
viii
LIST OF TABLES -- Continued
Table Page
18. Ranking of Alternatives Using MCQA-II Techniques 98
19. Alternative Ranking Using Compromise Programmingfor the 4 Sets of Weights and p=1,2 and 101
20. First Through Fourth Ranked Alternatives inEach of the Six Models 109
21. Effects of Model Sensitivity Analysis with Respect toParameters and Model-Wise Preferred Alternatives 115
LIST OF FIGURES
Figure Page
1. Location of Wastewater Treatment Plantin the Upper Santa Cruz River Basin 8
2. Nogales International Wastewater Treatment System 15
3. Average Daily Wastewater Flow (1972-1985) 16
4. Comparison of Wastewater Treatment PlantInfluent and Effluent Rate 17
5. Relationship Between Objectives, Specifications,Criteria and Alternative Schemes 34
6. Graphical Illustration of the Concept ofDistance Based Techniques: CompromiseProgramming and Cooperative Game Theory 70
7. Composite Graph of ELECTRE I Used toObtain the Kernel (Nondominated Alternatives)for (p,q) Values of (0.7,0.2) 78
8. Occurrence Frequency of Alternatives in a Kernelout of Total of 31 Trials Using ELECTRE I 80
9. Number of Alternatives Selected (in a Kernel) withRespect to Different Pairs of Combinations ofthe Thresholds p and q Values 81
10. Reduced Graph of the Strong Relationshipof ELECTRE II Application 85
11. Reduced Graph of the Weak Relationshipof ELECTRE II Application 86
12. Connectivity Structure of the Simplicial Complex Kx(Y;L). 91
13. Connectivity Structure of the Conjugate Simplicial Complexthat is the Inverse of Figure 12 92
14. Illustration of the Number of Selected AlternativesVerses Slicing Parameters-the Lower the SlicingParameter the Less the Selectivity of Alternatives . . . . 94
ix
X
LIST OF FIGURES -- Continued
Page
15. Graphical Illustration of the Most and Least PreferredAlternatives Using Compromise Programming 102
16. Ranking Specificity of Cooperative Game Theory 105
ABSTRACT
Multicriterion modeling of wastewater management problem is
presented in order to select the most preferred wastewater scheme. The
Nogales International Wastewater Treatment Plant which serves the
binational cities of Nogales, Arizona and Nogales, Sonora is used as
case study in the modeling process. The process includes identifying of
objectives, specifying of treatment alternatives and defining criteria
to relate the objective satisfactum level to the alternative schemes.
Six different multicriterion decision making techniques are
applied to analyze and obtain preference ordering among the alternative
treatment schemes. Analyses on the individual techniques and comparison
among them are performed to arrive at the following conclusions: (1)
all the techniques except one can be confidently used to obtain complete
ordering of alternatives, (2) there is inter-model consistency in the
ordering process, (3) in performing this function, the techniques are
fairly robust with respect to parameter changes, and (4) only two
treatment alternatives of fifteen considered are consistently ranked
higher than the rest.
x i
CHAPTER 1
INTRODUCTION
1.1. Preliminary Considerations.
This study is concerned with the application of multicriterion
decision making techniques to select an appropriate wastewater
management scheme. The need for this kind of investigation has
manifested itself in different ways. Phenomenal population growth and
urbani zati on i nrecentyearshave 1 ed to i ncreased production of
municipal and industrial wastes which must be properly treated and
disposed of. Not long ago, some surveys by the U.S. Environmental
Protection Agency showed that more than 60% of the wastewater treatment
plants in the United States were not operating as well as they should
(Council on Environmental Quality, 1979). Inadequately treated sewage
is being discharged into steams, rivers, and lakes which in many
instances may be due to improper operation and maintenance of wastewater
treatment plants. This has been a matter of great concern in the United
States for sometime now.
To cope with the problem, stricter regulations on wastewater
treatment, and disposal mechanisms have been issued at many levels.
Congress passed the Federal Water Pollution Control Act of 1977 (PL 92-
500) and, subsequently, the Clean Water Act of 1977 (PL 95-217) which
require stringent water quality management practices by municipalities,
industries and other dischargers by 1984. Section 208 of PL 92-500
1
2
requires regional facility planning through phasing out and integration
of existing treatment plant facilities.
The Nogales International Wastewater Treatment Plant (NIWWTP) is
such a regional facility serving the twin cities of Nogales, Arizona
(U.S.A.) and Nogales, Sonor (Mexico) and is projected to serve other
nearby growing communities such as Kino Springs and Rio Rio. By
treating wastes from Mexico, the NIWWTP serves not only within-country
regional level as dictated by section 208 of PL 92-500 but international
communities, the growth of which in the last few years seem to approach
a critical stage. The opening of border industries through the Mexican
Border Industrialization Program (Dominguez, 1980), the worsening of the
Mexican economy coupled with the continuing drastic devaluation of the
peso, and the desire of many Mexicans to cross the border and find
employment in the United States are combined to lead to an exploding
population growth on the Mexican side of the border. Thus wastewater is
being produced well above the projected level making the existing
treatment plant unable to achieve its mandated performance level,
instead resulting in the release into the Santa Cruz River of effluent
that does not meet EPA and Arizona Department of Health Services
standards. In addition sewage from broken sewer lines and unanswered
systems have been entering and polluting the Nogales wash (Montano,
1981; Vega, 1983). The situation has affected businesses and proved to
be health hazard at many instances in Nogales, Arizona (Alegria, 1980;
Greenberg, 1982).
3
The wastewater pollution problem has caught the attention of
officials at all levels of government (Dandoy, 1978; Friedkin, 1978;
Lindeman, 1978; Condes and Alegria, 1979; Vega, 1983; Arizona Department
of Health Services, 1985) resulting at times in authorization of studies
to determine the most appropriate treatment schemes to solve the problem
(John Carollo Engineers, 1979; Arthur Beard Engineers, Inc., 1982,
1984). These studies used a traditional cost-effectiveness approach
which expresses all aspects of the problem in monetary terms to
recommend certain treatment alternatives. Although usually useful, such
methods are sometimes grossly inadequate and/or inappropriate because of
the inherent multiobjective nature of the problem of wastewater
management planning (Major, 1977; Nakamura and Riley, 1981; Hiessl et
al., 1985; Tecle and Fogel, 1986). One major weakness of the economic
oriented single objective wastewater management screening method is the
difficulty to handle non-commensurable conflicting objectives such as
cost and water quality. Another problem with the traditional method is
its inability to handle non-numerical objectives such as aesthetic
values of wastewater treatment projects. Consequently, the need for
research on multicriterion wastewater management system cannot be
understated.
If properly managed wastewater may serve as an important
resource. The nutrients and other chemicals in it may enhance
aquacultural and agricultural productivity. Treatment plant sites may
become important recreational facilities and haven for wildlife. Most
importantly, the treated wastewater can become an essential water
4
resource of an area. This is particularly true in areas of scarce water
resource such as the region in which the wastewater treatment plant
under study is located. Thus, the recognition of wastewater both as a
waste product in one hand, and a useful resource on the other makes it a
convenient subject for application of multicriterion evaluation methods
and strengthens further the need for research on its multicriterion
management aspect as stated above.
Even though the need for multicriterion planning in water
resources in general (Maass et al., 1962; Marglin, 1967; U.S. Water
Resources Council, 1973; Major, 1977; Duckstein and Opricovic, 1980;
Gershon et al., 1982), and wastewater management in particular (Lohani
and Abulbhau, 1979; Nakamura and Riley, 1981; Hiessl et al., 1985; Tecle
and Fogel, 1986) has long been recognized, the practical application of
MCDM techniques are not widespread (United States General Accounting
Office, 1978). This study, therefore, attempts to prove the
applicability and promote the wide use of multicriterion decision making
techniques in wastewater management.
1.2. Purpose and Organization.
1.2.1. Purpose.
This study is conducted with two purposes in mind. The first
one is concerned with multicriterion formulation of a wastewater
management problem which is suitable for analysis using six different
multicriterion decision making techniques. The second one, on the other
hand, is focused at evaluating the comparative performances of the six
multicriterion decision making techniques in selecting the most
5
'satisficing' wastewater management scheme. The satisficing condition
is viewed with respect to 12 non-commensurable criteria while 15
different wastewater treatment alternatives are presented to compete for
selection.
1.2.2. Organization.
The thesis is organized to present a step by step development of
multicriterion modelling of the problem under study. Chapter 2 provides
a descriptive overview of the case study. At first, the area's
geographical features considered to be relevant to this investigation
are discussed. Then the physical status of the existing wastewater
treatment plant including its design and present treatment capacities,
future trends with respect to wastewater flow and major quality
parameters followed by a brief review of the institutional and budgetary
arrangements for the wastewater treatment plant are presented.
Chapter 3 develops multicriterion formulation of the problem to
make it suitable for evaluation using MCDM techniques. The formulation
consists of six separate but not necessarily independent steps that
include identification of project objectives, specifications, criteria
and criterion scales, generation of alternative treatment schemes, and
constructing an evaluation matrix. In the process 5 objectives, 12
criteria and 15 treatment alternatives are presented and explained.
In chapter 4 the theory and mathematical procedures behind each
of the six MCDM techniques applied in this study are described. These
procedures are by no means exhaustive but they do adequately reflect the
6
algorithms of each technique. The six MCDM techniques utilized are
ELECTRE I, ELECTRE II, MCQA I, MCQA II, compromise programming and
cooperative game theory. The first four belong to the class of
outranking types while the last two are of the distance based group of
MCDM techniques. All of them, however, are conveniently used to
evaluate a complex wastewater management problem with discrete and non-
commensurable objectives.
Applications of the six MCDM techniques to the case study are
discussed in chapter 5. In addition application results and model
sensitivity analyses with respect to criterion weights and other
parameter changes in each technique are made. Then a comparative
evaluation of techniques and their application results are provided
toward the last part of this chapter. At the end a comparison between
the two top-ranked alternatives is made to gain more insight of their
relative attributes.
The last chapter, chapter 6, contains a summary of the lessons
gained in this study and certain conclusions drawn from it.
CHAPTER 2
CASE STUDY PROBLEM
An essential requirement to resolving a problem is a complete
understanding of its background. This chapter, therefore, focuses on
the status of the existing wastewater treatment plant and its immediate
and relevant environment. This chapter is made up of two sections. The
first one consists of a physical description of the case study in which
the historical status of the existing wastewater treatment plant along
with the area's physiography and population trends are treated. The
second section, on the other hand, reviews the economic and
institutional aspects of wastewater management in the study area.
2.1. Physical Description of the Case Study.
Numerous field trips and extensive literature review have been
made by the author in the course of three years to study the water
quality in the upper Santa Cruz River Basin (Figure 1) in general, and
the problems of wastewater management in the Ambos Nogales area in
particular (Tecle et al., 1985; Tecle and Fogel, 1986, Fogel and Tecle,
1986). The descriptive features of the case study in this
investigation, the Nogales International Wastewater Treatment Plant
henceforth abbreviated as N1WWTP is, therefore part of the product of
the above efforts.
7
ARIZONA
MEXICO
0 6 12 16
Seale In Kilometers
8
2.1.1. Geography.
Geographical features can play important roles in an area's
waste assimilative capacity. As a result, a complete knowledge and
understanding of these features is necessary in the selection and design
of biological wastewater treatment systems suitable for the particular
area (Gloyna, 1971). Factors such as climate and soil type may
influence the rate of wastewater treatment while the population size and
regional activities condition wastewater production and concentration
level. For these reasons, a brief synopsis of the study site's
geographical conditions is provided.
Figure 1. Location of wastewater treatment plant in the Upper SantaCruz river Basin.
9
a. Location. The Nogales International Wastewater Treatment
Plant is located 14.5 kilometers north of the U.S.-Mexico international
boundary line at the confluence of the Nogales Wash and Santa Cruz River
(Figure 1). The Santa Cruz River is an ephemeral stream that comes from
the southeast side of the Treatment Plant and flows northward while, the
Nogales Wash is a polluted perennial stream that comes through the
centers of both Nogales, Arizona (U.S.A.) and Nogales, Sonora (Mexico)
and joins the Santa Cruz River near the Wastewater Treatment Plant.
Geographically, the Wastewater Treatment Plant is respectively located
at 31°251 north latitude and 110057, west longitude. It has an
0 *2. qi < f(n,i)-f(m,i) < q i : average discordance
(f(m,i),f(n,i))cD; andf 4
*3. qi < f(n,i)-f(m,i) : high discordance (unacceptable)
(f(m,i),f(n,i))cD.1
57
Now, given the above relationships, the strong and weak outrankings are
defined as follows:
1. m strongly outranks n if:
mR sn <==> ( E 4 > E wj )fi (C(m,n) > pES 1 (m,n) itS2 (m,n)
and (f(m,i),f(n,i))eD; andi
or
mR sn <==> ( E > z wj )fi(C(m,n) >icS i (m,n) icS2 (m,n)
and (f(m,i),f(n,i))1D;)
where S i (m,n)-(iimPn} and S2 (m,n)=IiimEn} and all other terms are as
described above (Goicoechea et al.,1982; Duckstein et al., 1983).
2. m weakly outranks n if:
taR w n <==> ( E 4 > E VIT )11 (C(m,n) > p-icSi (m,n) icS2 (m,n)
and (f(m,i,f(n,i))ED;)
or
mRw n <==> ( E wI > E w.T )(1 (C(m,n) picS i (m,n) icS2 (m,n)
and (f(m,i),f(n,i))eD; and fiD*i
o
The possible outranking relationships are summarized in Table 8
(Duckstein et al., 1983; Szidarovszky et al., 1986).
The two binary relations determined, in 1. and 2. are
respectively the R s and R w described above from which the corresponding
acyclic graphs, G s and G w are constructed. Using these graphs, the
(9)
(10)
(12)
Table 8. Type of Outranking as a Function of Concordance andDiscordance Levels.
concordance level
high average low
lowdiscordance
strong(equation(10))
strong(equation(10))
weak(equation(11))
averagediscordance
strong(equation(9))
weak(equation(12))
alternatives are ranked with respect to the criteria provided. The
ranking procedure follows a certain sequence of steps (Goicoechea et
al., 1982; Szidarovszky et al., 1986).
b. Ranking procedure. The complete ranking procedure follows
three consecutive steps: forward ranking, reverse ranking and average
ranking (Duckstein and Gershon, 1982; Duckstein et al., 1983).
(i). Forward ranking: In this stage a subgraph of G s (the set of all
alternative systems) is selected and denoted as Y(k). The set of
preferred alternatives, A(k), is chosen from Y(k) and the forward
ranking (v') is obtained by using the following steps:
1. Start with k=1 and Y(1)=Y (the nondominated set of alternatives in
Gs ).
2. Select all nodes of Y(k) not having a precedent (that is, the
alternatives not outranked by others) and denote this by C(k).
3. Next, use Gw (the graph of weak outranking) to remove as many ties
58
59
as possible between systems in C(k). To do this identify all nodes in
C(k) that are joined by an arc in Gw and represent these nodes by U.
4. Select all nodes in U not having a precedent in Gw. Denote this set
as B.
5. Define A(k) as A(k) = (C(k)-U)U B
where C(k)-U ={xixe C(k),xcUI
6. Rank every alternative x CA(k) by setting v'(x) = k.
7. Identify Y(k+1)=Y(k)-A(k) and delete all arcs emanating from A(k).
This eliminates alternatives that have been ranked from repeated
consideration in the forward ranking process.
8. If Y(k+1) is an empty set, then all the representative elements in
the reduced graph of R s have been ranked. If Y(k+1) is not empty set,
then set k=k+1 and go to step 2 above (Goicoechea et al., 1982;
Duckstein et al., 1983).
(ii). Reverse ranking: This procedure embodies the above process and
consists of three steps:
1. Reversing the directions of the arcs in Gs and G.
2. Determining a ranking, a(x), for each alternative x in the same way
as was done in the forward ranking, but replacing a(x) for v'(x) in
step 6.
3. Re-establishing the correct ranking order using the relationship:
v"(x) = 1 'I- amax a(x), Vxa
(13)
where X is the set of all nondominated alternatives and
amax = Maxxexa(x).
60
(iii). Average ranking: This is the final ranking, V obtained from v'
and v" using the ranking function (Duckstein et al., 1983; Szidarovszky
et al., 1986):
V(x) = (v'(x) + v"(x))/2 + 0.5 (14)
where 17, v' and v" are integers.
The ranking procedure for the alternative wastewater management systems
is similar to that of Duckstein and Gershon (1983).
4.1.3. Multicriterion g-analysis I.
Like ELECTRE, multicriterion Q-analysis is a technique for
modeling discrete multi objective problems from the viewpoint of multiple
criteria. The criteria can be non-commensurable, quantitative or
qualitative in scale. This shows that MCQA is convenient for analyzing
the evaluation matrix of Table 5.
a. Payoff and preference matrices. In multicriterion Q-
analysis, the elements of the evaluation matrix, can be defined to
represent the relations between finite sets, the set of alternatives,
X =.(x(i)li=1,....,I1 and the set of criteria, Y =-ry(i)ii=1,---,J}
(Atkin, 1974; Johnson, 1981). In order to make the evaluation matrix
easier to map into a preference matrix, all the entries on the
evaluation matrix are transformed into dimensionless quantitative values
making the payoff matrix of Table 9. The allocation of these values is
based on the range of scales selected for each criterion (Table 6). To
express it algebraically the payoff matrix may be represented as
D =-[d(i,j)1i=1,...,I;j=1,...,J1 (15)
CD CD CD CD CD CD CZ) CD CD CD CD CDLI) • • • • • • • • • • • •r-1 CD CD C:D 01 CD C•J CD CZ) LC) CD LC) lC)ccC CD 0.1 CX) ,-. (7) r-- CD 01 C•J CC) di- Cr)
,-4 n-•1 ,-4 ,--i ,--t g-i
CZ) CD CD CZ) CD CZ) CD 0 CD 0 CD CZ)dr • • • • • • • • • • • •1--4 Lo c:) CD 01 LC) dr CD CZ) LC) CZ) CZ) C•Jc:C r-- cp co r-4 C\J CO C•J 01 C•J LC) Cr) r--
,--I r-i r-4 4-4 r-4 r-4
C:) CD CD CD CD CD CD CD CD CD CD CDCe) • • • • • • • • • • • •r-4 I.C) C) C) C71 0 dr 0 0 CD CD CZ) crc:C r-- 0 co ,-1 Lc) co c • i a, Lc> c=> cv") co
r-4 4-4 r-1 r-4 r-4 r-4 1-4
CD CD CD CD CD CZ) CD CD CD CD CZ)CsJ • • • • • • • • • • • •1-1 C:) C:) C=) r-4 0 04 CZ) LC) CD CD LC1 cd-.1C LC) Rd- r-4 LC1 CD r,. Lo cp Lo Lc) r-. CV
r-4 r-4 C‘J r-4 r-4
CD CD CD CD CZ) CD CD CD CD CZ) CZ)v-4 • • • • • • • • • • • •
CZ) CZ) co co Lc) .tr c) c) c) c) c) coc:c LC1 cd- r-4 1.4) CNJ CO C•J C71 CD di- LC) .11-
consists of the alternatives selected at the highest dimensional level
for each slicing parameter in column 1. Columns 2 and 3 show the
structure vector which indicates the q-connectivity of the alternatives
with respect to criteria taken globally. According to these results, the
best choice or choices varies with the value of the slicing parameter
selected. As the value of the slicing parameter becomes bigger, the
number of best choices becomes narrower until it becomes one,
alternative 13 when the slicing parameter value lies between 0.55 and
0.80 (Figure 14 and Appendix E). This Figure and the Appendix were
7
IDQ) 6
5
ro
. 4
34-
o
* 2C32:
0
Slicing parameter
Figure 14. Illustration of the number of selected alternatives versesslicing parameters - the lower the slicing parameter theless the selectivity of alternatives.
95
included to illustrate further the optimal range of slicing parameters
to choose. In this application that range appears to be between 0.55
and 0.80.
Since the above procedure did not produce a complete ranking of
the alternatives, the latter was determined using the indices PSI, PCI
and PRI-I as shown in Table 17. Except for the value-type index, PSI
Table 17. Ranking of Alternatives Using MCQA-I Techniques.
ELECTRE I -- NA NA VA VA 10 3ELECTRE II SA NA NA R R 10 3MCQA I VA R MA NA 13 5MCQA II -- VA SA NA MA 13 3CP MA NA SA NA NA 10 3CGT NA NA NA NA 10 .rr
Note: NA = Not applicableSA = Slightly affectedVA = Very much affected
R = Robust (not affected)MA = Moderately affected
= No sensitivity analysiswas done
6.2. Conclusions
The following concluding remarks can be made concerning the
lessons learned in this study:
1. Multicriterion analysis makes it possible to study the
systematically the complex relationships among the basic components of a
problem which can be described in terms of a set of criteria and
alternative schemes. In this case study, a multicriterion formulation
of the problem is provided to make the problem suitable for application
of mathematical MCDM techniques. The techniques in return are used to
reduce the set of criteria into few indices to obtain a preference
ordering of the alternative schemes. The structural relationship
between criteria and alternative actions has proven to be the essential
116
stage upon which the six multicriterion decision making techniques were
applied in order to yield individual solutions to the problem under
consideration.
2. With respect to data input type, both CP and CGT require a
cardinal scale, while ELECTRE I, ELECTRE II, MCQA I and MCQA II can he
used to analyze discrete MCDM problems with non-commensurable multiple
ordinal criteria.
3. A comparison of the results obtained showed that all six
techniques can be conveniently used to determine the preference ordering
of a competing finite number of alternative schemes in the wastewater
management problem, even though these techniques may require different
procedures to accomplish the same task. ELECTRE I and ELECTRE II use
pairwise comparisons among alternatives to rank them; compromise
programming incorporates preferences under the form of weights to
determine solutions in terms of L distances; MCQA I and MCQA II
combines q-connectivity, and outranking relationships among alternatives
to get solutions in L p distance form, while cooperative game theory uses
geometric distance as its objective function to arrive at the solution.
4. In ELECTRE I, ELECTRE II, CP, MCQA I and MCQA II, the DM
can choose the weights, specify the value of the metric parameter p in
the last three techniques, select the threshold values of p and q in the
first two, and provide the slicing parameter vector s(k) in the last two
techniques. In CGT, however, the optimum solution is uniquely
determined once the DM has accepted the axioms and chosen the °status
quo' point.
117
5. Table 21 describes the effects of a limited sensitivity
analyses on the results of the problem considered with respect to
parameter and weight changes. In general, except for MCQA I and MCQA II
with respect to slicing parameter changes, and for ELECTRE I with
respect to changes in the threshold parameters p and q values, the
techniques appear to be fairly robust. Similar conclusions were made in
previous studies for ELECTRE I and ELECTRE II in Gershon et al. (1982),
Duckstein and Gershon (1983), for MCQA I and MCQA II in Hiessl et al.
(1985) and for compromise programming in Duckstein and Opricovic (1980)
and Tecle and Fogel (1986).
6. Given the criterion set used in this study (Table 3 and
Table 5) the most preferred wastewater management schemes from the
viewpoint of all six techniques are alternatives 10 and 13 (see last
column of Table 21). According to ELECTRE I, ELECTRE II, CP and CGT,
alternative 10, which consists of facultative lagoons with filtration
algae removal and nutrient removal facilities, is the most preferred.
Alternative 13, consistiny of facultative lagoons and land application
activities, on the other hand, is preferred by both MCQA I and MCQA II
techniques.
7. A choice between the above two alternatives or a compromise
between them will depend on the tradeoffs the DM is willing to make as
described at the end of section 5.2.2.
To end the concluding remarks, it is possible to formulate a
complex problem with non-commensurable, discrete objectives in ways
suitable for application of different types of MCDM techniques.
118
Furthermore it can safely be argued that arriving at the same solution
using different techniques not only proves the applicability of each
technique to the problem under consideration but also enhances the
credibility of the final solution at least from the analyst's point of
view. In this study all six MCDM techniques utilized were consistent in
selecting the two top-ranked alternative treatment schemes. These
results conform to alternatives preferred in previous Engineering
studies (Appendix G).
APPENDIX A
DESIGN PARAMETERS OF THE EXISTINGNOGALES INTERNATIONAL WASTEWATER TREATMENT PLANT
Design year, population served, average daily flow, andBOD per capita, are in accordance with International Boundaryand Water Commission Minute 227, dated September 5, 1967.
1. Design year2. Population served3. Average daily flow
4. Average daily flow5. Peak flow rate (plant effluent)6. Ratio of peak flow rate to
average daily flow (planteffluent)
7. Raw sewage BOD8. Raw sewage BOD9. Raw sewage suspended solids10. Raw sewage temperature range
PLANT CCMPONENTS:
1. Aerated lagoonsDesign flaw, averageDetention time design flowVolume of lagoonsNumber of lagoonsVolume each lagoonDesign water depthNominal surface area per lagoonApplied BOD at design flowApplied BOD at design flowApplied BOD at design flowDesign BOD removalMinimum D. O. concentrationin aerobic layerMethod of aerationNumber of aeratorsFreeboardSide slopesBenn width at ton
2. Stabilization pondsDesign flowApplied BOD at design flow
Applied BOD at design flowApplied BOD at design flowTotal surface area of pondsDesign water depthVolume of ponds at 3 feet depthVolume of ponds at 5 feet depthDetention time at design flawDetention time at design flowNumber of pondsSurface area, each pondPond flow arrangementNUmber of ponds first stagePond surface area first stageApplied BOD to first stage at
design flowNumber of ponds second stagePond surface area second stageFreeboardSide slopesBerm width at top
3. Chlorine contact basinDesign flowPeak flaw rateNumber of basinsDetention time at peak flow rateDesign chlorine residual at peak
flowVolume of basinDepthWidthLengthForm of Chlorine appliedPoint of application
4. Chlorination facilitiesNumber of ChlorinatorsMaximum rated capacity each
chlorinatorMaximum dosage rate per
chlorinator at peak flowrate (10.66 mgd)
Nominal dosage rate anticipatedfor 1 ppm residual in effluent
8.20 mgd50 lbs/acre/day
20% of raw sewage BOD3,470 lbs/day69 acres3 feet nominal (5 feet maximum)207 acre feet345 acre feet8 days (at 3 feet depth)14 days (at 5 feet depth)323 acres2 stage (series flow)246 acres
Note. Based on Information in Arthur Beard Engineers, Inc. (1984).
122
APPENDIX C
OPTIMAL (P,Q) VALUE DETERMINATION AND SENSITIVITY OF ELECTRE IWITH RESPECT TO CHANGES IN (P,Q) VALUES
Threshold Parameters Kernel
.3 .1 6,10,13,15
.3 .2 4,5,6,7,8,9,10,11,13,14
.3 .3 all hut 3
.4 .1 6,10,13,15
.4 .2 4,5,6,7,8,9,10,11,13,14
.4 .3 all hut 3
.4 .4 all hut 3
.5 .1 6,10,13,15
.5 .2 4,5,6,7,8,9,10,11,13,14
.5 .3 all hut 3
.5 .4 all hut 3
.5 .5 0
.6 .1 6,10,13,15
.6 .2 4,5,6,7,10,11,13,14
.6 .3 10,11
.6 .4 8,9,10,11,12,13,14,15
.7 .1 6,10,13,15
.7 .2 6,10,11,13
.7 .3 10,11
.7 .4 10,11
.8 .1 6,10,13,15
.8 .2 6,10,13,15
.8 .3 6,10,13
.8 .4 10,13
.8 .5 10,13
.8 .6 10,13
.9 .1 3,6,10,12,13,15
.9 .2 6,10,12,13,15
.9 .3 6,10,12,13,15
.9 .4 6,10,12,13,15
.9 .5 6,10,12,13,15
Lower p - Willing to accept less preferred alternatives.Higher q - Willing to accept alternatives at higher discomfort
or dissatisfaction.
123
APPENDIX D
ILLUSTRATION OF THE STEP BY STEPRANKING PROCEDURE IN ELECTRE II
This illustration demonstrates the derivation of the actual
alternative rankings shown in column 2 of Table 14. To carry out this
procedure, the strong and weak graphs of Figures 10 and 11, respectively
must be a priori determined.
A. Forward Ranking
Initial Valuek=1, Y(1)=G5
a. Iteration One.(1) C=[10,13] (nodes in G, without precedent)(2) U=[13] (nodes in C reated through Rw )(3) B=[10] (nodes in U without precedent in Gw )(4) A(k)=A(1)=(C- U) UB=[10](5) Ranking: v'(10)=1(6) k=k+1=1+1=2(7) Y(k)=Y(2)=Y(1)-A(1)=[1,2,3,4,5,X1,11,13,14,15]Af
01 S- CT) -0 •,-= co CU 0:5 •r•• CIC.) -J cc _J XMS 0LI-
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