Journal of Systems Engineering and Electronics

Vol. 18, No. 3, 2007, pp.534-539

Ranking environmental projects model based on multicriteria

decision-making and the weight sensitivity analysis*

Jiang Yan1, Tian Dagang1 & Pan Yue2

1. Coll . of M a n a g e m e n t , Univ . of S h a n g h a i for Science a n d Technology, S h a n g h a i 200093, P . R. C h i n a ;

2. D e p t . of Con t ro l Science a n d Eng inee r ing , H u a z h o n g Univ . of Science a n d Technology, W u h a n 430074, P . R. C h i n a

(Received Apr i l 16, 2007)

Abstract: W i t h t h e fast g r o w t h of Ch inese economic , m o r e a n d m o r e cap i t a l will b e invested in e n v i r o n m e n t a l

p ro jec t s . How t o select t h e e n v i r o n m e n t a l inves tmen t p ro jec t s (a l t e rna t ives ) for o b t a i n i n g t h e bes t e n v i r o n m e n t a l

qua l i ty a n d economic benefi ts is a n i m p o r t a n t p r o b l e m for t h e decis ion make r s . T h e p u r p o s e of t h i s p a p e r is t o

deve lop a dec i s ion-making mode l t o r a n k a finite n u m b e r of a l t e rna t ives w i t h several a n d some t imes conflicting

cr i te r ia . A mode l for r a n k i n g t h e p ro jec t s of munic ipa l sewage t r e a t m e n t p l a n t s is p roposed by us ing e x p o r t s '

i n fo rmat ion a n d t h e d a t a of t h e real p ro jec t s . A n d , t h e r a n k i n g resu l t is given based on t h e P R O M E T H E E m e t h o d .

F u r t h e r m o r e , by m e a n s of t h e concep t of t h e weight s tab i l i ty in tervals ( W S I ) , t h e sens i t iv i ty of t h e r a n k i n g resu l t s

t o t h e size of c r i t e r i a values a n d t h e change of weights va lue of c r i t e r i a a r e d iscussed. T h e resu l t shows t h a t some

cr i te r ia , such as " p r o p o r t i o n of benefit t o p ro jec t cos t" , will influence t h e r a n k i n g resu l t of a l t e rna t ives very s t r o n g

whi le o the r s no t . T h e influence a r e no t only from t h e va lue of c r i t e r ion b u t a lso from t h e chang ing t h e weight of

c r i te r ion . So, s o m e c r i t e r i a such as "p ropo r t i on of benefit t o p ro jec t cost" a r e key c r i t e r a for r a n k i n g t h e p ro jec t s .

Decis ion make r s m u s t b e cau t ious t o t h e m .

Keywords: mu l t i c i r t e r i a dec i s ion-making , r a n k i n g e n v i r o n m e n t a l p ro jec t s mode l , P R O M E T H E E m e t h o d , sensi-

t iv i ty ana lys is , weight s tab i l i ty in tervals .

1. Introduction

With the fast increase of Chinese economic, more

and more capital will be invested in environmental

projects. How to select the environmental investment

projects (alternatives) for obtaining the best environ-

mental quality and economic benefits is an important

problem for the decision makers.

Selecting the environmental investment project is

a typical mutlicriteria decision-making problem in

which a finite number of alternatives must be ranked

considering several and sometimes conflicting criteria.

There are many factors can influence the ranking

results, such as the local social-economic development

situation, the local environmental quality condition,

the subjective preference of decision makers and so

on. The criteria of those factors are often conflictive.

For obtaining the optimized ranking result of

projects, it is necessary to discuss the questions such

as selecting the essential criteria and evaluation in-

dex system, determining the weight of each criterion,

choosing the method of ranking projects etc.

The preference ranking organization method for

enrichment evaluation (P R O ME T H E E ) has been

used. The P R O M E T H E E method is a multicriteria

decision-making method developed by Brans et al.

I 1 - 2 1 . It is a quite simple ranking method in concep-

tion and application compared with other methods for

multicriteria analysis. It is well adapted to problem

where a finite number of alternatives are to be ranked

on the different criteria' 3!. This method has some

strengths as compared with the analytic hierarchy

process (ΑΗΡ) method, such as: the P R O M E T H E E

does not aggregate good scores on some criteria and

* T h i s p ro jec t was s u p p o r t e d by S h a n g h a i Lead ing A c a d e m i c Discipl ine P r o j e c t (T0502) ; S h a n g h a i Mun ic ipa l E d u c a t i o n a l

C o m m i s s i o n P ro j ec t (05EZ32) .

Ranking environmental projects model based on multicriteria decision-making and the weight 535

bad scores on other criteria, it has less pairwise com-

parison and it has not the artificial limitation of the

use of the 9-point scale for evaluation ' 4 1 .

P R O M E T H E E has been applied in different ar-

eas such as ranking environmental project ' 5!,locating

the reservoir' 6!, designing IT (information technol-

ogy) strategies' 7 ! and planning and producing renew-

able energies' 8!. Almost all existing researches show

tha t the P R O M E T H E E method is a comprehensive

method to solve a mutlicriteria decision-making prob-

lem.

2. The municipal sewage treatment plant projects evaluation model

2.1 D e t e r m i n i n g eva luat ion cri ter ia

According to the features of the economic develop-

ment and environmental situation of China, the pri-

mary factors which influence the evaluation of the mu-

nicipal sewage t reatment plant projects can be consid-

ered from the following four par ts :

(1) Project performance states;

(2) The local economic situation of a location where

the project will be located;

(3) The local environmental situation of a location

where the project will be located;

(4) The local environmental objectives of a location

where the project will be located.

The integrated and simplified evaluative criteria are

as follows:

• Proport ion of benefit to project cost (f\): The

quanti ty of t reated wastewater in a day by a plant

which will be bui l t / the sum of investment throughout

the te rm of planning;

• Project phase ( ^ 2 ) · The phase when the project is

undertaken (Draft plan\feasibility repor t \ suggestion

repor t \ initial design\on bu i ld ings 1 \2 \3 \4 \5 ) ;

• Local G D P per capita ( ^ 3 ) : G D P per capita of

a location where the project will be located (GDP of

the te rm of planning / population);

• Increase in local wastewater t reatment ra te

(Λ):Wastewater t reatment ra te which will be in-

creased in a location where the project will be located;

• Reduction in local discharge of COD

(/δ):Discharge of COD which must be reduced

in a location where the project will be located.

The greater the criterion value is, the more possibly

the project will be selected.

2.2 D e t e r m i n i n g a l t ernat ives se t

Based on the initial technical-economic analysis and

logical analysis, 7 alternatives were selected from all

alternatives recommended. Each of these 7 alterna-

tives is feasible and reasonable alternative.

2.3 D e t e r m i n i n g cri ter ia w e i g h t s

The weight survey is carried out with a writ ten

questionnaire. According to the questionnaire from

nine exports and two decision-makers, it can be con-

cluded tha t the importance of all criteria are equal.

So, the weight of each criterion is equi-weight.

2.4 D e t e r m i n i n g eva luat ion m e t h o d

To help the decision-maker in selecting the 'best ' al-

ternatives or ranking all these alternatives from the

best to the worst, most multicriteria decision aid

(MCDA) methods build a preference structure (P,

I, R) on the A . Here, "A" denotes a set of fea-

sible alternatives, "P" denotes preference, "I" de-

notes indifference, and "R" denotes incomparability.

The P R O M E T H E E method is an outranking method

based on such preference structure. P R O M E T H E E

I constructs a part-preorder While P R O M E T H E E II

constructs a complete-preorder on the A.

The following steps are required for the implemen-

tat ion of the method:

(1) Alternatives are compared in pairs for each cri-

terion. The preference is espressed by a number in

the interval [0,1] (0 for no preference or indifference

to, 1 for strict preference). The function relating the

difference in performance to preference is determined

by the decision maker.

(2) A multicriteria preference index is formed for

each pair of alternatives as a weighted average of

the corresponding preference computed in step (1)

for each criterion. The index π(α^,α^)(in the inter-

val [0,1]) expresses the preference of alternatives

over au considering all criteria. The weighting factors

express the relative importance of each criterion and

are chosen by the decision maker.

536 Jiang Yan, Tian Dagang & Pan Yue

(3) Alternatives can be ranked according to :

• The sum of indices π(α^,α) indicating the prefer-

ence of alternative α ι over all the others. It is termed

"leaving flows" </>+(α^) and shows how "good" the al-

ternative ai is.

• The sum of indices Π(α,α^) indicating the pref-

erence of all other alternatives compared to α^. It is

termed 4 entering flow' φ~(αι) and shows how "infe-

rior" the alternative ai is.

According to P R O M E T H E E I : α^Ρα^, if the leaving

flow((/>+) of cii is greater than the leaving flow of α& and

the entering flow (φ~) of ai is smaller than the entering

flow of α&; a ja&, if φ+ and φ~οί both ai and α& are

equal; and, a^Ra^, if the leaving flows indicate tha t

ai is bet ter than α&, while the entering flows indicate

the reverse. Therefore, the P R O M E T H E E I provides

a part ial ranking of the alternatives.

In P R O M E T H E E II the net flow φ (the difference

of leaving minus entering flows) is used, which permit

a complete ranking if all alternatives. The alternative

with the higher net flow is superior.

2.5 D e t e r m i n i n g preference funct ion

For each criterion, there are six preference function

types tha t can be selected. The six types of preference

function and their mathematic description are shown

in Ref. [2].

All essential parameters for ranking the munici-

pal sewage t reatment plant projects can be built a

spreadsheet, namely a decision matr ix, as shown in

Table 1. This decision matr ix includes: the criteria,

type (maximization or minimization), weights, types

of preference functions and their defined parameters ,

and the criteria values of project according to the cri-

teria. Where, the preference functions are selected

from six types of P R O M E T H E E method according to

the exports ' opinions.

3. Ranking result analysis

According to the Decision matr ix and the values of the

parameters shown in Table 1, the values of π(α^,α^)

solved by P R O M E T H E E I method are in Table 2 and

the values of φ+(a^,φ~ (a^,φ(α{) are in Table 3.

Using the dera of Table 2 and Table 3, a part- pre-

order of the P R O M E T H E E I method is

alP^a2P{l)abP^a7P^aA,

α ι Ρ ( 1 ) α 3 Ρ ( 1 ) α 5 Ρ ( 1 ) α 7 Ρ ( 1 ) α 4 ,

α ι Ρ ( 1 ) α 3 Ρ ( 1 ) α 6 Ρ ( 1 ) α 7 Ρ ( 1 ) α 4 ,

and a2Rasa 2Ra^a 5 · ^ α 6 ·

A complete preorder of the P R O M E T H E E method is

a1pMa2pMa3pMa6pMa5pMa7pMa4

So, we have the following conclusion: not only in

P R O M E T H E E I but also in P R O M E T H E E II, the

priority of a\ has a highest and the priority of a4 has a

lowest when each criterion has been given equi-weight.

T a b l e 1 D e c i s i o n m a t r i x a n d t h e v a l u e s o f t h e p a r a m e t e r s

C r i t e r i a h h Λ h h

Uni t T o n / d a y . Ten t h o u s a n d Y u a n / p e r s o n % Ten t h o u s a n d

M a x or M i n y u a n t o n / y e a r

Pre fe rence funct ion t y p e III I I II I II I II

P re fe rence funct ion p a r a m e t e r s ( m ) 10.15 2357 14.5 2.03

C r i t e r i a weight 0.2 0.2 0.2 0.2 0.2

P r o j e c t s / c r i t e r i a values

P r o j e c t a\ 4.15 5 14 667.39 54.43 1 685

P r o j e c t a,2 5 1 14 667.39 54.43 1 629

P r o j e c t az 9.34 5 7 219.68 37.92 710

P r o j e c t a± 3.27 3 4 908.98 36.28 10

P r o j e c t a s 5 4 4 356.99 58.53 640

P r o j e c t a,6 9.56 2 8 667.45 56.57 590

P r o j e c t αγ 1 2.7 2 6 786.3 38.16 820

Ranking environmental projects model based on multicriteria decision-making and the weight · · · 537

T a b l e 2 T h e v a l u e s o f 7 r ( a i , a k )

α ϊ « 2 az C I 4 a§ a>6 α 7

- 0.2 0.407 8 0.769 5 0.524 8 0.447 0 0.601 0

CL2 0.018 0 - 0.407 8 0.587 5 0.324 7 0.247 0 0.401 0

az 0.110 0 0.292 0 - 0.471 7 0.356 1 0.214 3 0.208 4

C I 4 0 0.2 0 - 0.010 9 0.2 0.2

a 5 0.054 6 0.236 5 0.183 6 0.510 1 - 0.223 4 0.381 5

« 6 0 .133 8 0.315 8 0.198 9 0.456 3 0.180 4 - 0.200 5

a 7 0.181 3 0.363 3 0.086 5 0.349 8 0.232 1 0.094 1 -

T a b l e 3 T h e v a l u e s o f Φ+(&ϊ)φ- (a i ) a n d φ(αί)

αϊ az 0,4 α 5 α 7

Φ+{αί) 2.950 0 1.986 1 1.652 6 0.610 9 1.589 7 1.485 6 1.307 2

φ~{αι) 0.497 8 1.607 7 1.284 7 3.144 9 1.629 0 1.425 9 1.992 2

Φ(α>ζ) 2.452 2 0.378 4 0.368 0 -2.534 -0.039 3 0.059 7 -0.685 1

4. Sensitivity analysis of ranking result

4.1 W e i g h t s tabi l i ty intervals ( W S I )

Weight is a kind of quanti ty tha t can be quantified de-

cision maker 's subjective preference. Due to the deci-

sion makers are not very clear to add what weight each

criterion in the beginning, the weight of the criteria

will vary continuously through the process of ranking

the projects, and the ranking results may change with

the change of the weight. To help decision makers un-

derstand how the varied weight influence the ranking

results, the concept of weight stability intervals' 9! is

introduced to discuss weight sensitivity of the ranking

result.

When the weights of other criteria are invariable, to

vary the weight of one criterion can induce the ranking

result to change or not. The definition of WSI is a

varying range of weight tha t the ranking result has no

change while the weight is continuous varied. Define

Ω° =

Ω+ =

Ω"

(ai,ak) e Ax A, ..s.t..A(a,i,ak) = 0.

.and. .Δ j (a i ,a k ) φ 0

(ai,ak) e Ax A,..

s.t..A(ai,ak)Aj(ai,ak) > Δ 2 (α; ,α&) J

(di,ak) £ Ax A,..

s.t..A(ai,ak)Aj(ai,ak) < 0

then the model for solving the WSI can described

as follows:

(1) If Ω 0 = 0, the WSI of ft is

WSIj = (w~,w+) = (1 - (1 - 1 - (1 - Wj)aj).

Here

A(ai,ak)Ai(ai,ak) a. max (ai,ak)eQ- A(ai,ak)Aj(a,i,ak) - A2{ai,ak)'

>

af = m m A(ailak)Ai(ailak)

1 (ai,ak)eQ+ A{ai,ak)Aj{ai,ak) - A2(a,i,ak)

A(a,i,ak) = φ(αι) - φ(α^

Aj(a,i,ak) = 0 j(oi) - <t>j(ak)

(2) If Ω° φ 0, there are not WSI.

4.2 T h e W S I of t h e ranking resul t

The WSI of each Criterion can be calculated thought

the model of WSI. For ensuring the sum of weights is

one, the weights of other cirteria will be reduced or

increased while the weight of a criterion is increased

or reduced. When w\, W2, W3, W4 and is changed

individually in their WSIthe range of other weights

will change. All da ta are shown in Table 4.

4 .3 Sens i t i v i ty analys i s a b o u t t h e ranking

R e s u l t

Based on Table 4, the conclusion yielded from sen-

sitivity Analysis is tha t the WSI of / i , / 2 , / 4 , / 3 and

/ δ is increased in tu rn and the sensitivity degree of

the ranking result with the change of each weight is

reduced correspondingly in turn. Namely, the ranking

538 Jiang Yan, Tian Dagang & Pan Yue

T a b l e 4 T h e W S I o f e a c h c r i t e r i o n

Cr i t e r i on h h h h h

WSIj = (w-,wp

(1 .03, 0.997)

(0.176,0.207)

(0.206,0.199)

(1.04, 0.999)

(0.168,0.201)

(0.206,0.199)

(1.002, 0.761)

(0.198,0.391)

(0.200 4,0.155)

(1.002, 0.95)

(0.198,0.24)

(0.200 4,0.19)

(1.003, 0.678)

(0.198,0.457)

(0.200 6,0.136)

result is most sensitive to the change of the weight

relative to the criterion / i a n d is most non-sensitive

to the change of the weight of the criterion fa. Be-

cause the criterion fi means 'Proport ion of benefit to

project cost', it is very clear tha t 'Proport ion of ben-

efit to project cost' is a key criteria for ranking the

projects. Decision makers must be cautious to change

the weight of "Proportion of benefit to project cost"

or not.

5. Conclusions

In the paper, a model for ranking the projects of mu-

nicipal sewage t reatment plants is proposed by using

exports ' information and the da ta of the real projects.

This model includes selecting essential criteria, estab-

lishing a evaluation index system, determining the

weight and preference functions of each criterion, etc.

The ranking result about 7 real projects is given based

on the model.. Furthermore, the sensitivity of the

ranking results about the weights of criteria is dis-

cussed through the concept of the weight stability In-

tervals (WSI).The result shows:

(1) The result of the application of this model is

largely dependent upon the decision makers ' informa-

tion, such as their preference about weight of criterion,

which preference function of each criterion they want

to use, and so on. The raking result may be differ-

ent according to the different preference given by each

individual.

(2) Some criteria, such as 'Proport ion of benefit to

project cost', will influence the ranking result of alter-

natives very strong while others not. This influence is

not only from the value of the criterion but also from

the changing weight of the criterion. So, some criteria

such as 'Proport ion of benefit to project cost' are key

criterion for ranking the projects. So, decision makers

must be cautious to the key criterion which may be

change the whole ranking result of alternatives.

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J i a n g Y a n is an associate professor of systems sci-

ence & systems engineering in the College of Man-

Ranking environmental projects model based on multicriteria decision-making and the weight 539

agement at Shanghai for Science and Technology.

She received her Ph .D. degree in systems engineer-

ing form Huazhong University of Science and Tech-

nology. Her research interest is in the decision-

making theory, methods and their applications. E-

mail: ppjyan@263.net

T i a n D a g a n g is a professor of information systems

& systems engineering in the College of management

at University of Shanghai Science and Technology.

He received his Ph .D. in system engineering from the

Huazhong University of Science and Technology. His

research interests include evolutionary computation,

operations research, neural networks, decision support

system, and dynamical system.

P a n Y u e is a student of Department of Control Sci-

ence & Engineering at Huazhong University of Science

and Technology. Her research interest is in system

modeling and decision support system.