the role of weights in multi-criteria decision aid, and the ranking of water projects in jordan

EUROPEAN JOURNAL

OF OPERATIONAL RESEARCH

ELSEVIER European Journal of Operational Research 99 (1997) 278-288

T h e o r y a n d M e t h o d o l o g y

The role of weights in multi-criteria decision aid, and the ranking of water projects in Jordan

B a s h a r A 1 - K l o u b a, *, T a r i k A 1 - S h e m m e r i a, A l a n P e a r m a n b

a School of Engineering, Staffordshire University, Stafford, ST180DF, UK b School of Business and Economic Studies, Leeds University, Leeds, LS2 9JT, UK

Received November 1995; revised January 1996

Abstract

A case study to build the water sector objectives hierarchy and their weights utilising a structured group brainstorming workshop is described. This became an input to rank the major water projects in Jordan utilising a multi-criteria decision aid method. Finally, weights sensitivity analysis was conducted to judge the stability of the results. © 1997 Elsevier Science B.V.

Keywords: Multi-criteria analysis; Objectives; Weights

1. In t roduc t ion

The water resources issue is a major complicating factor in the socio-political situation of the Middle East. In addition, the lack of comprehensiveness and efficiency in managing water resources has become one of the serious problems facing countries in the region. Jordan already suffers one of the lowest levels of water resources per capita in the Middle East, as well as one of the highest rates in population growth (A1-Kloub and A1 Shemmeri, 1995). Water scarcity is becoming a significant restraint to development and the need to develop a national water strategy is imperative.

The use of Multi-Criteria Decision Aid (MCDA) provides a means to develop future strategies and a system methodology to rank water projects in the presence of different objectives and constraints to

* Corresponding author.

satisfy the broad objectives defined by the socio- political conditions which are sometimes non-com- mensurable and conflicting.

These techniques can be applied to problems with either deterministic or stochastic characteristics, with continuous or discrete variables. In this paper, pri- marily because of space limitations, the methodology adopted to specify the objectives, weights, ranking and weights sensitivity analysis is described, while detailed application of the MCDA methodology to rank and select water resources projects is described in A1-Kloub (1995).

2. Weight ing method selection

Many procedures for the determination of weights have been proposed over the past twenty years. The following, a limited selection of methods are described to reflect the various techniques for weight evaluation as applied to ranking.

0377-2217./97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PI1 S0377-2217(96)00051-3

B. Al-Kloub et al. / European Journal o f Operational Research 99 (1997) 278-288 279

Keeney and Raiffa (1976) presented the trade off method. The key idea of the procedure is to compare two alternatives described on two attributes (for the remaining attributes both alternatives have identical values). One alternative has the best outcome on the first and the worst outcome on the second attribute, the other has the worst on the first and the best on the second attribute. By choosing the preferred alternative out of the two the decision maker decides on the more important attribute. The critical step is the adjustment of attribute outcome in order to yield indifference between the two alternatives. This is typically done by either worsening the chosen alternative in the good outcome or improving the non- chosen alternative in the bad outcome. Such indifference's have to be elicited for n - 1 meaningfully selected pairs of alternatives. If the conditional value functions are known, attribute weights can be derived.

Von Winterfeldt and Edwards (1986) presented the ratio method. This requires the decision maker to first rank the relevant attributes according to their importance, with the least important attribute is assigned a weight of 10 and all others are judged as multiple of 10. The resulting raw weights are then normalised. The swing method was also presented by Von Winterfeldt and Edwards (1986) based on an alternative with the worst outcomes on all attributes; the attribute with the most preferred swing is most important and is assigned 100 points. The magnitude of all other swings are expressed as percentage of the largest swing but normalised to yield the final weight.

Green and Srinivasan (1990) presented the conjoint procedures. These procedures (statistical, holis- tic, and indirect) require the decision maker to rank or rate alternatives. Weights are derived that best fit the alternatives' evaluations. Deriving weights using regression analysis is one of the conjoint procedures.

Saaty (1994) presented the Analytic Hierarchy process (AHP) method in which at first a hierarchy is constructed, and then to set priorities a pairwise comparison matrix is constructed - based on a subjective scale (1-9).

Other methods cited in the literature are, e.g. the Churchman-Ackoff Procedure, Ranking, Categorisa- tion, Rating, Ratio Questioning, Metfessel Alloca- tion, and Observed Derived Weighting (Hobbs, 1979).

For the purpose of this study the JAS method (Judgmental Analysis System proposed by Islei, 1986) was selected due to its availability as software, its user-friendliness and most important because it reduces subjectivity of the analysis by showing the inconsistency of the evaluations of the decision makers, and accordingly, assessment of weights for each member of the decision makers can be compared to highlight sources of agreement and disagreement within the group.

3 . M u l t i - c r i t e r i a a n a l y s i s

To aid the decision maker in solving problems and to introduce the value judgements and trade-offs, different types of multi-criteria techniques have been developed (Goicoechea et al., 1982; Bana e Costa, 1990), these include: outranking, trade-off, distance based, utility or value, and various interactive methods.

The outranking methods are the most commonly used because of their adaptability to real problems and the fact that they are more easily comprehended by decision makers. The PROMETHEE method (Preference Ranking Organisation METHod for En- richment Evaluation) (Brans, Vincke and Mareschal, 1986) was adopted for use in this study. This method is software driven, user-friendly, provides direct in- terpretation of parameters, and a sensitivity analysis of results. The method incorporates the following steps:

• building an evaluation matrix for projects according to the developed set of criteria;

• enrichment of the preference structure by introducing generalised criteria to remove scaling effects;

• enrichment of the dominance relation by building: - multi-criteria preference index to express to which degree an option is preferred to another; - an associated outranking graph and outranking flow to express how each option relates to the other options (strength and weakness of the option);

• exploitation for decision aid. PROMETHEE I provides a partial ranking, including possible incom- parabilities. PROMETHEE II shows complete ranking of options. PROMETHEE V extends the applica-

280 B. AI-Kloub et al. / European Journal o f Operational Research 99 (1997) 278-288

tion of the PROMETHEE II method to the problem of selection of several options given a set of constraints.

• the GAIA software (Geometrical Analysis for Interactive Aid). It provides a geometrical presentation of results obtained by PROMETHEE. GAIA is based on reducing the multi-dimensional criteria space to a two-dimensional criteria plane to allow direct visual presentation. It gives an effective presentation of results and prediction of (what if?.) situations;

• the application of PROMETHEE. A survey to identify feasible options reflecting the values developed in the brainstorming workshop was carried out. Inputs to PROMETHEE include: the generalised criteria, associated weights, options, types of preference functions for each criterion and their defined parameters, evaluation of each option according to objectives selected, the problem type (minimisation or maximisation), and constraints (initial cost, operation and maintenance costs, and regional development). The output of PROMETHEE includes: partial and complete ranking, general sensitivity analysis, geo- metric representation of results using GAIA software, solution of the problem subject to different constraints, and descriptive statistics.

4. Formulat ion of the sector objectives

This is a statement about purpose, philosophy and goals to reflect the values and priorities of the decision makers. It is a necessary step to ensure unity of purpose, develop basis for allocating resources, establish a general tone of the sectors' climate, serve as a focal point, and to facilitate the translation of objectives into a work structure in such a way that cost, time, and performance parameters can be as- sessed and controlled.

In order to establish the water sector mission, an organised brainstorming workshop was carried out with the help of key decision makers and a facilitator (co-author) in Jordan to identify the problems, hierarchy of objectives, weights, and the fundamental objectives. As a result a problem tree describing the core problem, the causes-effects relationship and an objective tree describing the means-ends relationship were constructed. The fundamental objectives

set (composed of 24 objectives) which has certain necessary properties to be used in analysis (com- pleteness, and being essential, controllable, decom- posable, non-redundant, minimal, measurable, and understandable), type (minimisation or maximisation), and their measurement scale were constructed (see Table 1). The following ideas were utilised to complete the above tasks as part of the present research:

• Nominal Group Technique (NGT) as a creative process to identify objectives: In order to build an ownership for objectives a group decision making process is needed, the NGT method was imple- mented according to steps described in (Delbecq et al., 1976).

• Value focused thinking to establish the fundamental objectives: Values should be the driving force for decision making, focusing on values is constraint free thinking (Keeney, 1992), by beginning with values we can think of situations not as decision problems but as decision opportunities, conse- quently, projects are developed to best achieve the values specified for the decision situation in the brain storming workshop rather than selecting projects from the environment.

• Demand management to overcome the short- comings of the existing supply augmentation approach:

• The traditional approach in solving water short- age problems has relied mainly on supply augmentation (Winpenny, 1994), which encounters hydrologi- cal limits, and increasing costs. The demand approach where water is considered as an economic resource is neglected, and actions are required at a number of levels to promote the more efficient use of water. This includes: incentives, direct interven- tions, and pricing policies. Criteria based on the demand options entails predicting consumers' re- sponses and placing economic weights on these changes.

5. Implementation of JAS

After selecting the set of fundamental objectives from the objectives tree the set was broken down into lower objectives. Because of space limitations and as an example one objective tree is shown in

B. A I-Kloub et al . / European Journal of Operational Research 99 (1997) 278-288 281

Fig. 1 for the objective 'water supply is increased' (level 1). Maximising water supply could be achieved by using conventional water resources, non-conventional resources, and management and optimisation (level 2) to name a few options in order of prece- dence. Further specifications for this objective are shown to indicate the various levels and elements of the tree. The weights are shown in brackets which are evaluated using the JAS software. The decision makers were asked to provide their subjective value judgement in the pairwise comparison matrix. Table 2 provides the comparison between the higher fundamental objectives (first level) and the calculated

vector of priorities for that level as a result of JAS analysis (i.e. the calculated weight of the objective 'water supply is increased' is 18.6%), while Table 3 shows priorities at the second level for the objective tree shown in Fig. 1 (i.e. the calculated weight of the objective 'conventional water resources development is 27.5%').

6. Discussion of results

A complete ranking of projects was carried out. A comprehensive survey to identify possible options

Table 1 The fundamental objectives, types, measurement scale, weights and weight stability intervals

Objective/Criterion Type: Measurement/Scale Weight Weight stability interval Min/Max (min. max)

CI: Ground water extraction Min C2: Surface water quality Max C3: Surface water quantity Max C4: Ground water quality Max C5: Ground water quantity Max C6: Sedimentation Min C7: Land quality Max C8: Aesthetics Max C9: Air quality Max C10: Sanitation Max C11: Water supply Max

C12: Conservation Max C 13: Energy requirement Min C14: Foreign labour Min C15: Irrigated area Max C16: Output Max C17: Efficiency Max C18: Commitment to Max

comprehensive and stable plan

C19: Commitment to Max restructuring of water sector

C20: Utilise demand Max management

C21: Public awareness Max

Min

Min Max

C22: Evaporation

C23: Capital cost C24: Cost recovery

+ / - MCM 2.0 (2.00, 2.07) Subjective (1-4) 1.0 (1.00, 1.00) + / - MCM 1.0 (1.00, 1.00) Subjective (1-4) 1.5 (1.50, 1.50) + / - MCM 1.0 (0.93, 1.00) Millions of tons 1.0 (1.00, 1.07) Subjective (1-6) 0.5 (0.50, 0.50) Subjective (1-6) 0.5 (0.50, 0.50) Subjective (1-6) 0.5 (0.50, 0.54) % Change 2.0 (2.00, 2.02) MCM* Relative 18.6 (18.53, 18.60)

Importance MCM Saved 1.3 (1.21, 1.30) MWH 4.1 (4.06, 4.24) Number of labours 4.1 (4.07, 4.10) Thousands hectares 3.08 (3.07, 3.08) Million JD 3.08 (3.07, 3.09) MCM saved 3.08 (3.06, 3.14) Constructed 17.1 (17.10, 17.16)

Attribute

Constructed 8.8 (8.76, 8.83) Attribute (1 - 100)

Constructed 9.7 (9.86, 10.03) Attribute (1-100)

Constructed 7.8 (7.43, 7.83) Attribute (1-100)

Subjective scale 1.0 (0.97, 1.00) (1-6) Million JD 4.1 (4.10, 4.11) Percentage of 3.08 (3.07, 3.15)

investment

282 B. A l-Kloub et al. / European Journal o f Operational Research 99 (1997) 278-288

Management a n d optimisation techniques are utilised (52.8)

Protection of Water resources from pollution is carried out (6.2).

Reduction of losses froln water supply systems (10).

Improve irrigation efficieneies and crop yield (10).

Improve water use efficiency in households (4.5).

Shared international water resources are utilised through international a~eements (19 ).

Balance between resources and populatioJ (redistribution of population) (3.1).

Wastewater(3,441. reuse ]

Water Supply @ is Increased (18.6)

T "t Non-conventional Conventional [ I~sonrces development resources development (19.8) (27.5)

T' i

Ground water Development of surface ] recharge (3.4). water resources (22.9) I

Desalination of brackish water for nmnicipal and industrial ttse (1.2).

Utilisation of brackish water for irrigation and industry(2.26).

t Tectmologies to reduce [ surface water losses (3.0).

~ Rainfall halwesting | [4.o).

T Construction of storage fi~ci ities (22.9). ]

1 Irrigation use (2.80). ]

Drinking use (14).

~ l~dustrial use (4.6).

v•'l]nportation of t Other users (1.5). water (1.0).

-~'-Cloud seeding (1.51.

I I

Developnlent 4 of ground water resources (4.59)

T Development of renewable water resources (3.82).

Irrigation use (0.5).

Drinking use (2.3).

P ~ Developmeut

of fossil (';7°;r °es

H Irrigation use (0.1).

~ Drinking use ] (0.50).

Industrial use I ~ Industrial (0.8). use (0.16). ]

Other users (0.22)] ~ Other(0.0usersl/. ]

Fig. 1. The objective tree for the objective ' water supply is increased', and the calculated weights using the JAS software.

Table 3 The pairwise comparison matrix for the fundamental objectives, and the calculated vector of priorities (Level 2)

Objectives Objectives 4. Calculated

1. Conventional 2. Non-conventional 3. Management and vector of resources resources optimisation techniques priorities (%) development development

1. Conventional resources * development

2. Non-conventional resources 0.7 development

3. Management and 1.9 optimisation techniques

1.5 0.5 27.6

* 0.4 19.8

2.8 * 52.8

B. AI-Kloub et al. / European Journal o f Operational Research 99 (1997) 278-288 283

o':, > ' ~

~ N e • = N

N ~ • 0

d

o

~ e

g ~ s

. ~ × . - ~

~ 8 .~ .~, g

o

&

g

~ N

kO

• -= -4 d d d * d d

~ 0 0 0 0 0 0

o g ~

~ ~ ~ i ~

284 B. AI-Kloub et a l . / European Journal of Operational Research 99 (1997) 278-288

reflecting the values developed in the brainstorming workshop was carried out. The options were classi- fied into five categories: technical, regional, managerial, pricing, and regulatory. The options were deduced from different available documents (including the Jordanian investment plan 1995-1998). As an example, according to the values elicited, highest priorities were given to alternatives, including reducing water losses, increasing water supplies, and improving performance of the sector. The set of constraints (initial cost, operation and maintenance costs, and regional development) were defined by the group of the decision makers who participated in the brainstorming workshop.

A complete analysis for 72 water actions was carried out (A1-Kloub, 1995). Complete ranking was demonstrated and a sensitivity analysis was under- taken by changing the weights of the criteria and observing the changes in the ranking of the actions. The following five special cases for ranking were investigated:

1) all water resources actions without introducing constraints;

2) all water resources actions after introducing

cost constraint; 3) each category of actions independently after

introducing costs constraints; 4) all possible projects (this is the current situa-

tion case where implementing some of the projects is not possible due to different reasons such as political) after introducing costs constraints;

5) technical options based on the current situation (possible projects) and introducing regional development, and cost constraints.

For example, results of case 1 (part of it shown in Fig. 2) shows that the highest priority was given to managerial options X3, 2 (cease pumping from Qa- Disi aquifer, the second project in the third category) and X3, I (limit of agricultural sufficiency, the first project in the third category) respectively. This result is consistent with the values of the water sector regarding the necessary change in the way we view and use water. The water pumped from Qa-Disi is fossil non-renewable water and unfortunately it is used in agriculture, while the agricultural sector is consuming 79% of the available water resources and contributing to less than 7% of the Gross National Product (compared to industry which consumes 5%

I P R O M E T H E E I I ConD le te Rank ing I

Direction of Increasing Priority

1 IA.67 I 3 [A,47 1 5 IA.46-~ x3.2 .i.47 I xl.4, I

Phi = 0 ,26. Phi : 0 .25 4.

l 2 IA.6~ I 4 I A . ? ~ I ~ fA.~z i xa, i ] ×4, x ~4 J Ph-i -----3,--~ Ph i = 0 , 2 5 Ph i = 0 , 1 7

t / .'{ ~i" f " ~ __.--~:-: /:---

0 2 9 0 O -O . 2 9

Fig. 2. A complete ranking (Phi scale) of the first few alternatives and the clusters.

B. AI-Kloub et al. / European Journal of Operational Research 99 (1997) 2 78-288 285

I G A I A P l a n e I

849. A2

~56o A68 ~67 ~71 °

. .A51 ~7 1~3+ ~50

~,. AI3 8~4 870 820.

? ~3 +R72 ~ 6 2 * * ~

853* 833 +~32

Decision Stick (Optimal Direction)

L5 #~I*~ f~55,

165 , A5 +AI 836.

7 ~46

*A~8

C,.I C..2 C. .3 C, .4 C, .5 C. ,6 C. .7 C. .8 0 . . 9 C. IO

: E x t r a c t i o n (W = 2.00) < : 8N Qua l i t g <W = 1.00)

SW Quant i t (W = 1.00) i 8N Q,Jal i tg (N = 1,50)

GW 8 u a n t i t (W = 1.00) : Sediment (H = l. O0) : Land Qual (W = 0.50) : Aes the t i cs (N = 0.50) : Air 8ual (W = 0.50) : S a n i t a t i o n (W = 2.00)

C. 11 : Supplg (H = 18.60) C. 12 : (W 1.30) Conservat = C. 13 : Energg Rq (W = 4.10) C, 14 : (W 4. I0) For, Labor = C. 15 : Irrigated (W = 3.08) C, 16 i Output (H = 3.08) C. 17 Efficiencg (W = 3.08) C. 18 Co~m. plan (N = 17. I0) 0.18 C o ~ . res t (W = 8.80) C. 20 : Demand mag (~4 = 10,00) C.21 : P u b l i c au. (N 7,80) C. 22 : E,xapora, (N = 1.00) C. 23 : Capital co (W = 4.10)

/ / / k ,/' / /

I--Y: ............. / ....

f:/ / :V; / /

Fig. 3. The G A I A plane, including al ternatives, the decis ion axis, and criteria.

I T h e H a l k i n ~ N e i g h t s I

PROMETHEE I I N e t F l o w

A,G? A , 6 6 A,47 A , ? I A . 4 6 ~ . 5 2 A . 5 3 A . 6 9 A . 4 0 A . 3 6 X 3 , 2 H 3 , 1 x i , 4 X 4 , i ~ & , 4 x 4 ~ 5 X 3 , ~ x l , ~ x l . 3

~ei~hts of the Criteria

II

c , . 2 o~ , 3 c . . 4 C. , 5 C . .6 O. , ? ID. , 8 C. . 9 1~,10 S ~ Q SN Q GN (3 GI,.~ Q Sedi L~nd Ae~t A i r ~ a n i

Fig. 4. The walk ing we igh t faci l i ty in P R O M E T H E E (cri ter ion 1 we igh t is 2%).

286 B. AI-KIoub et al . / European Journal of Operational Research 99 (1997) 278-288

of the available water resources and contributes to 22% of the Gross National Product). The next projects in the ranking are technical option X1,47 (hy- draulic analysis and improvement of water system in the country), X4,1 (pricing option) and again this is consistent with the values that policies should be demand driven. The next projects in the ranking are regional options X 4 (Al-Wehda dam), and X 5 (Hasbani dam) and this is consistent with the values regarding obtaining the full entitlement of water resources shared with other neighbouring countries.

The associated net dominance values (Phi scale) were calculated using PROMETHEE (Fig. 2) and this shows the cluster of alternatives which are close to each other, so the first three options form a cluster, and the next two in the ranking form another cluster.

The GAIA plane (Fig. 3) is consistent with the results of ranking shown in Fig. 2, the decision stick (the direction of the optimal solution) is located as far as possible in this direction, and the length of this stick indicates the strength of the decision towards the optimal solution, from which it can be observed

that managerial options X3, 2 (or A67) and X3, ~ (or A 66) are first priorities.

The PROMETHEE model solution is able to supply the intervals of weights for which the ranking does not change, for example in the first case, the 'water supply' criterion with a normalised weight of 18.6% may be weighted between 18.53% and 18.60% without affecting the ranking, all other factors remaining unchanged (Table 1). This indicates that the optimal solution is stable to minor changes in the weights of the criteria. Stability of results for different criteria weights is quite sensitive and using different set of weights will give another set of priorities as demonstrated in weight stability intervals and the walking weights facility in PROMETHEE which allows interactive modification of the values of the weights and the resulting change on ranking (part of it is shown in Fig. 4). For example, if the relative weight of criterion C1 (minimise ground water extraction) is increased from 2% to 10%, then the ranking of projects is changed, and project XI, 4 (or A47) becomes first priority instead of X3, 2 as shown in Fig. 5 for the first few options.

The Walking Weights I

PROMETHEE I I Net Flo~

A.~? A.66 A . 4 7 A .71 A~4G A.52 A . 5 3 A . 6 9 A ~48 A , :36 X3~2 X3,1 x 1 , 4 X4,1 ×I,4 x4 x5 X3,4 x1,4 xl~3

1 4 e i g h t s of the C t - i i e t - i a

3~4 Q E ~ Q GH Q G~ Q ) e d i Land A~st A i r )ani

Fig. 5. The walking weight facility in PROMETHEE (criterion 1 weight is 10%).

B. Al-Kloub et a l . / European Journal of Operational Research 99 (1997) 278-288 287

GALA Plane [

,~70

~ 6 3 " ~33 ~66. ~ 5 9 ~

~67 ~71* ~60"

A25..6) 35

~1:3

Decision Stick (Optimal Direction)

~2~

~37 ~54

~:3~.

~48

C..1 C..2 C..3 C,.'~ C--5 C..6 C,,7 C,,8 C,,9 C, 10 C. II C. 12 C. 13 C. 14 [:.15 C. 16 C.l? C. 18 C. 19 C, 20 C. 21

~:~

E x t r a c t i o n O l = 1 0 , 0 0 ) SN Q u a l i t g <~4 = t . 0 0 > SN Quaa t i t ( N = I, 00) 8H Qualitg <N = 1.50) 8N Q u a n t i t d4 = 1.00) Sedir~ent <N = 1.00> L a n d Q u a l (W = 0 . 5 0 ) Aesthetics <N = O. 50> Rir Qual (W : 0.5@ S a n i t a t i o n (14 = 2~00> Supplg (W = 18.5~) Con~ervat (W = 1.30) Enerqu Rq (W = 4.09> For.d~bor <W = 4.09> Irrigated (W = 3 , 0 7 ) Output <N = 3 . 0 7 ) Efficiencg <t,Â = 3 . 0 7 ) Co~#. p lan (N = 17.07> Com~. r e s t (W = 8.7S)

P u b l i c au. ( N 7,78) Evapora. <~I = 1.00) Capital CO (W = "{. 09)

Fig. 6. The GAIA plane, including alternatives, the decision axis, and criteria (criterion 1 weight is 10%).

The decision stick represents the weight vector (Fig. 3). The decision maker can move according to his preferences in favour of a particular criterion. When the weights are changed the stick moves to an optimal direction and the positions of the criteria and the alternatives in the GAIA plane remain unchanged. The movements of the stick corresponding to modifications of the weights are directly displayed in the bottom right side (as shown in Fig. 3). As an example a change in the weight of criterion C 1 from 2% to 10% causes a resulting change in the decision stick towards X~. 4 (or A47) as an optimal solution (as shown in Fig. 6).

When the decision maker is not able or does not want to allocate precise weights, it is possible to specify intervals of possible values for each weight and this indicates whether the problem is soft or hard: it is soft when the decision axis always remains in the same general direction for the weight distribu- tion that is compatible with the intervals, and it is hard when opposite directions are possible. In the case of a hard problem, it is difficult to decide and the decision maker should concentrate on more pre-

cise values of the weights. For the current weights with a tolerance of _+ 10%, the problem is considered soft and the decision makers were satisfied with this result.

References

A1-Kloub, B. (1995), "Application of multi-criteria analysis to ranking and evaluation of water development projects", in: K. Ellis, A. Gregory, B. Mears and G. Ragsdell (eds.), Critical Issues in System Theory and Practice, Plenum, New York, 89-94.

A1-Kloub, B., and A1-Shemmeri, T. (1995), "Possible enhance- ment technologies and application in Jordan", Water Interna- tional Journal 20, 106-109.

Bana e Costa, C.A. (1990), Readings in Multiple Criteria Deci- sion Aid, Springer-Verlag, Berlin.

Brans, J., Vincke, Ph., and Mareschal, B. (1986), "How to select and how to rank projects: The PROMETHEE Method", Euro- pean Journal of Operational Research 24, 228-238.

Delbecq, A. and Van de Ven, (1976), Group Techniques for Program Planning, A Guide to Nominal Groups and Delphi Process, Scott, London.

Gershon, M. (1984), "The role of weights and scales in the application of multiobjective decision making", European Journal of Operational Research 15,244-250.

288 B. AI-Kloub et al. / European Journal of Operational Research 99 (1997) 2 78-288

Goicoechea, A., Hansen, D., and Duckstein, L. (1982), Multiob- jective Decision Analysis with Engineering and Business Ap- plications, Wiley, New York.

Green, P.E., and Srinivasan, V. (1990), "Conjoint analysis in marketing: New developments with implications for research and practice", Journal of Marketing 54, 3-19.

Hobbs, B. (1979), "Analytical multiobjective decision methods for power plant sitting: Review of theory and applications", Prepared for site standards designation branch, office of standards development, US Nuclear Regulatory Commission con- tract No. DE-AC02-76CH00016.

Islei, G. (1986), "An approach to measuring consistency of preference vector deviation using least square distance", in: Lecture Notes in Economics and Mathematical Systems 294, 265-284.

Keeney, R. (1992), Value Focused Thinking: A Path to Creative Decision Making, Harvard University Press, Cambridge, MA.

Keeney, R., and Raiffa, H. (i976), Decision with Multiple Objec- tives, Preferences and Value Trade Offs, Wiley, New York.

Saaty, T., (1994), The Analytical Hierarchy Process, Wiley, New York.

Von Winterfeldt, D., and Edwards, W. (1986), Decision Analysis and Behavioural Research, Cambridge University Press, Cam- bridge, MA.

Weber, M., and Borcherding, K. (1993), "Behavioural influences on weight judgements in multiattribute decision making", European Journal of Operational Research 67, 1-12.

Winpenny, J. (1994), "Managing water as an economic resource", Development Policy Studies, Overseas Development Institute, London.

the role of weights in multi-criteria decision aid, and the ranking of water projects in jordan

Documents