Relative Efficiency Evaluation on Water Resource Utilization

Journal of Northeast Agricultural University (English Edition)

Sep. 2011

Vol. 18 No. 3 60-64

Relative Efficiency Evaluation on Water Resource Utilization MA Ying School of Agriculture and Forestry Economics and Management, Lanzhou University of Finance and Economics, Lanzhou 730020, China

Abstract: Water resource allocation was defined as an input-output question in this paper, and a preliminary input-output index system was set up. Then GEM (group eigenvalue method)-MAUE (multi-attribute utility theory) model was applied to evaluate relative efficiency of water resource allocation plans. This model determined weights of indicators by GEM, and assessed the allocation schemes by MAUE. Compared with DEA (Data Envelopment Analysis) or ANN (Artificial Neural Networks), the model was more applicable in some cases where decision-makers had preference for certain indicators. Key words: water resource allocation, group eigenvalue method, multi-attribute utility theory, evaluation CLC number: X322

Document code: A

Article ID: 1006-8104(2011)-03-0060-05

and output indicators. Indexes should be chosen in con-

Introduction

formity to two rules: reasonableness and practicability.

As the development of economy, water resources

the model would be too complicated to lose the value

become more and more scarce. Therefore, the ques-

of practicability.

The number of indexes should be concise; otherwise,

tion that how to optimize the allocation of finite water resources attracts extensive attention, but the

Input indicators

past related studies often just highlighted the benefits

There are few researches on input indicators of

and production effects on allocation plans without

water resources distribution. At present, area water

paying enough attention to allocation costs. In this

resource allocation behaviors can be divided into

paper, water resource allocation was defined as

four categories according to its inner mechanism:

an input-output question, and a preliminary input-

configuration by verge costs price, distribution by

output index system was set up. Then GEM (group

administrative management, configuration by water

eigenvalue method)-MAUE (multi-attribute utility

market and allocation by users' demand, so there

theory) model was applied to assess water resource

are main four kinds of water resource configuration

allocation plans. This model determined weights of

resolutions: market configuration, administrative

indicators by GEM, and assessed the allocation

configuration, users participating configuration and

schemes by MAUE.

synthesis configuration[1]. No matter which allocation model it is, each configuration resolution has its own

Evaluation Indexes

configuration cost. How to reckon the allocation costs

Assessment indexes are composed of input indicators

assessment, so further studies on it should be done.

reasonably is very important to the allocation plans'

Received 6 April 2010 MA Ying (1981-), male, lecturer, Master, engaged in the research of population and environmental economics. E-mail: [email protected]

E-mail: [email protected]

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MA Ying. Relative Efficiency Evaluation on Water Resource Utilization

Here, distribution costs are divided into three sub-

assessment model sententious.

indicators: EC, EEC, and UC.

Environmental and ecological costs (EEC)

Economic costs (EC)

EEC is the environmental and ecological sacrifice

Water resource allocation economic costs are the costs

that corresponds to configuration resolutions. There

which can be measured and expressed by currency

are many causes which can induce EEC, and it can

directly during water resource configuration process.

appear in many different forms, which also include the

The constitution of EC varies according to distribution

environmental and ecological losses of areas losing

methods. Except for the costs of water resource

water discussed above. In the early 1990, Colby BG

transfer, transport, store, etc., there are two kinds of

who studied the western water market of America

costs which are easy to be ignored:

yet talked about the environmental and ecological

　(1) The costs which are produced during the process

external diseconomy produced by water right transfer

of introducing water rights market, such as information

from agriculture to non-agricultural usages [3], and

collecting fee, institution design fee, corresponding

this external diseconomy was a form of EEC. There

laws, regulations' design and approval fee, water rights

had been researches on the quantification of EEC[4-5];

initial allocation fee, litigation fee caused by con-

here EEC was monetized, and was presented by the

tradictions during the allocation process, the main-

currency equivalent.

tenance and supervision fee of water rights market.

Uncertain costs (UC)

Past assessment studies of the efficiency of water

Because water resource allocation processe is so

rights market configuration often just emphasized that

complicated and uncertain, there will be many random

water market can make the verge benefit of water users

costs which can't be expected beforehand in processes

come to the same level so as to maximize the social

of real configuration assessments; therefore, UC

total welfare, but ignored the relative institutional

indicator is used to describe them.

transfer costs. Laura McCann had pointed out that transaction costs of introducing water right market on

Output indicators

the base of administrative allocation was decided by

According to the principles of reasonability and

the local water resources' own characteristics, related

practicability talked above, roundly considering the

institutions, more comprehensive social institutional

large scale system of the human-ecology and environ-

[2]

environment and interactions among them .

ment-economy involved in water distribution pro-

　 (2) In the past, evaluations of water resources

cesses, an output indicator system like this (Fig. 1)

transfer from one area to another area, researchers

was set up. The indicator c5 (the degree of satisfaction

often underlined the social, economic, environmental

for water resource allocation) was used to express

and ecological benefits obtained by the area accepting

the fairness and social agreement of water resource

water, but didn't pay enough attention to the side

configurations.

effects for the area losing water. So when the measure of water transfer is taken, direct and indirect economic losses of the area losing water resources should be

GEM-MAUE

credited to EC; its environmental and ecological

These two models, DEA (data envelopment analysis)

sacrifice should be credited to the next indicator EEC.

and ANN (artificial neural networks), needn't fix

Meanwhile, there are some chance costs, time costs

indicators' weights, and just constitute the production

and so on caused by judicial litigations and democratic

frontier by processing indicator values then to evaluate

participations during the configuration process which

the relative efficiency of solutions. Compared with

also should be credited to EC in order to make the

them, GEM-MAUE model in this paper was more http: //publish.neau.edu.cn

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Vol. 18 No. 3 2011

Journal of Northeast Agricultural University (English Edition)

applicable in some cases where decision-makers

possible to develop area economy; but for developed

have special preference for indicators. For example,

areas or some areas where the tourism of natural

in the inchoate period of economy development,

landscapes is regarded as economic polar, they will

on the premise of assuring that the ecological and

pay more attention to the environmental and ecological

environmental status wouldn't degenerate seriously,

qualities. This kind of preference can be expressed by

the decision-makers often use as much water as

weights of indicators.

Output indicator system Economic benefit indicators

Domestic production gross per ton of water (c1)

Area GDP increase rate (c2)

Environmental and ecological indicators Ratio of the water amount used by environment and ecology to the total water amount (c3)

Rate of rivers' water quality reaching standards (c4)

Social benefit indicators

Degree of satisfaction for water resource allocation (c5)

Contribution ratio of scientific progress (c6)

Fig. 1　Output indexes system

Group eigenvalue method (GEM)

ideal expert's scoring vector can make ∑αi become minimum. After fixing the indexes weights vector,

Group eigenvalue method abbreviated as GEM is

MAUT model can be used to assess the relative

[6]

proposed by Professor Qiu . This method fixes the

efficiency of plans in the following.

indicators' weights by constituting experts' judgment matrix, which makes the decision process more simple

Multi-attribute utility theory (MAUT)

and convenient. It includes two steps:

Multi-indicator decision making, also known as multi-

　(1) Constructing experts' scoring matrix.

attribute decision making, is an important part of

　Let each one of the expert groups score all the in-

multi-objective decision to build the theory, and is

dicators directly so as to form an m×n scoring matrix

mainly used to rank decision making schemes with

(integer m is the number of experts; and integer n is

multiple attribute-indicators. According to MAUT,

the number of indicators):

the result value of every attribute has some utilities

　X=(xij)m×n

for decision makers. So the result value of every

　Here, xij is the ith expert's scoring value for the jth

attribute can be converted into dimensionless utility

indicator.

value through some utility function relationships. As

　(2) Calculating the indicators' weights. T

　Make the matrix F=X X, and then figure out the *

utility values are dimensionless, different attributes' utilities can be synthesized into an integrated utility

eigenvector X according to the largest eigenvalue of

value, which makes the result value of multi-attribute

matrix F. At last, normalize the eigenvector to form

quantified completely; then the best plan can be

the indicators' weights vector which is also called

chosen in accordance with the quantification value.

"the ideal expert's scoring vector". Marking the

　The idea of multi-attribute analysis is to set up a

intersection angle between a n-dimensional vector and

"super target", whose total utility target U (p1, p2, …,

the ith expert's scoring vector as αi ( i=1, …, m), the

p n) is the largest, (here, p 1, p 2, …, p n are different

E-mail: [email protected]

MA Ying. Relative Efficiency Evaluation on Water Resource Utilization

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attributes). The principle of the method is just as

　Mark the standardized decision-making matrix as

[7-8]

follows

B=(bij)m×n, and the weighted standardized decision-

:

　 Mark the set of multi-attribute decision-making

making matrix as C=(cij)m×n, here cij=wj×bij.

plans as X={x1, x2, …, xm}, the set of indicators as

+ 　Set c j= max{cij|i=l, 2, …, m}=max{wjbij|i=l, 2, …, m}

P={p1, p2, …, pn}, and the index right weight vector

　

is figured out by GEM as W={w1, w2, …, wn}, which

+ 　 Here, b j is the ideal value in the jth column of

has been normalized. aij represents the attribute value

matrix B, and then the ideal solution C={c+1, c+2, …,

of plan xi for indicator pj, and A=(aij)m×n is the deci-

c+n} is acquired. The evaluation target value of a plan

sionmaking matrix. Normally, there are different

is defined as the distance between the plan and the

types of indicators, such as cost-based pattern, bene-

ideal point, which is expressed by the sum of error's

fitbased pattern, fixed pattern, interval pattern and

square:

so on. Because there are contradictions among diffe-

= max{bij|i=l, 2, …, m}wj=b+jwj j=1, 2, …, n

n

n

j=1

j=1

di=∑ (cij–c+j)2=∑(wjbij–wjb+j)2

rent types of indicators and they can't be measured together, the decision-making matrix needs standar-

n

=∑ wj2(bij–b+j)2(i=l, 2, …, m)

dizing.

j=1

　The indicators proposed in this paper just involved

　Obviously, the less the value of di is, the closer

in cost-based patterns and benefit-based patterns.

the plan is to the ideal point, which means the plan

Benefit-based indicators are processed as below:

further close to the ideal plan. Plans should be ranked

bij=

according to the value of di; thus, the relative effi-

min

aij–aj ajmax–ajmin

ciency of plans is obtained.

　i=l, 2, …, m; j=1, 2, …, n max

　Here, aj

and ajmin are the maximum and minimum

Example

in the jth column, respectively. 　As for cost-based indicators, they are processed as

A calculation example is established to demonstrate

below:

the using of GEM-MAUE model. Supposing there are five schemes for an area's decision makers to choose,

max

bij=

aj –aij ajmax–ajmin

those plans have different index values which are

　i=l, 2, …, m; j=1, 2, …, n

shown in Table 1.

Table 1　Index values of decision-making units Plan

ec (Ten thousand Yuan)

eec (Ten thousand Yuan)

uc (Ten thousand Yuan)

c1 (%)

c2 (%)

c3 (%)

c4 (%)

c5 (%)

c6 (%)

1

100

80

20

30

7

8

80

80

40

2

80

120

5

40

8

10

50

70

60

3

120

60

5

50

6

15

70

75

30

4

60

100

10

30

10

12

85

65

35

5

90

50

25

50

5

7

75

70

50

　 The above model is applied to assess the plans.

0.155, 0.114, 0.115)T by using GEM model and then

There are five experts (S1, S2, …, S5) who score the

standardize Table 1 to get Table 3.

above nine indicators, and the results are shown in

　 At last, figure out "d 1=0.0419, d 2=0.0318, d 3=

Table 2.

0.0544, d4=0.0416, and d5=0.0505", so the sequence of *

　Get x =(0.093, 0.121, 0.104, 0.100, 0.103, 0.095,

plans is as below: Plan3>Plan5>Plan1>Plan4>Plan2. http: //publish.neau.edu.cn

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Vol. 18 No. 3 2011

Journal of Northeast Agricultural University (English Edition)

Table 2　Experts scoring matrix Item

S1

S2

S3

S4

S5

ec

5

4

2

6

1

eec

7

2

3

8

3

uc

1

7

2

7

3

c1

5

2

3

4

6

c2

2

3

6

7

1

c3

2

5

8

1

3

c4

4

7

7

5

8

c5

2

2

5

8

4

c6

7

2

6

3

5

Table 3　Standardized index values Plan

ec

eec

uc

c1

c2

c3

c4

c5

c6

1

0.333

0.571

0.250

0

0.400

0.125

0.667

1.000

0.333

2

0.667

0.000

1.000

0.500

0.600

0.375

0.667

0.333

1.000

3

0.000

0.857

1.000

1.000

0.200

1.000

0.000

0.667

0.000

4

1.000

0.286

0.750

0.000

1.000

0.625

1.000

0.000

0.167

5

0.500

1.000

0.000

1.000

0.000

0.000

0.333

0.333

0.667

3 Colby B G. Transactions costs and efficiency in western water

Conclusions GEM-MAUE model which is concise and practical suited some situations where people have special

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5 Schluter M, Savitsky A G, McKinney D C, et al. Optimizing

could be chosen, according to the concrete background

long-term water allocation in the Amudarya River delta: a water

of real cases. And the configuration plans should be

management model for ecological impact assessment [J]. Environ-

measured in more comprehensive input-output views.

mental Modelling and Software, 2005, 20(5): 529-545. 6 Qiu W H. An eigenvalue method on group decision [J]. Applied

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E-mail: [email protected]