An Evaluation Model for Emergency Logistics System

Zhang Guanxiang, Zhang Meng, Zhang Zhiyong, Li Guihai Department of Logistics Engineering

South China university of technology Guangzhou, China

Abstract—The emergency logistics system plays an important role in fighting against diseases and natural disasters. Evaluation of the emergency logistics system provide a basis for system optimization. An evaluation model for emergency logistics system based on hierarchy gray method is presented, which can solve uncertainty and complexity problems of emergency logistics system evaluation. The model establishes an evaluation index system of emergency logistics system, determines the weights by analytic hierarchy process(AHP) method, and then, finishes the comprehensive evaluation by hierarchy gray method with improved triangular whitenization weight function. The disaster of Wenchuan earthquake is taken for example to show the practicability of this evaluation model.

Ke yword：emergency logistics; evaluation; analytic hierarchy process; hierarchy gray method; triangular whitenization weight function

I. INTRODUCTION The development of human civilization make a comfortable

living and working condition for people. But, when we face disasters, the community is becoming increasingly fragile. In recent years, a large-scale of public emergencies happened frequently, such as natural disaster, accident, war and public health emergency, etc. which lead to colossal loss all over the world. Disastrous events during recent years include: SARS in China (2003), Iraq war (2003), tsunami in Indonesian regions (2004), Katrina hurricane in America (2005), Bangladesh cyclone Sidr (2007), snowstorm in China (2008), etc. Now the most important and sad thing is the earthquake happening in qinghai province yushu city.[1][2]

All of those emergency events required huge amount of relief materials should be allocated and distributed in a short period. So it is an important way to establish an emergency system to deal with public emergencies. Emergency logistics, one special kind of logistics, comes out along with emergency incidents. It refers to supplying emergency materials to those affected areas and people attacked by emergency incidents timely and seeking for maximization of time utility and minimization of loss through transportation, storage, processing, distribution and information processing operations [3].

Evaluation of emergency logistics system provide a basis for system optimization. But the research on the evaluation the emergency logistics system is still in its initial stage, and has less research result. Yoshitaka Kuwata (2002) discussed a new simulation methodology and an approach to assess, design and evaluate the emergency decision support system which can quantitatively evaluate the effectiveness of decision support system of emergency response[4]. Zhong Li-jun (2009) establishes the performance evaluation system of emergency logistics system by fuzzy comprehensive evaluation model and ensure weight by AHP analytical method[5]. An improved comprehensive fuzzy evaluation is proposed for evaluation of emergency logistics plan of local government by Ding Bin ect[6]. Zhang Zhi-yong proposed a evaluation model for emergency logistics system based on set pair analysis (SPA)[7]. In this paper an evaluation model for emergency logistics system based on hierarchy gray method is presented, which can solve uncertainty and complexity problems of emergency logistics system evaluation. An evaluation index system is established, the weights are determined by analytic hierarchy process(AHP). And then, finishes the comprehensive evaluation of emergency logistics system by hierarchy gray method with improved triangular whitenization weight function. The disaster of Wenchuan earthquake is taken for example to show the practicability of this evaluation model.

II. EVALUATION INDEX SYSTEM FOR EMERGENCY LOGISTICS SYSTEM

The evaluation index system is the basis of evaluation. In this paper, we use group decision-making method to establish the evaluation index system of emergency logistics system. Group decision-making is a type of participatory process in which multiple individuals acting collectively, analyze problems or situations, consider and evaluate alternative courses of action, and select from among the alternatives a solution or solutions.

The evaluation index system of emergency logistics is listed as Table 1 by analyzing the results of group decision-making process. Emergency logistics evaluation index system is divided into two levels. The first level includes four indexes: "service level", "logistics efficiency", " infrastructures " and

This work was supported by the Philosophy and Social Sciences Foundation of Guangdong Province (No 09GO-08)) and supported by the Fundamental Research Funds for the Central Universities (2009SM0055)

978-1-4244-5326-9/10/$26.00 ©2010 IEEE

"information technology". The second level includes twelve indexes.

Table 1. Evaluation indexes

The evaluation

index system of

emergency logistics

Service Level

the reliability of distribution time SL1 the rate of the transport emergency

materials is good SL2

the rate of the distribution of emergency material is timely

SL3

Logistics Efficiency

the cost-effective rate LE1 the using rate of common materials

distribution system LE2

the rate of transportation facility are full-loaded

LE3

Infrastructures

the transit capacity of transit point for materials

I1

the capacity of emergency materials warehouses

I2

the flexibility of transport modes I3

Information Technology

the availability of information of the transportation facilities in transiting

IT1

the availability of instant information of roads conditions

IT2

the using rate of Global Positioning System for transportation facilities

IT3

III. DETERMINE THE WEIGHTS OF INDEX SYSTEM The analytic hierarchy process is the most popular

method[8] to determine the weights in evaluation, it quantify the experience of decision-makers. The judgment matrix of criterions at all levels should be established in order to work out the indexes’ weights. Due to limited space, we only introduce the determination of the weights of first level.

Step I: build a judgment matrix of first level’s four indexes by paired-comparisons method as shown in table 2.

Table 2. The judgment matrix of first level

Service Level

Logistics Efficiency

Infrastructures Information Technology

Service Level 1.00 3.00 4.33 5.33

Logistics Efficiency

0.36 1.00 2.33 3.67

Infrastructures 0.24 0.44 1.00 2.00

Information Technology

0.19 0.28 0.50 1.00

Step II: calculate the weight of index.

(1) calculate the product of every value in the same row of matrix.

1

( 1, 2,3... )n

i ijj

M a i n=

= =∏

Result of product is as follows: M=(69.33，3.09，0.22，0.03)T (2) calculate the nth root of Mi.

ni iW M

−=

The result is as follows: W−

=(8.33，1.76，0.47，0.16)T (3) Normalization processing

1/

n

ii ii

W W W− −

=

= ∑

The result obtained is: W= (0.78, 0.16, 0.04, 0.02) T. The weights of the second level can be obtained by using the same method, the results are as follows:

Service Level: W1=(0.23,0.08,0.69)T Logistics Efficiency: W2=(0.96,0.03,0.01)T Infrastructures: W3=(0.69,0.18,0.13)T Information Technology: W4=(0.21,0.49,0.30)T

IV. GREY COMPREHENSIVE EVALUATION BASED ON IMPROVED TRIANGULAR WHITENIZATION WEIGHT FUNCTION

Because the end-point of normal triangular whitenization weight function has the defect that the grey class crosses with each other, a new function called center-point triangular whitenization weight function is used. This new method divides the value range into several grey classes by using the very point that is belong to each grey class mostly as dividing point. We define four grey classes 1, 2, 3 and 4 which respectively corresponding to excellent, good, middle and bad. The detailed steps are :

(1) Define values that are belong to the corresponding grey classes.

This part define those value respectively as follows: λ1=9，λ2=6，λ3=3，λ4=0.5. The value that is mostly belong to grey class 1 is λ1=9, the corresponding whitenization weight function is as follows:

0( [6,10])6( [6,9])

31 1( [9,10])( )

xx x

xf x

∉− ∈

∈

⎧⎪= ⎨⎪⎩

The value that is mostly belong to grey class 2 is λ2=6, the corresponding whitenization weight function is as follows:

0( [3,9])3( [3,6])

32 9 ( [6,9])

3

( )

xx x

x xf x

∉− ∈

− ∈

⎧⎪= ⎨⎪⎩

The value that is mostly belong to grey class 3 is λ3=3, the corresponding whitenization weight function is as follows:

0( [0.5,6])0.5( [0.5,3])

2.53 6 ( [3,6])

3

( )

xx x

x xf x

∉− ∈

− ∈

⎧⎪= ⎨⎪⎩

The value that is mostly belong to grey class 4 is λ4=0.5, the corresponding whitenization weight function is as follows:

0( [0,3])1( [0,0.5])

4 3 ( [0.5,3])2.5

( )xxx x

f x∉∈

− ∈

⎧= ⎨⎩

All the weight functions are presented in FIGURE I.

FIGURE I GRAPH OF ALL FUNCTION

(2) Calculate the gray coefficient vector of each index by the whitenization weight function and normalization process. And obtain the gray coefficient matrixs of each first level indexes by the corresponding gray coefficient vectors.

(3) Calculate the comprehensive gray evaluation vectors of each first level indexes and system by multiply the corresponding gray coefficient matrix and AHP weight vector.

(4) Calculate final comprehensive evaluation values of each first level indexes and system by multiply the corresponding comprehensive gray evaluation vector and grey classes value vector.

The detail of step(2)~(4) is shown in section V.

V. EXAMPLE ANALYSIS The 2008 Sichuan earthquake is also known as the

Wenchuan earthquake.Official figures state that 69,197 are confirmed dead, and 374,176 injured, with 18,222 listed as missing. The earthquake left about 4.8 million people homeless. It was the deadliest earthquake to hit China since the 1976 Tangshan earthquake, which killed at least 240,000 people。

Four experts are invited to do an evauation for the emergency logistics system of Wenchuan earthquake, which are presented in Table 3

Table 3 Experts’ evaluation

SL1 7 5 6 5

SL2 6 6 7 6

SL3 8 8 9 8 LE1 4 2 1 2 LE2 3 2 2 6 LE3 7 8 7 7 I1 5 8 7 7 I2 6 8 6 5 I3 4 3 3 5

IT1 5 7 6 4 IT2 2 1 2 3

IT3 8 8 7 8

We take the computation of gray coefficient matrix of index "the reliability of distribution time" for example:

The gray coefficient of excellent level is as follows: 4

1 1 1 1 11

1 1( ) (7) (5) (6) (5) 0 0 03 3k

f x f f f f=

= + + + = + + + =∑

The gray coefficient of good level is as follows: 4

2 2 2 2 21

2 2 2( ) (7) (5) (6) (5) 1 33 3 3k

f x f f f f=

= + + + = + + + =∑

The gray coefficient of middle is as follows: 4

3 3 3 3 31

1 1 2( ) (7) (5) (6) (5) 0 03 3 3k

f x f f f f=

= + + + = + + + =∑

The gray coefficient of bad is as follows: 4

4 4 4 4 41

( ) (7) (5) (6) (5) 0 0 0 0 0k

f x f f f f=

= + + + = + + + =∑

The gray coefficient vector after normalization processing is (0.08，0.75，0.17，0).

We use the same steps to processing the other secondary evaluation indexes, finally the gray coefficient matrixs can be obtained:

Service Level:

0.08 0.75 0.17 01 0.083 0.917 0 0

0.75 0.25 0 0R

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

Logistics Efficiency:

0 0.083 0.517 0.42 0 0.25 0.55 0.2

0.264 0.368 0.368 0R

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

Infrastructures:

0.333 0.583 0.083 0.0013 0.2 0.7 0.1 0

0 0.25 0.75 0R

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

Information Technology:

0.114 0.545 0.341 04 0 0 0.6 0.4

0.583 0.417 0 0R

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

The comprehensive gray evaluation vectors of first level indexes are computed as follows:

1 1 [0.543,0.418,0.039,0]W R× = 2 2 [0.003,0.091,0.517,0.39]W R× =

3 3 [0.266,0.561,0.173,0]W R× = ]196.0,366.0,24.0,198.0[44 =× RW

The comprehensive gray evaluation vector of the system is computed as follows:

]067.0,127.0,368.0,438.0[=× RW

The final comprehensive evaluation value of each first level indexes is computed as follows:

468.3

1234

]0,039.0.418.0,534.0[1 =

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

×=P

709.1

1234

]39.0,517.0,091.0,003.0[2 =

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

×=P

093.3

1234

]0,173.0,561.0,266.0[3 =

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

×=P

44.2

1234

]196.0,366.0,24.0,198.0[4 =

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

×=P

The final comprehensive evaluation value of the system is computed as follows:

178.3

1234

]067.0,127.0,368.0,438.0[ =

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

×=P

The results of final comprehensive evaluation value of first

level indexes: the evaluation value of service level is between excellent and good, the evaluation value of logistics efficiency is between middle and bad, the evaluation value of infrastructures is good, the evaluation value of information technology is between middle and good. The evaluation results show that Wenchuan earthquake emergency logistics system mainly seeks for maximization of time utility and minimization of loss, as a result the the evaluation value of service level is between excellent and good, it is the highest evaluation value among four indexes. For the same reason the evaluation value of logistics efficiency is between middle and bad, it is the lowest evaluation value. The evaluation results of the Wenchuan earthquake emergency logistics system based hierarchy gray method basically accords with the actual situations. This evaluation model has good practicability.

VI. CONCLUSIONS An evaluation model for emergency logistics system based

on hierarchy gray method is presented. The model establishes an evaluation index system, determines the weights by analytic hierarchy process method , and then finishes the comprehensive evaluation of emergency logistics system by hierarchy gray method with improved triangular whitenization weight function. The disaster of Wenchuan earthquake is taken for example to show the practicability of this evaluation model.

REFERENCES

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[2] Wei Cheng, Jing Lu.Operational Analysis on Emergency Logistics System and Emergency Response Model. IEEE International Conference on Service Operations and Logistics, and Informatics. 12-15 Oct. 2008, Volume: 1 : 1323 - 1328

[3] Cao jie, Yang xiaoguang ,Wang shouyang. The important scientific problems of emergency management research on sudden public events [J]. Journal of Public Administration,2007,4(2).

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[5] Zhong Li-jun.Performance Evaluationg of Emergency Logistics System. Logistics engineering and management, 2009(3)

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