PERFORMANCE EVALUATION OF EMERGENCY LOGISTICS

BASED ON DEA-AHP ALGORITHM

Jiyong Zhang and Shaochuan Fu

Schoole of Economics and Management, Beijing Jaotong University, Haidian District, Beijing, P.R.China

Keywords: Emergency logistics, DEA, AHP.

Abstract: In recent years, much more natural disasters, public health events and a variety of disasters, accidents have

occurred. This paper proposes an index system for the evaluation of the performance of emergency logistics.

Performance evaluation of a group of entities is frequently based on the values of several attributes and

usually requires the weights of the attributes to be set in advance. After an index of logistics system being

built and with the Data Envelopment Analysis (DEA) algorithm and Analytical Hierarchical Process (AHP)

algorithm being integrated. This hybrid model takes the best advantages of both AHP and DEA and at the

same time, avoids either the subjectivity of AHP or the dichotomy of DEA. The results show that the

evaluation method can measure the emergency logistics performance more effective and feasible.

1 INTRODUCTION

2011.3.11, the earthquake and tsunami disasters

have brought great suffering to the Japan. In the

process of disaster relief, the importance of

emergency logistics becomes the focus of people

again.

With the rapid development of science and

technology, the ability of predicting natural disasters

has been significantly improved. However, heaven

decides the weather. Localized, regional, even global

emergencies have occurred, serious threat to human

life and property safety.

The emergency logistics just meet the need to

complete sudden logistics demand from the various

situations.

1.1 Research Significance

The purpose of evaluating the performance of

emergency logistics is to identify the weak links of

the emergency operation in the logistics. Then, with

continuous improvement of the emergency logistics

system can make the system more efficient.

Currently, the assessment of emergency logistics

performance is still in the exploratory stage. The

most correspondingly published literature focus on

the study of response to emergency situation and the

logistics system itself. There are few studies on the

evaluation of the methods to evaluate the

performance of the emergency logistics system.

Now the main measurement methods are as follow:

Fuzzy Comprehensive Algorithm, Analytical

Hierarchy Process (AHP), Data Envelopment

Analysis (DEA). These methods are flawed during

the process.

In this text, the first step is to calculate the

weight of each layer index using the AHP method.

The second step is to obtain the relative efficiency of

each system of indicators for each layer separately

with the method of using the DEA. Finally, integrate

the weight of each index and the relative efficiency

to calculate the overall efficiency of the emergency

logistics system and sorting. The method effectively

combines the advantages of both DEA and AHP, at

the same time, is good to make up for the lack of the

two methods. All of this makes the method

applicability and operability.

2 DEA-AHP EVALUATION

PRINCIPLES

2.1 Basic DEA Methodology

Built upon the earlier work of Farrell (1957), DEA is

a well established methodology to evaluate the

relative efficiencies of a set of comparable entities

by some specific mathematical programming

527

Zhang J. and Fu S..

PERFORMANCE EVALUATION OF EMERGENCY LOGISTICS BASED ON DEA-AHP ALGORITHM.

DOI: 10.5220/0003589305270532

In Proceedings of the 13th International Conference on Enterprise Information Systems (DMLSC-2011), pages 527-532

ISBN: 978-989-8425-55-3

Copyright

c

2011 SCITEPRESS (Science and Technology Publications, Lda.)

models. These entities, often called decisions

making units (DMU

s

), perform the same function by

trans- forming multiple inputs into multiple outputs.

A main advantage of DEA is that it does not require

any prior assumptions on the underlying functional

relationships between inputs and outputs (Seiford

and Thrall, 1990). It is therefore a nonparametric

approach. In addition, DEA is a data-driven frontier

analysis technique that floats a piecewise linear

surface to rest on top of the empirical observations

(Cooper et al., 2004).

Since the work by Charnes et al. (1978), DEA

has rapidly grown into an exciting and fruitful field,

in which operations research and management

science (OR/MS) researchers, economists, and

experts from various application areas have played

their respective roles (Førsund and Sarafoglou,

2002, 2005). For DEA beginners, Ramanathan

(2003) provided an excellent introductory material.

The more comprehensive DEA expositions can be

found in the recent publication by Cooper et al.

(2006). In the sections that follow, we shall briefly

introduce the basic DEA methodology.

Assume that there are K DMU

s

, e.g. electricity

distribution utilities, to be evaluated that covert N

inputs to M outputs. Further assume that DMU

k

consumes x

nk

>=0 of input n to produce y

mk

>=0 of

output m and each DMU has at least one positive

input and one positive output (Fare et al., 1994b;

Cooper et al., 2004). Based on the efficiency

concept. in engineering, the efficiency of a DMU,

says DMU

o

(o=1,2,...,K), can be estimated by the

ratio of its virtual output(weighted combination of

outputs) to its virtual input(weighted combination of

inputs). To avoid the arbitrariness in assigning the

weights for inputs and outputs, Charnes et al. (1978)

developed an optimization model known as the CCR

in ratio form to determine the optimal weights for

DMU

o

by maximizing its ratio of virtual output to

virtual input while keeping the ratios for all the

DMU

s

not more than one.

2.2 Basic AHP Methodology

Analytic Hierarchy Process(AHP) is theorized by

U.S. Operations Research Professor Saaty TL. It is a

simple, flexible and practical method for multiple

criteria decisions making. It is based on a hierarchy

of multi-objective, subjective judgments based on a

range of options for calculating the relative

importance, followed by a top down basis, through

the decision-makers for each sub-index layer and

index layer provided by the importance of subjective

judgments in pairs, for each unit down to the

pairwise comparison matrix to establish.

Comparison of first through calculating the feature

vector matrix elements get the same level on a level

for the relative importance of the same unit, and then

in accordance with the order from the bottom up

Yici, calculate aggregate importance, end up ranking

value of each option. AHP process was people's

thinking process by fully reflect the preferences of

decision makers, decision makers experience will be

quantified, so as to provide decision makers with

quantitative forms of decisions making. But its

limitations can not be ignored: it relies heavily on

people's experience, subjective factors is large, it can

only rule out the thought process up to the serious

non-compliance, but can not rule out the possible

existence of individual decision-makers A serious

one-sidedness.

2.3 Evaluation of the Significance

of AHP-DEA

The above method of DEA-AHP method described

shows, DEA methods for assessing the results of the

program is totally dependent on the objective

evaluation of indicator data, without considering the

preferences of decision makers, and can only be

divided into units based on the dichotomy of

decision-making both active and inactive Part of

effective decision-making unit of the information

given is too small, can not be a reasonable sort; and

simple AHP, due to the characteristics of semi-

qualitative semi-quantitative determined by its lack

of strict objectivity, subjective factors, too. Taking

into account the practical problems of evaluation

reflects the degree of importance among may vary,

so the decision makers in order to reflect the

preferences of the different level of evaluation, so

that the evaluation of a more comprehensive and

reasonable, considering the above two methods the

author Advantages and disadvantages in use of data

envelopment analysis and analytic hierarchy process

method are combined to establish the subjective and

objective integrated multi-objective comprehensive

evaluation model. The model make up the traditional

method of data envelopment analysis does not

consider the lack of decision-makers preferences,

and overcome the many levels of analysis and

decision making the current weakness of

subjectivity, the evaluation results more

comprehensive and more realistic.

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528

3 THE STEPS OF OPERATION

3.1 Determine the Comprehensive

Evaluation Index System

After the disaster, need to provide emergency

support by emergency logistics. Information systems

in the process of the establishment may be abreast of

the situation and help the government and relief

workers to better organize the relief work. After the

disaster, a different geographic location should adopt

different means of transportation, but they are time

efficient in order to achieve the ultimate goal.

Organize and direct the work of the emergency

logistics, largely depends on the functioning of the

Government, pragmatic and efficient government

departments to organize and command the

emergency key to the success of logistics.

Emergency funds management, resource

availability, quality, utilization, efficiency is the

focus of government management. The performance

of government logistics performance directly affects

the level of emergency. Greater chance of sudden

disasters, as in emergency logistics will face many

problems can not be predicted, which requires the

strain relief workers have the ability to act

decisively, through peacetime training and exercises

in dealing with real problems can be quickly and

effectively. A state of emergency to deal with

emergency incidents is the key to effective

functioning of government functions and

coordination. When the disaster occurred, the

government needs through statistical property loss

rate, affected by the number and scope of post-

disaster disaster feedback, documentation kept

facilitate future reference to justice. We can set up

an emergency measure logistics performance

evaluation system, see Table 1.

Table 1: Emergency Evaluation System of logistics

performance measurement.

Framework

Elements

Index name

Form and

Content

Emergency

Information

System A

1

Normative B

11

Index

Timely feedback B

12

Index

Safety and secrecy B

13

Index

Condition

Of Disaster

A

2

Natural Factors B

21

Level

Human factors B

22

Level

Location A

3

City B

31

Index

Rural B

32

Index

Natural Area B

33

Index

Table 1: Emergency Evaluation System of logistics

performance measurement (cont.).

Traffic A

4

Port Facilities B

41

Level

Road Facilities B

42

Level

Aviation facilities B

43

Level

Pipeline facilities B

44

Level

Governmen

t

Administrat

i-on A

5

Emerge-

ncy

Logisti-

cs Costs

B

51

Transportation

costs

Proportion

Warehousing costs Proportion

Handling costs Proportion

Labor costs Proportion

Avail-

ability

of

Suppl-

ies

B

52

Avai

labili

ty

Convenience

Index

Timely

Index

Complete

Index

Reso

urce

call

Usually

reserves

Proportion

Proportion

Proportion

Social

contributions

Proportion

Emergency

Procurement

Proportion

Quality

B

53

Quality materials Index

Shipping Quality Index

Utilizati

on of

Supplies

B

54

Type Proportion

Quantity Proportion

Specifications Index

Recycling Rate

Efficien

-cy B

55

Material Delivery

Time

Time

People Arrival

Time

Time

Rescue

workers A

6

Organizers B

61

Index

Training B

62

Level

Experts B

63

Proportion

Governmen

t

coordinatio

n

mechanism

A

7

Advantage of Government

Coordination B

71

Index

Aftermath

A8

Loss of Property B

81

Proportion

Number of People Affected

B

82

Proportion

Areas B

83

Proportion

PERFORMANCE EVALUATION OF EMERGENCY LOGISTICS BASED ON DEA-AHP ALGORITHM

529

3.2 Determine the Weight of Each

Index System

As the special nature of emergency logistics,

emergency logistics management capabilities in

building evaluation system should be strengthened

in terms of speed indicators, and weakening

economic indicators system, it can be reflected by

the weight.

The index weight was determined by expert

evaluation of. The determination of one, two weight

is show in Table 2, Table 3.

Table 2: Logistics performance indicators weight

determination of level 1.

N

.

Mea-

sure

E1 E2

…

En Mean Normalized

1 A

1

A

11

a

12

…

a

1n

a

1=

na

n

i

i

/

1

1

∑

=

c

1

=

∑

=

8

1

1

/

i

i

aa

2 A

2

a

21

a

22

…

a

2n

a

2=

na

n

i

i

/

1

2

∑

=

c

2

=

∑

=

8

1

2

/

i

i

aa

… … … … … … … …

8 A

8

a

81

a

82

…

a

8n

a

8=

na

n

i

ni

/

1

∑

=

c

8

=

∑

=

8

1

3

/

i

i

aa

Table 3: Logistics performance indicators weight

determination of level 2.

L1

L

2

E1

…

En Mean Normalized

A

1

B

1

1

b

11

1

…

b

11n

b

11=

nb

n

j

j

/

1

11

∑

=

d

11

=

∑

=

3

1

111

/

j

j

bb

B

1

2

b

12

1

…

b

12n

b

12=

nb

n

j

j

/

1

12

∑

=

d

12

=

∑

=

3

1

112

/

j

j

bb

B

1

3

b

13

1

b

13n

b

13=

nb

n

j

j

/

1

13

∑

=

d

13

=

∑

=

3

1

1

/3

j

j

bb

Table 3: Logistics performance indicators weight

determination of level 2 (cont).

… … …

…

… … …

A

8

B

8

1

b

81

1

…

b

81n

b

81=

nb

n

j

j

/

1

81

∑

=

d

81

=

∑

=

3

1

881

/

j

j

bb

B

8

2

b

82

1

…

b

82n

b

82=

nb

n

j

j

/

1

82

∑

=

d

82

=

∑

=

3

1

882

/

j

j

bb

B

8

3

b

83

1

…

b

83n

b

83=

nb

n

j

j

/

1

83

∑

=

d

83

=

∑

=

3

1

883

/

j

j

bb

3.3 Quantify the Indicators of Level2

Use interval [0, 1] as indicate the pros and cons of

each index. 0 is the worst, 1 is the best.

Index system can calculate the value of the index

should be calculated by using actual data, for data

can not be quantified or non-comparable should deal

with expert evaluation.

Table 4: Logistics performance measurement indicators of

level 2.

NO. Indicators Pros and cons of degree

1 B

11

e

11

2 B

12

e

12

… … …

24 B

83

E

83

The value of A

1

, A

2

, …, A

8

are set with Q

01

, Q

02

,

…, Q

08

.

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

•=

11

13

12

),,(

13121101

e

e

e

dddQ

…

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

•=

81

83

82

),,(

83828108

e

e

e

dddQ

Q

0

= (Q

01

, Q

02

, …, Q

`

)

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

530

This problem can be further transformed into an

equivalent output maximization linear programming

problem as follows:

∑

=

=

M

m

mom

yu

1

max

s.t.

0

11

≤−

∑∑

==

N

n

nkn

M

m

mkm

xvyu

k=1,2,…,K.

1

1

0

=

∑

=

N

n

nn

xv (1)

u

m

, v

n

≥

0, m= 1,2,…,M;

n= 1,2,…,N.

Model (1) is known as the CCR in multiplier

form. The efficiency scores of DMU

1

to DMU

K

can

be derived by solving K such models. Despite the

linear form of (1), efficiency score is usually

calculated based on its dual problem:

Min

θ

s.t.

∑

=

≤

N

n

nknk

xx

1

0

ϑλ

n=1,2,…,N;

∑

=

≥

M

m

mkmk

yy

1

0

λ

m=1，2，…,M; (2)

0≥

k

λ

k=1,2,…,K.

Input units include A

1

-A

7

, Output unit includes

A

`

. Bring the data into the formula (2).

4 CONCLUSIONS

In this paper, the establishment of logistics system

performance bases on evaluation index system.

Propose the method DEA-AHP. Firstly, use AHP to

assessment the weights of the indicators of the

performance. Secondly, use DEA to calculate the

relative efficiency of indicators for each level of the

system. Last, sort the weight of each index and the

relative efficiency of the logistics system. The

method combines well the advantages of DEA and

AHP. Make up the problem of DEA method which

can not consider the preferences of decision maker,

and the problem of AHP is too subjective. Further

analysis of the results of evaluation of each program

can be obtained and the corresponding improvement

of weak links in each program.

ACKNOWLEDGEMENTS

Our thanks go to everyone who supported our work,

and who provided us lots of material. We also thank

the team members from the company who sponsored

this work, whose support is greatly appreciated.

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