An Integrated Model to Evaluate the Performance of Solar PV Firms

Chun Yu Lin

, Amy H. I. Lee

1,2,3

, He-Yau Kang

and Wen Hsin Lee

Program of Technology Management - Industrial Management, Chung Hua University, Hsinchu, Taiwan, ROC

Department of Technology Management, Chung Hua University, Hsinchu, Taiwan, ROC

Department of Industrial Management, Chung Hua University, Hsinchu, Taiwan, ROC

Department of Industrial Engineering and Management, National Chin-Yi University of Technology,

Taichung, Taiwan, ROC

Keywords: Analytic Hierarchy Process (AHP), Data Envelopment Analysis (DEA), Fuzzy Set, Solar Cells.

Abstract: The use of renewable energy resources is being stressed in the 21st century due to the depletion of fossil

fuels and the increasing consciousness about environmental degradation. Renewable energies, such as wind

energy, fire energy, hydropower energy, geothermal energy, solar energy, biomass energy, ocean power and

natural gas, are treated as alternative means of meeting global energy demands. After Japan's nuclear plant

disaster in March 2011, people are aware that a good renewable energy resource not only needs to produce

zero or little air pollutants and greenhouse gases, it also needs to have a high safety standard to prevent the

chances of hazards from happening. Solar energy is one of the most promising renewable energy sources

with an infinite sunlight resource and environmental sustainability. However, photovoltaic products

currently still require a high production cost with low conversion efficiency. In addition, the solar industry

has a rather versatile market cycle in response to economic conditions. Therefore, solar firms need to

strengthen their competitiveness in order to survive and to acquire decent profits in the market. This

research proposes a performance evaluation model by integrating data envelopment analysis (DEA) and

analytic hierarchy process (AHP) to assess the business performance of the solar firms. From the analysis,

the firms can understand their current positions in the market and to know how they can improve their

business. A case study is performed on the crystalline silicon solar firms in Taiwan.

1 INTRODUCTION

As technology advances, the demand for various

energy resources increases sharply. In addition to the

fluctuations in commodity prices, a heavy burden on

the environment is resulted, and this brings climate

changes, environmental degradations, etc. The

combined effects of the depletion of fossil fuels and

the gradually emerging consciousness about

environmental degradation have made many

countries to realize the importance of making good

use of natural resources and developing renewable

alternative energy resources in the 21st century. In

December, 2009, world leaders met at the United

Nations Climate Change Conference (COP15) in

Copenhagen to tackle with the issue of CO

reduction for stopping global warming before it

causes irreversible damage (SolarCOP 15, 2009).

Intense debate was centered on the challenge of

reducing CO

emissions in each country without

limiting its economic growth and ability to make life

better for the citizens. One of the consensuses was

that renewable energy is the key to CO

reduction

now and in the future. The main advantages of

renewable energy are the absence of harmful

emissions and the conversion of infinite availability

of renewable resources into electricity. Despite the

global economic recession that has an impact on the

demand for clean energy, many developed and

developing countries have recognized that the

development of renewable energies is necessary for

the environment as well as the economy (Mints and

Hopwood, 2009).

While there are many types of PV solar cells,

they basically can be categorized into two main

groups: crystalline silicon and thin film. The

ultimate goal for all kinds of PV technology is to

produce solar electricity at a cost comparable to

currently marked dominating technologies like coal

and nuclear power in order to make it the leading

primary energy source (Wikipedia, 2009). PV

technologies currently face a wide range of problems

609

Yu Lin C., H. I. Lee A., Kang H. and Hsin Lee W..

An Integrated Model to Evaluate the Performance of Solar PV Firms.

DOI: 10.5220/0004030606090613

In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics (OMDM-2012), pages 609-613

ISBN: 978-989-8565-22-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

from a lack of knowledge of basic material

properties, availability of production technologies, to

legal concerns about patent infringements and

market perspectives. The PV industry is

transitioning from production in relatively small

factories, with capacities of 10 to 100 MW per year,

to much larger ones producing up to 1 GW or more

per year (Applied Materials, 2008). Such

manufacturing transition is analogous to the early

years of semiconductor industry and recent flat panel

display (FPD) industry, both of which depend on

highly automated, high-volume manufacturing

technologies. Thus, some technologies from the two

industries are immediately applicable to making

solar cells in volume production.

In this paper, an incorporation of fuzzy analytic

hierarchy process (FAHP) and data envelopment

analysis (DEA) is used in the proposed model. The

rest of the paper is organized as follows. In the next

section, FAHP and DEA are introduced. In section

3, FAHP model incorporated with DEA is

constructed. A case study is presented next in

section 4. Some conclusion remarks and future

research directions are made in the last section.

2 METHODOLOGIES

2.1 Fuzzy Analytic Hierarchy Process

(FAHP)

AHP is a mathematically-based multi-criteria

decision-making (MCDM) tool (Saaty, 1980). Under

AHP, a complex problem is decomposed into

several sub-problems in terms of hierarchical levels,

and the factors of the same hierarchical level are

compared relative to their impact on the solution of

their higher level factor. Since uncertainty may need

to be considered in some or all pairwise comparison

values, the incorporation of fuzzy set theory into

AHP is recommended (Yu, 2002). The application

of FAHP has gained popularity in the past decade,

and an approach can be as follows (Lee, Kang and

Wang, 2006):

1. Form a committee of experts to define the

problem and to decompose the problem

hierarchically.

2. Formulate a questionnaire based on the proposed

structure to compare pairwise elements, or factors, in

each level with respect to every element in the next

higher level. Five-point scale is usually applied in

fuzzy AHP rather than nine-point scale, which is

often used in the traditional AHP method. Triangular

membership functions can be defined to represent

linguistic terms for facilitating judgment and

integrating different experts’ opinions (Chi and Kuo,

2001).

3. Establish fuzzy judgment matrix. With a fuzzy

number,

, to represent the relative

contribution of each element on the objective or the

adjacent upper-level criterion, a fuzzy judgment

vector can be built for each element, and the

triangular fuzzy numbers

are defined as in

Table 1.

]

[

321 ijiiiij

xxxx ⋅⋅⋅

(1)

where

is the relative contribution of element j on

element i.

A fuzzy judgment matrix can next be built to

compose all fuzzy judgment vectors:

⎥

⎦

⎤

⎢

⎣

⎡

mnmm

xxx

~~~

22221

11211

MMMM

(2)

Table 1: Characteristic function of the fuzzy numbers.

Fuzzy number Characteristic (Membership) function

(1, 1, 3)

(x –2, x, x+2) for x =3,5,7

(7, 9, 9)

4. Establish fuzzy weight vector. The weights of

criteria, which are supplied by experts’ opinion, can

be represented by a fuzzy weight vector,

[

]

www

⋅⋅=w

, where 9

w .

5. Establish and rank aggregate fuzzy numbers. The

aggregate fuzzy numbers,

, are obtained by

multiplying the fuzzy judgment matrix

with the

corresponding fuzzy weight vector,

(Lee et al.,

2006):

⊗X

⎥

⎦

⎤

⎢

⎣

⎡

mnmm

xxx

~~~

22221

11211

MMMM

⊗

⎥

⎦

⎤

⎢

⎣

⎡

⋅

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

610

⎥

⎦

⎤

⎢

⎣

⎡

⊗⊕⊕⊗⊕⊗

nmnmm

wxwxwx

~~~~~~

2211

2222121

1212111

(3)

⎥

⎦

⎤

⎢

⎣

⎡

⋅

6. Fuzzy numbers can then be ranked by one of the

many different methods, and each method has its

own advantages and disadvantages (Klir and Yuan,

1995). A popular method is the

-cut method. Let

be (p

, q

, s

). By defining the interval of

confidence at level

, the triangular fuzzy number

can be characterized as

[]

() ()

[]

sqsppqsp

+−−+−==

ααγ

ααα

(4)

[]

1,0∈∀

2.2 Date Envelopment Analysis (DEA)

DEA, introduced by Charnes, Cooper and Rhodes in

1978, was first applied to investigate not-for-profit

organizations whose success cannot be measured by

a single measure, such as profit (Charnes et al.,

1978). A relative efficiency score of decision

making unit (DMU) is obtained under multiple

inputs and outputs, and the DMUs that locate on the

frontier, the envelopment, are considered to be the

most efficient.

The most popular two models of DEA are CCR

and BCC. CCR, introduced by Charnes, Cooper and

Rhodes, generates efficiency in ratio form by

obtaining directly from the data without requiring a

priori specification of weights nor assuming

functional forms of relations between inputs and

outputs. Because nonlinear programming of

fractional form cannot be solved easily, the problem

is transformed into a linear programming problem.

The input-oriented CCR model, CCRd-I, is

introduced briefly here (Charnes et al., 1978; Chung,

Lee, Kang and Lai, 2008). Assume that there are n

DMUs, and each is represented by DMUj

where

nkj ...,,...1=

. For each DMU, there are m

inputs (

;

mi ,...,1=

) and r outputs (

;

,1=r

…,s). The input of factor i for DMU j is

and the output of factor i for DMU j is

. The

efficiency of DMU

can be obtained as follows:

Min

⎟

⎠

⎞

⎜

⎝

⎛

∑∑

+−=

+−

rikk

ssh

εθ

(5)

s.t

∑

=+−

−

iikkijj

sXX

θλ

mi ,...,1=

(6)

∑

=−

rkrrjj

YsY

,1=r

…, s

(7)

,0,, ≥

+−

rij

nj ,...,1

mi ,...,1

,1=r

…, s

(8)

where

+−

ss ,

are the slack variables of inputs and

outputs respectively,

is the weight for DMU

and

is the relative efficiency indicator of the kth

DMU.

3 AN INTEGRATED MODEL FOR

PERFORMANCE OF SOLAR PV

FIRMS

In this research, an integrated FAHP/DEA model for

evaluating the business performance of PV firms is

proposed. In the conventional DEA, quantitative

factors can be evaluated objectively, and

productivity (output/input) can be measured

effectively. However, the weighting of each factor

cannot be subjectively determined by experts. On

top of these, a good decision-making model should

be able to tolerate vagueness or ambiguity, and

fuzzy set theory, thus, is recommended to solve the

problem. As a result, this research integrates the

concepts of fuzzy set theory, AHP and DEA, and

proposes a FAHP/DEA methodology. The steps of

the proposed model are summarized as follows:

Step 1: Define the performance evaluation

problem in the PV industry.

Step 2: Determine the competitive factors for

evaluating PV firms.

Step 3: Collect the data of each factor from the PV

firms under study.

Step 4: Calculate the assurance ranges (AR) of the

factors by the FAHP.

Step 5: Determine the efficiencies of the PV firms

by the DEA.

The DEA/AR model (Shang and Sueyoshi, 1995;

Zhu, 1996; Liu, 2008) is used to calculate the

efficiencies of the PV firms. The outcomes from

Step 3 and 4 are used in the model, and the overall

performance of the firms can be generated. The

DEA/AR model for measuring the AR efficiency of

AnIntegratedModeltoEvaluatethePerformanceofSolarPVFirms

611

a selected DMUr is as follows:

max

rkrk

∑

(9)

s.t. 1

jrj

∑

(10)

kik j ij

uY vX

−≤

∑∑

1, 2,3......in=

(11)

≥>

(12)

where the E

is the relative efficiency of the rth

DMU taking into account the minimum and

maximum influence that each factor can have on E

is the amount of jth input (j=1,…,s) of the ith

DMU, Y

is the amount of the kth output (k=1,…,t)

of the ith DMU, v

and u

are the weights of the jth

input and the kth output respectively, and

is a

small non-Archimedean number. Set the relative

importance elicited from the experts range from L

to U

for output p and from L

to U

for output q,

and from L

to U

for input p and from L

to U

for

input q. The associated constraints are as following:

tqpLUuuUL

qpqp

OOqpOO

,.....2,/// =<≤≤

(13)

sqpLUvvUL

qpqp

IIqpII

,.....2,/// =<≤≤

(14)

With the above model, the efficiencies of the PV

firms can be calculated.

4 CASE STUDY

The proposed model is applied to evaluate the

current position of firms in a specific sector in the

PV supply chain in Taiwan. Five inputs and three

outputs are selected in the case study. The five

inputs are fixed assets (I1), cost of goods sold (I2),

general and administrative expenses (I3), research

and development expenses (I4), and selling expenses

(I5). The three outputs are sales revenue (O1),

income before income taxes (O2) and earnings per

share (O3). A questionnaire based on the hierarchy

is filled out by the experts, and pairwise comparison

matrices for each expert are prepared. The pairwise

comparison matrix of the inputs for the first expert is

shown as follows:

123 45

III I I

(1,1,1) (1,2,3) (1,2,3) (1/6,1/5,1/ 4) (1,1,1)

(1/ 3,1 / 2 ,1) (1,1,1) (1,1,1) (1 / 5,1 / 4,1/ 3) (1 / 5 ,1 / 4,1/ 3)

(1,1,1) (1,1,1)

(1,1,1)

Expert

Input

⎡

⎤

⎢⎥

⎣⎦

Using the geometric average method to synthesize

the experts’ opinions, the aggregated pairwise

comparison matrix of the inputs is:

123 45

III II

(1. 0000, 1. 0000,1. 0000) ( 0. 6988,1. 0000, 1.4310 ) ( 0. 8027,1. 1914,1. 7188) ( 0. 2205, 0. 2841, 0. 4014) ( 0. 4353, 0. 5173, 0.6598 )

(1. 0000, 1. 0000,1. 0000) (0. 4152, 0. 5743,1. 000) ( 0. 2422, 0. 3222, 0. 4

Inputs

884) ( 0. 2565, 0.349 4, 0.5610)

(1. 0000, 1. 0000,1. 0000) ( 0. 3155, 0. 4503, 0.6598) ( 0. 2782, 0. 3342, 0. 4251)

(1,1,1) ( 0. 5173, 0.6598 ,1, 0000)

(1,1,1)

⎡

⎤

⎢

⎥

⎢

⎥

⎢

⎥

⎢

⎥

⎢

⎥

⎢

⎥

⎣

⎦

The priorities of the inputs are:

Inputs

I1 (0.12,0.12,0.13)

I2 (0.10,0.10,0.12)

I3 (0.12,0.12,0.13)

I4 (0.29,0.30,0.31)

I5 (0.32,0.33, 0.33)

⎡

⎤

⎢

⎥

⎢

⎥

⎢

⎥

⎢

⎥

⎢

⎥

⎢

⎥

⎣

⎦

By applying the

-cut method and setting

to be

0.5, the priorities of the inputs are:

Inputs

I1 [0.13,0.13]

I2 [0.10,0.11]

I3 [0.12,0.13]

I4 [0.30,0.31]

I5 [0.32, 0.33]

⎡

⎤

⎢

⎥

⎢

⎥

⎢

⎥

⎢

⎥

⎢

⎥

⎢

⎥

⎣

⎦

The same procedure is carried out to calculate the

priorities of the outputs, and they are:

Outputs

O1 [0.21, 0.22]

O2 [0.39, 0.39]

O3 [0.38,0.38]

⎡

⎤

⎢

⎥

⎢

⎥

⎢

⎥

⎣

⎦

Let the weight for input I1 to input I5 be v

,…, v

respectively, the ratio v

has the lower bound of

1.18 (0.13/0.11) and upper bound of 1.3 (0.13/0.10).

The AR for each pair of inputs and each pair of

outputs can be calculated, as shown in Table 2.

5 CONCLUSIONS

A good evaluation of the firms in the PV industry

and an understanding of a firm’s position in the

market are important for the firm to improve its

competitiveness in the market. In this study, a

FAHP/DEA model is proposed to evaluate the

efficiencies of the firms in a market. The assurance

ranges for inputs and outputs are calculated. A case

study of crystalline silicon solar firms in Taiwan will

be carried out using the proposed model.

Taiwan has a strong background and foundation

for developing the PV industry because of the

successes of the semiconductor and TFT-LCD

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

612

manufacturing industries in Taiwan. After the

analysis is performed using the proposed model, the

findings shall help the firms determine their

strengths and weaknesses and provide directions for

future improvements in business operations.

Table 2: Assurance range for inputs and outputs.

Ratio Lower bound Upper bound

0.13/0.11

0.13/0.10

0.13/0.13

0.13/0.12

0.13/0.31

0.13/0.30

0.13/0.33

0.13/0.32

0.10/0.13

0.11/0.12

0.10/0.31

0.11/0.30

0.10/0.33

0.11/0.32

0.12/0.31

0.13/0.30

0.12/0.33

0.13/0.32

0.30/0.33

0.31/0.32

0.21/0.39

0.22/0.39

0.21/0.38

0.22/0.38

0.39/0.38

ACKNOWLEDGEMENTS

This work was supported in part by the National

Science Council in Taiwan under Grant NSC 100-

2628-H-216-001-MY3.

REFERENCES

Applied Materials (2008). Thin films solar cells. Retrieved

from:

http://www.appliedmaterials.com/products/thin_films_

solar_cells_5.html.

Charnes, A., Cooper, W. W., Rhodes, W., (1978).

Measuring the efficiency of decision making units.

European Journal of Operational Research, 2, 429-

444.

Chi, S. C., Kuo, R. J., (2001). Examination of the

influence of fuzzy analytic hierarchy process in the

development of an intelligent location selection

support system of convenience store. IFSA World

Congress and 20th NAFIPS International Conference,

3, 1312-1316.

Chung, S. H., Lee, A. H. I., Kang, H. Y., Lai, C. W.,

(2008). A DEA window analysis on the product family

mix selection for a semiconductor fabricator. Expert

Systems with Applications, 35, 379-388.

Klir, G. I., Yuan, B., (1995). Fuzzy Sets and Fuzzy Logic:

Theory and Applications. London: Prentice-Hall

International.

Lee, A. H. I., Kang, H. Y., Wang, W. P., (2006). Analysis

of priority mix planning for semiconductor fabrication

under uncertainty. International Journal of Advanced

Manufacturing Technology, 28(3-4), 351-361.

Liu, S. T., (2008). A fuzzy DEA/AR approach to the

selection of flexible manufacturing systems.

Computers & Industrial Engineering, 54(1), 66-76.

Mints, P., Hopwood, D., (2009). Can solar PV beat the

downturn. Renewable Energy Focus,

January/February, 62-65.

Saaty, T. L., (1980). The Analytic Hierarchy Process, New

York: McGraw-Hill.

Shang, J., Sueyoshi, T., (1995). A unified framework for

the selection of a flexible manufacturing system.

European Journal of Operational Research, 85, 297-

315.

SolarCOP 15, (2009). Why SolarCOP 15? Retrieved from:

http://www.solarcop15.org/.

Wikipedia, (2009). Solar cell. Retrieved from:

http://en.wikipedia.org/wiki/Solar_cell.

Yu, C. S., (2002). A GP-AHP method for solving group

decision-making fuzzy AHP problems. Computers &

Operations Research, 29, 1969-2001.

Zhu, J., (1996). Data envelopment analysis with

preference structure. Journal of the Operational

Research Society, 47(1), 136-150.

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