the operational efficiency of spa case in taiwan an application of dea

Australian Journal of Asian Country Studies

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The Operational Efficiency of Spa Case in Taiwan - An

Application of DEA

PUREVDULAM Altantsesteg

Department of Business Administration, College of Management, Asia University

500, Liofeng Rd, Wufeng, Taichung 41354

+886(0)978843521 [email protected]

Abstract

The Spa industry in Taiwan has been identified as one of the fastest growth industry. As the

result, this industry has become one of vital sectors of the Taiwan Economy. The present study will use

case company which is experiencing fast business growing in spa. There are twenty spa centers will be

measured its efficiency by using Data Envelopment Analysis (DEA) and Meta-frontier.

The inputs chosen for the DEA Model used in this study including Total Operating Cost and

Treatment Room and for the outputs are Total Revenue and Number of Customers. The findings show

that there are 3 spa branches operating efficiently in central area, 2 spa branches operating efficiently in

northern area.

Afterward, continued to run Meta-frontier analysis in both areas. The result shows that there

are only two spa branches from twenty samples are identified as efficient spa branches. This study

suggests to the management of spa to take some actions by input reductions and/or augment the outputs

in order to increase the efficiency.

Keywords: Data Envelopment Analysis (DEA), Meta-frontier, Efficiency, SPA

Introduction

This paper will study about spa industry as area of leisure and tourism industry which is growing

very fast in Taiwan. In Taiwan the fast spa growing was pioneered by the promotion of living

standards and the increase of leisure activities and tourism in Taiwan. Leisure tourism has become

the important area of the modern life in Taiwan. This condition also supported since the

implementing the new holiday policy in 2001 in Taiwan. This new policy, however, has been responded

positively by most of Taiwanese people, especially who live and work very hard with many pressures

during working hours. As the result, most of Taiwanese, either man or woman will prefer to go to Spa

for healing and nourishing mind, body, and spirit, or in another word; the holistic beauty and health. As

a type of service industry with target customers from big city, most of spas in Taiwan are located in

Taipei. Intelligent Spas Data (released in 2007), mentioned that around 48% Spas are located in Taipei

city, and the rest of Spas are located in the other big cities such as Taichung, Kaohsiung and Tainan.

Key Terminologies of this study: Some terminologies will be employed in this study, such as:

- Operational Efficiency: In a business context, operational efficiency can be defined as the

ratio between the input to run a business operation and the output gained from the business

(Farrell, 1957).

- Data Envelopment Analysis: Data Envelopment Analysis (DEA) is one of the measurement

techniques that is used for efficiency analysis, is a nonparametric and linear Programming-

based technique which is useful to measure the relative efficiency of profit-oriented and

non-profit-oriented firms. It was first introduced in the literature in 1978. Charnes et al.

(1978) are the first who introduced the DEA to describe the mathematical programming

approach to the construction of production frontiers and the measurement of efficiency of

developed frontiers.

- Decision Making Unit (DMU): DMU is commonly used to refer any groups, institutions such as

branch stores, organization divisions, business offices, different manufacturing sites, work teams,

and so forth. A DMU is regarded as the entity responsible for converting inputs (i.e., resources,

money, etc.) into outputs (i.e., sales, profits, certain performance measures, etc.) and whose

performance is to be evaluated (Charnes et al., 1978).

- Meta-frontier: A meta-frontier is a useful concept when the aim of the analysis is to compare

the efficiency of different groups (e.g., regions, countries) when there is the suspicion that each

group operate under different technologies and therefore their productive frontiers are different.

- Spa: Spa has been defined as ‗a business offering spa treatments based on authentic

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water-based therapies which are practiced by qualified personnel in a professional and relaxing

environment‘ (Intelligent Spas, 2007). This definition incorporates a water element based on the

original definition of spa interpreted as ‗healing through water‘, as well as includes a relaxation

element to address contemporary spa consumers ‘ definition of spa as ‗a place to relax‘ (Garrow,

2005) .

By doing this study, it will enrich the academic literatures especially in the leisure industry by

employing DEA application to measure the operational efficiency in case of spa business in Taiwan.

One factor which is also crucial for spa business is maintaining the operational efficiency. As

part of business in the leisure tourism sector, spa becomes one of the most rapid growth industries

which also need to concern about its efficiency. Operational efficiency is affected not only by

controllable input and output variables but also by uncontrollable factors such as environmental

effects, location, economic environment, and years of operation.

In this study, we chose to use DEA due to its capability of estimating efficiency of the Decision

Making Units (DMUs) that typically use multiple inputs to produce multiple outputs.

The type of DEA which is used in this study is the input-oriented envelopment CRS Model in order to

identify the efficient and inefficient DMUs (refer to Spa branches). In this study, Data Envelopment

Analysis (DEA) is used as the research methodology.

Operational Efficiency Concept

The productivity and efficiency are important for firms, especially in competitive environments.

Efficiency should be considered as a key element for achieving greater revenue and enhancing market

position. In recent, years, a nonparametric technique namely data envelopment analysis (DEA) has

been used successfully in measuring the efficiency of organizations in the service industry, such as

banks, hospitals, educational institutions, nonprofit organizations, etc.In order to produce meaningful

efficiency scores, there are some crucial factors must be considered before the DEA analysis is done,

such as:

A sufficient number of DMUs is needed to perform DEA. The number of degrees of freedom

increases with the number of DMUs and decreases with the number of inputs and outputs. As

proposed by Cooper, W.W., Seiford, L.M., and Tone, K. (2007), a general rule for the minimum

number of DMUs (n) is that it should exceed the greater of the product of the input (m) and

output (s) variables or three times the sum of the number of input (m) and output (s) variables.

Hence, the Formula can be defined as: n > max { m x s,3 (m+s)}

Appropriate inputs and outputs must be chosen to represent the unit‘s production process as the

model requires, including all the resources impacting the outputs and all useful outcomes for

evaluation. Furthermore, such inputs and outputs must be controllable by the management to

produce significant results that can be applied in the industry.

Generally, efficiency can be measured as the ratio of outputs/inputs. The higher this ratio is, the more

efficient the unit is:

Efficiency Score of DMU = Max (Outputo/ Inputo)

= Max {(u1y10+u2y20+…) / (v1x10+v2x20+...)}- - - - - - -

Data Envelopment Analysis (DEA)

DEA is a linier (mathematical) programming based technique and the basic model only requires

information on inputs and outputs (Charnes et al., 1978). As a mathematical programming model, Data

Envelopment Analysis (DEA) is defined as a mathematical programming model applied to the

observational data that provides a new way of obtaining empirical estimates of external relations –

such as the production functions and/or efficient production possibility surfaces that are a cornerstone

of modern economics.

DEA utilizes inputs to produce outputs. DEA provides a scalar measure of relative

efficiency by comparing the efficiency achieved by a decision making unit (DMU) with the

efficiency obtained by similar DMUs. The method allows us to obtain a well-defined relation

between outputs and inputs. As a simple view, DEA is (Charnes et al., 1978):

Therefore, efficiency indicator of a particular DMU depends on the relationship between the

weighted inputs and the weighted outputs. The original DEA model selects weights for each DMU

to maximize the efficiency. With assessing all the DMUs, DEA makes an ―efficiency frontier‖ and

identifies each DMU relative efficiency.

DEA is designed to identify the best practice DMU without a priori knowledge of which inputs and


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outputs are most important in determining an efficiency measure (i.e., score) and assessing the extent

of inefficiency for all other DMUs that are not regarded as the best practice DMUs (Charnes et al.,

1978). Since DEA provides a relative measure, it will only differentiate the least efficient DMU from

the set of all DMUs. Thus, the best practice (most efficient) DMU is rated as an efficiency score of

one, whereas all other less efficient DMUs are scored somewhere between zero and one.

Since DEA in its present form was first introduced in 1978; researchers in a number of fields

have quickly recognized that it is an excellent and easily used methodology for modeling operational

processes for performance evaluations. This has been accompanied by other developments. For

instance, Zhu (2002) provides a number of DEA spreadsheet models that can be used in performance

evaluation and benchmarking. DEA‘s empirical orientation and the absence of a need for the numerous

a priori assumptions that accompany other approaches (such as standard forms of statistical regression

analysis) have resulted in its use in a number of studies involving efficient frontier estimation in the

governmental and nonprofit sector, in the regulated sector, and in the private sector.

In a summary, DEA is a method to measure relative efficiency of different decision making

units (DMUs) or producers based on their observed inputs and outputs. The most efficient for DMU

efficiency score is one (1) and for those whose efficiency score is between 0 and 1 are identified as

inefficient DMUs . DEA is an effective and widely used method for evaluating the relative efficiency of

peer decision-making units (DMUs) with multiple inputs and outputs. The basic ideas and concept

definition of DEA were already introduced by Farrell (1957).

The Meta-frontier

A meta-frontier is a useful concept when the aim of the analysis is to compare the efficiency of

different groups (e.g., regions, countries) when there is the suspicion that each group operate under

different technologies and therefore their productive frontiers are different. In this brief overview we

follow O‘Donnell et al. (2007). The starting point of the meta-frontier analysis is the idea that there is a

space (i.e., a meta-technology set) that encompasses all the possible combinations of outputs (y) and

inputs (x). Associated to such set are output and input sets. Graphically, the meta-frontier and the

frontiers can be represented by Figure 2.2 below, where the efficiency of all firms within the regions

farms can be measured relative to their own frontier (a, b, c) or with respect to the meta-frontier (C,A).

Spa case company is currently one of the largest and most professional beauties SPA in Taiwan

that has already had more than 40 branches.

Recently, there are 45 spa branches of the Company located in Taiwan, with the total

number of employees about 500 people. The policy about human resources in the company is well

designed in order to make their employees feel comfortable to work and serve their customer.

As we look into the characteristic of this day spa, normally day spa is larger in terms of

indoor space when compared to the average of all spas. In addition, day spas also contained more

treatment rooms, and mostly located in metropolitan cities. The customers for this type of this type of

spa are mostly women.

As with many businesses that rely on customer interaction, location is the most important

aspect in any venture. Most of the branch location of the spa case company are located in the area

where customers can access either by public transportation or by their own vehicles such as

motorcycle (in Taiwan called scooter) or by car. Most of spa branches are concentrated in Northern of

Taiwan such as Taipei City compared to central of Taiwan such as Taichung city and surrounding

areas.

Finally, under the area department of Spa Company, there are some deputy area managers who

responsible for the spa branches in a specific area (region). These deputy area managers will also lead

the branch managers who responsible for running the spa branches. The branch managers‘ position

refers to a position that responsible for at least three spa branches. In case less than 3 spa branches, the

position is called as deputy branch managers. In addition, these branch managers will also have to

manage the staffs including therapists, estheticians that exist in the spa branches.

Nowadays Spa in Taiwan has become a lifestyle. Most of the Spa customers in Taiwan are

Taiwanese, and only 5 percent of the Taiwan spa industry's customers are non-Taiwanese (Intelligent

Spas, 2007). However, if we look into the case company, most of the customers of case company are

over than 35 years old. Hence, the case company is still having an opportunity to target the customers

lower than 35 years old. In addition, the case company is also still having a chance to add new

branches to reach 50 branches until 2014.

In this study, data (input and output variables) that are going to be processed can be defined as

follows:

1. Input variables


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Total Operating Cost (X1): the items of operation cost of spa case company include salary,

measured in units of thousands NT$ dollars. The number of treatment room (X2): refer to

the amount of treatment rooms that can be provided for the treatment, for example

massages. The unit of measurement is simply ―rooms‖ without subsequent adjustment

being made for size and quality.

2. Output variables

Total revenue (Y1): the operational revenues of spa branches from 20 spa branches (samples),

measured in units of thousands NT$ dollars.

The Number of customers (Y2): the total of customers visits the spa center for having

treatments provided by the spa branches. The unit of measurement is simply

―persons‖.

Method

Survey is a method used to collect in a systematic way, data information from target respondents. In

this study, the target respondent is the General Manager of the spa case company who has the dataset

of all spa branches. The survey methods used in this study were personal interview and questionnaire.

Interview

Interview is one of data collection for primary data in this research. Interview is defined as ―a method

of data collection that involves researchers seeking open-ended answers related to a number of

questions, topic areas or themes‖ (O‘Leary, 2010). The interview used in this study is judgmental

sampling method. This method is chosen because of the knowledge and professional judgment of the

selected sample (Westfall, 2009). Hence, the interview was undertaken few times with General

Manager of the spa case company in the office during working hour. The questions that the General

Manager was asked was for the most part open-ended. The interview also was accompanied by an

assistant as translator because the General Manager of the spa case company only fluent in Chinese and

a little bit English for conversation.

Questionnaire

Questionnaire is a form that people fill out, used to obtain demographic information and views and

interests of those questioned. Kirakowski (1998) defines a questionnaire in a more structural way as "a

method for the elicitation, and recording and collecting information". The data of the questionnaire

were taken as of the year 2011. The data survey was carried out between April and May 2012 in

selected spa branches in two main areas: Central area of Taiwan (such as Taichung City) and Northern

area of Taiwan (such as Taipei City). The questionnaire delivered to 20 spa branches in the two main

areas of Taiwan.

Primary data is a data which gathered for first time for any specific study. The primary data for this

study was derived from spa case company via questionnaire to the selected spa branches. The

selection of the spa branches used in this study based on the characteristics such as the years of

establishment. We will measure the operational efficiency of the spa branches which have already

established over than or equal to 3 years. In fact, most of the spa branches are located in central and

northern area of Taiwan have been established more than 3 years, compared to the spa branches in

the southern area which are still new (less than 3 years).

In addition, regarding to the availability of data given by the respondent, then there were only 20 spa

branches are chosen to be used in this study and these 20 spa branches became the representatives of 45

spa branches because the twenty spa branches are matching with the characteristics mentioned above.

The questionnaire will be designed according to the required data needed to develop DEA Model and

by referring to the previous studies which similar to this study.

As the result, the questionnaire design for this paper consists of three sections. First section part is

asking about some basic information about the case company. Second section is asking about the inputs

(variable) used for the operational of case company. The third section is asking about the outputs

(variable) by given inputs in the operating of case company. For the convenience of the respondent to

fill the questionnaire, the language used in the questionnaire was translated into Chinese. But, in this

master thesis (see Appendix A), the questionnaire that attached here will be in English. In addition to

the questionnaire, interview with the spa General Manager was also conducted in order to get some

information about the company that will be explain later in the chapter 3 on this study.

Secondary data will be obtained through books, journals, and relevant websites, internet, or third

party reports that ever did the similar or related research topic.

Sampling Procedures

As one of the biggest spa businesses with 45 branches in Taiwan, the case company is a good


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example of case company for ‗fast growing spa‘ to be used in this study. The primary data for this

study was derived from spa case company via questionnaire to the selected spa branches. The

selection of the spa branches used in this study based on the characteristics such as the years of

establishment. We will measure the operational efficiency of the spa branches which have already

established over than or equal to 3 years.

How to run DEA and Meta-frontier Model

As DEA is conducted by linier programming, then it is possible to use any program that can solve linier

programming models using free software DEA Frontier Software which can be installed in Excel 97,

2000 and 2003 (Add In installation). This software is developed by Tim Joe Zhu and has been used for

calculating the efficiency scores in many academic researches. It is a kind of program developed to

calculate DEA efficiencies. First, we will run DEA in the Excel sheet containing the data for DEA

analysis. The sheet is required to be named ―Data‖. Please note that the first column is recognized as

the DMUs identifier, followed by two columns of inputs and two columns of outputs. Please also note

that there is a blank column between last input and first output column. In this current study also use

two outputs, then we need to define two columns for outputs.

Second, we will use DEA methodology to construct the meta-frontier model by separating frontiers for

different groups in the data set. The group frontiers are constructed by estimating a DEA model for

each group. The estimation of the meta-frontier then follows by applying the same DEA model to the

data set obtained through pooling all observations for firms from all groups

Research Design

Figure 1 shows that the DEA Model of Spa case Company. There are two input variables and two

output variables in this model. By using DEA software analysis, these all four variables will be

measured the efficiency scores and being analyzed to identify which DMU is operating efficiently

and which DMU is not efficient.

Figure 1. DEA Model Spa Case Company

Source: Own construction

In addition to the DEA Model of spa case company, we also apply meta-frontier concept that envelops

all the frontier of individual location/ area.

Table 1 Output Input Brief Explanation

Measure Description

Output

1. Total Revenue Including The daily treatment revenue per available treatment room,

Resource or Department Revenue per Guest for Facility Fee.

2. Number of Customers Total customers who visit the spa during a year including existing

per year customers and new customers.

Input


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1. Total Operating Cost Including all direct and indirect expenses which are charged to the spa

2. The Number of Including the number of rooms that provided for treatment and

Treatment Rooms relaxation.


Empirical result

Spa Branches (Sample Size)

The scope of location for this research includes two major areas; they are Central Area of

Taiwan and Northern Area of Taiwan. The total number of spa branches is 20 branches, 10 branches are

located in the Central Area of Taiwan such as Taichung City and Changhua; 10 branches are located in

the northern area of Taiwan such as Taipei City, New Taipei City, Taoyuan and Hsinchu. Each area has

a branch manager and has to report to the Area Department Manager in the Head office. all branches

used in this research most of them have already established more than 5 years, but there is one branch

that still established less than five years but over than 3 years which is located in central area of

Taiwan. This criteria is considered as a factor to select 20 spa branches samples among 45 spa

branches.

Input output Measures

This study only uses 20 DMUs (Spa branches) during the year 2011. The total operating cost for central

area of Taiwan is about NT 4.738.100. This number is generated by using 88 treatment rooms that

available in all spa branches in the central area of Taiwan. However, the total revenue for central area

of Taiwan can reach NT 11.853.000 with number of customers 63.908 people (including existing

customers and new customers. The data used in this master thesis is actually originating from the

average value in the year 2011 given by spa case company Vice General Manager. The value of the

input and output of each spa center which is located in Northern area of Taiwan. The total operating

cost for northern area of Taiwan is about NT 3.706.100. This number is generated by using 80

treatment rooms that available in all spa branches in the northern area of Taiwan. However, the total

revenue for northern area of Taiwan can reach NT 12.914.000 with number of customers 76.166

people (including existing customers and new customers). By comparing the cumulative values for the

two main areas we can conclude that the total value for input variables in Central area is higher than

input variables that exist in Northern area. Meanwhile, the total value for the output variables in

Central area is lower than output variables that exist in Northern area.

Table 1.1 Descriptive Statistics of the Variables Used in the DEA Model

Area

Total operating

cost Treatment Room Total Revenue

Number of

Customers

Central area of

Taiwan Maximum 819.500 15 2.012.000 10.563

Minimum 195.600 6 750.000 3.970

Mean 437.800 9 1.183.500 6.391

Northern of

area of Taiwan Maximum 582.100 9 1.669.000 10.241

Minimum 222.400 7 860.000 3.935

Mean 370, 61 8 1.291.400 7.617

Source: Own construction; Developed based on data from questionnaire

Heading 1

Central Area of Taiwan

Heading 1.1

a. Efficiency Score

3 out of 10 DMUs are currently operating efficiently, they are TZ2, TZ5, and TZ8. We could see that

these three DMUs are having efficiency score is 1 (one) or in another form is 100% efficient.

Meanwhile, DMU with initial TZ1, TZ3, TZ4, TZ6, TZ7, TZ9 have scores of less than 1 but greater


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than 0, and thus they are identified as inefficient (especially for TZ3 and TZ9), but for TZ1, TZ4,

TZ6, TZ7 are almost efficiency because the scores are closer to efficient frontiers.

Heading 1.2

b. DMU Ranking (DMUs in Central Area of Taiwan)

From Table 1.2, we could identify three DMUs (spa branches) are having efficiency score is equal to 1

(one), which means operating efficiently. Since TZ2, TZ5, and TZ8 is having the same score (efficiency

score = 1), then the ranking position applied for these three DMUs are actually equal. In other word, if

we look from the scope of DEA analysis, they have the same ranking (if we only consider internal

factors, controllable inputs and outputs). If further we want to see their ranking position, we could use a

combination between internal and external factors will show the real ranking each of these three

DMUs. For the other DMUs that has efficiency score less than 1 but greater than 0, we could see the

ranking on the Table 5.8. The lowest score is TZ9 with score 0.85951, which means that this DMU

only operating efficiently 85.95%.

Table 1.2 DMUs Ranking in Central Area of Taiwan

Ranking DMU Efficiency Score Ranking DMU Efficiency Score

1 TZ2 1.00000 6 TZ4 0.94421

2 TZ5 1.00000 7 TZ7 0.91588

3 TZ8 1.00000 8 TZ1 0.91124

4 TZ6 0.97354 9 TZ3 0.86108

5 TZ10 0.95090 10 TZ9 0.85951


Heading 2 Northern Area of Taiwan

Heading 2.1

a. Efficiency Score

Table 1.3 shows two DMUs are currently operating efficiently, they are TP3 and TP4. We could see

that these three DMUs are having efficiency score is 1 (one). Meanwhile, DMU with initial TP1, TP2,

TP5, TP6, TP7, TP8, TP9, TP10 have scores of less than 1 but greater than 0, and thus they are

identified as inefficient. These spa branches can improve their efficiency, or reduce their inefficiencies

proportionately, by reducing their inputs. For example TP1 can improve its efficiency by reducing

certain inputs up to 12.68% (1.0- 0.87320). Similarly, TP2, TP5, TP6, TP7, TP8, TP9, TP10 can do so

with approximately 16.26% for TP2, 21.94% for TP5, 35.39% for TP6, 26.72% for TP7, 20.41% for

TP8, 20.26% for TP9, 24.18% for TP10.

Table 1.3 Efficiency Score for DMUs Northern Area of Taiwan

Input-oriented

CRS

DMU

No

DMU

name

Efficeiency Sum of

lambdas

RTS Optimal

Lambdas

With

Benchmarks

1 TP1 0.87320 0.873 Increasing 0.195 TP3 0.678 TP4


3 TP3 1.00000 1.000 Constant 1.000 TP3

4 TP4 1.00000 1.000 Constant 1.000 TP4





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Total operating cost should be in amount of 215.79 (in NT 000), from previously 257.7

(in NT 000); and the treatment room should only 6.6 (rounded into 7) rooms (previously the

treatment room is 8 rooms). Accordingly, the efficient total revenue will be 1322.83 (in NT 000),

previously the total revenue is 1247 (in NT 000).

The results of DEA Analysis using efficient target for inputs and outputs above have shown how much

the definite resource allocation in the purpose of working efficiently.

Heading 2.2

b. DMU Ranking (DMUs in Northern Area of Taiwan)

From Table 1.4, we could identify 2 out of 10 DMUs (spa branches) are having efficiency score is

equal to 1 (one), which means operating efficiently, they are TP3 and TP4. Since these two DMUs are

having the same score (efficiency score = 1), then the ranking position applied for these three DMUs

are actually equal.

Table 1.4 DMUs Ranking in Northern Area of Taiwan


1 TP3 1.00000 6 TP8 0.79590

2 TP4 1.00000 7 TP5 0.78060

3 TP1 0.87320 8 TP10 0.75815

4 TP2 0.83739 9 TP7 0.73283

5 TP9 0.79737 10 TP6 0.64615


Heading 3

Central and Northern Area of Taiwan

Heading 3.1

a. Efficiency score

We run DEA to all spa branches (DMUs) from both areas, central and northern area of Taiwan. We

found that, there are only two DMUs who have efficiency score is almost all DMUs with initial TZ

(which means Taizhong City and surrounded area) have scores of less than 1 but greater than 0, and

thus they are identified as inefficient. These spa branches can improve their efficiency, or reduce their

inefficiencies proportionately, by reducing their inputs (since this master thesis use input oriented

model). But, there are two DMUs in Northern Area of Taiwan that has efficient score with value is 1

(one). The two DMUs in Northern Area of Taiwan are TP3 and TP4. The rest DMUs in Northern Area

of Taiwan are having less than 1 value which means they are identified as inefficient. For the inefficient

DMU, can improve its efficiency by reducing certain inputs.

Total operating cost should be in amount of 337.38 (in NT 000), from previously 445 (in NT 000); and

the treatment room should only 7(rounded from 6.8) rooms (previously the treatment roomis 9 rooms).

Accordingly, the efficient value for the total revenue is 1,379.74 (in NT 000); from previous value is

1,280 (in NT 000). Meanwhile the value for the number of customers is the same.

Heading 3.1

b. DMUs Ranking

We can conclude that there are only 2 Spa branches from 20 Spa branches who work efficiently

according to the given Inputs used to generate outputs. These two branches are located in the northern

area of Taiwan and the score of efficiency is 1. The rest of DMUs are having efficiency score less than

1 but greater than 0 which mean that these DMUs are operating inefficiently.

Table 1.4 DMUs Ranking for Both Area (Central and Northern Area of Taiwan)


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1 TP3 1.00000 11 TP10 0.75815

2 TP4 1.00000 12 TP7 0.73283

3 TZ8 0.91065 13 TZ2 0.71899

4 TZ5 0.87650 14 TZ6 0.67981

5 TP1 0.87320 15 TZ1 0.65869

6 TP2 0.83739 16 TP6 0.64615

7 TP9 0.79737 17 TZ9 0.64121

8 TP8 0.79590 18 TZ4 0.63883

9 TP5 0.78060 19 TZ7 0.60703

10 TZ10 0.77191 20 TZ3 0.60185


Heading 4

Meta-frontier Results

In this section we address the issue of comparing Spa branches efficiencies across location. Observe

from Table 5.19, we compare the efficiency scores of each DMU in the specific area (group frontier)

shows very significant difference between the efficiency score in each of DMU in central area of

Taiwan and the efficiency score of meta-frontier among all DMUs across location. Almost all DMUs in

central area of Taiwan are having scores lower than 1 and it means that all DMUs are identified as

inefficient, including the DMU TZ2, TZ5, and TZ8 whose having efficiency score is 1 (one) before.

This difference implies a low meta-technology ratio. Meanwhile, the efficiency score in each of DMU

in northern area and the efficiency score in a meta-frontier were the same.

Next finding, Table 1.5 shows the average of technical efficiency in group frontier 1central

area is higher than in northern area of Taiwan, but for the of meta-frontier scores we see the opposite

result. Northern area of Taiwan has higher meta-frontier efficiency score compared to central area of

Taiwan. Surprisingly, after we run meta-frontier analysis, there are only 2 out of 20 spa branches were

identified as efficient spa center, they are TP3 and TP4 which are located in northern area of Taiwan.

The other spa branches were identified as inefficient, includes 10 spa branches in central area of

Taiwan and 8 spa branches in northern area of Taiwan.

From the findings explained above, we could infer that the location appears to be an

explanatory factor of efficiency, by looking at the spa branches location, in, or near, the big cities

more efficient than those in more county locations. A rationale for this result is that demand plays

a role in organizational efficiency, with the spa branches near more populated zones attracting

more clients. This higher demand enables greater efficiency.

Although DEA identifies the inefficient spa branches in the sample, it does not reveal the

cause of the inefficiency. DEA suggests the slacks for the inefficient spa branches and gives to

each a reference set (peer group) which allows for specific recommendations to improve

efficiency. Adjustments for the inefficient spa branches can be identified for outputs and inputs

in order for them to join the efficient frontier.

Table 1.5 Meta-frontier Result

DMU Technical Efficiency Group Frontier Meta-frontier Meta-technology Ratio

Central Area of Taiwan (Frontier 1)

TZ1 0.91124 0.65869 0.72286


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TZ2 1.00000 0.71899 0.71899

TZ3 0.86108 0.60185 0.69895

TZ4 0.94421 0.63883 0.67658

TZ5 1.00000 0.87650 0.87650

TZ6 0.97354 0.67981 0.69829

TZ7 0.91588 0.60703 0.66279

TZ8 1.00000 0.91065 0.91065

TZ9 0.85951 0.64121 0.74602

TZ10 0.95090 0.77191 0.81176

MEAN 0.94061 0.70373 0.74574

Table 1.5 (Continued)

DMU Technical Efficiency Group Frontier Meta-frontier Meta-technology Ratio

Northern Area of Taiwan (Frontier 2)

TP1 0.87320 0.87320 1.00000

TP2 0.83739 0.83739 1.00000

TP3 1.00000 1.00000 1.00000

TP4 1.00000 1.00000 1.00000

TP5 0.78060 0.78060 1.00000

TP6 0.64615 0.64615 1.00000

TP7 0.73283 0.73283 1.00000

TP8 0.79590 0.79590 1.00000

TP9 0.79737 0.79737 1.00000

TP10 0.75815 0.75815 1.00000

MEAN 0.82216 0.82216 1.00000


Conclusions

In this study, explains about Data Envelopment Analysis (DEA) and its application to a famous Spa in

Taiwan that has 45 branches which are located widespread in Taiwan. However, the Data Envelopment

Analysis was used to analyze the efficiency of a sample of 20 spa branches located in central area and

northern area of Taiwan. The DEA CRS Model (Input oriented) was run first to each area in order to

identify which spa center operating efficiently in specific area. Afterward, all spa branches which are

located in both areas central and northern area were analyzed in a meta-frontier analysis. The empirical


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evaluation has the following three major findings. First, despite spa branches in the central area spend

more in inputs than the spa branches in the northern area of Taiwan, but after looking at the mean

score, in fact the spa branches in the central area have lower score for the outputs than the spa branches

in the northern area of Taiwan. From this finding, we could infer that even the spa branches spend

more in operating costs and use more treatment rooms, it does not guarantee that this spends will

produce more outputs (Total revenue and number of customers). Second, the findings after we running

DEA CRS (input oriented) in a specific area, show 3 spa branches (DMUs) out of 10 in central area of

Taiwan are identified as efficient; 2 spa branches (DMUs) out of 10 in the northern area of Taiwan are

identified as efficient spa branches. These efficient spa branches are having perfect score of efficiency

concept (the score for efficient DMU is equal to 1 or 100%). The three DMUs in central area of Taiwan

which are identified as efficient spa branches include TZ2, TZ5 and TZ 8. Meanwhile in the northern

area of Taiwan, the two spa branches are TP3 and TP4. Finally, after running the meta-frontier

analysis, it is found that only 2 DMUs which is located in Northern Area of Taiwan, they are TP3 and

TP4 that only have efficient score is one, which means these two spa branches operating 100%

efficient. The other Spa branches (DMUs) are operating inefficiently. The minimum score efficiency is

0.60185 or in another word, the spa center with this score only operating 60.18%. This score is about

39.82% (100% - 60.18%) lower than the efficient spa branches. The lowest efficiency score is existed

in central area of Taiwan.

Suggestions

Several suggestions regarding to the findings mentioned above are explained as follows:

For the inefficient spa branches need to adjust their allocation of resources for inputs and outputs.

By referring to the slack variables analysis, then in order to improve the operating efficiency of spa

branches, the inefficient spa branches should increase the outputs, either to increase total revenue or the

number of customers. This action can be followed up by exploring new potential customers from

different segmentation.

For the branch managers whose spa branches are identified as inefficient spa branches need to do

benchmarking to the efficient spa branches in order to be efficient.

Transferring knowledge about operational management from the spa branches with higher operational

efficiency to the spa branches that had low operational efficiency. By doing this, it might help to

improve operational efficiency and competitiveness in long run.