A Performance Study on

Kuang -Jung Tseng , Associate Professor, Dept. of International Business, Hsuan Chuang University Hui-Chen Shan, Military Education Instructor, China University of Technology Yuan-Jiing Liou, Director, Military Education Office, Tungnan University

ABSTRACT

This study applied DEA input-oriented Window Analysis model to evaluate the managerial performance of 6 lines in Taipei Metro system over 1999-2006. Empirical results show: (1) the C-Average efficiency scores and Average by Term efficiency scores performed all right in 6 lines of the Metro system; (2) Zhonghe Line had the best performance; Nangang Line ranked the second place; Muzha Line had the worst performance; (3) efficiency of average through window had unsteady changes；Banqiao Line had positive changes over the time period; however, Muzha Line had negative changes; (4)shops had a direct impact on managerial performance of these lines, especially on Muzha Line and Zhonghe Line. Keywords：Metro Taipei, managerial performance, Data Envelopment Analysis, window analysis

INTRODUCTION

The operation of the system owned by the London Metropolitan Railway Company, 6 kilometers from Paddington Station to Farringdon St., started in 1863. It is not only the first metro route in London but also the first one in the world (Chang, Chi-Jung, 1994). In 1967, the Taiwanese government had studied the feasibility of building a mass rapid transit system within the Taipei metropolis. Nevertheless, this project failed to be executed owing to a huge amount of budgets and no urgent requirement. In 1970s, the traffic volume in the Taipei metropolis gradually expanded with the continuous growth in economy. To solve this traffic jam, the project of the Metro Taipei system started. On February 1977, the Transportation Project Commission of the Ministry of Transportation and Communications drafted the “Preliminary Project of the Mass Rapid Transit System in Taipei” report, which included five planned routes U1, U2, U3, S1, and S2, as the original rapid transit program. On September 1981, the Transportation Project Commission invited “British Mass Transit Consultants (BMTC)” and “China Engineering Consultants, Inc.” to organize a project team for a further study. In 1982, the authorized National Chiao Tung University for the study of developing a rapid transit system with a medium capacity. On January 1984, the “Medium Capacity Task Force” under the Taipei City Government proposed the “Original Development Project of the New Medium Capacity Metro Taipei System”. On March 1 1985, the Council for Economic Planning and Development of signed a contract with “Taipei Transportation Consultants (TTC)”, which was composed of three American consultant companies, for a comprehensive study of the rapid transit system in the Taipei metropolis. In 1986, the Executive Yuan ratified the proposal, the Original Network Project of the Metro Taipei System, approved by the Council for Economic Planning and Development to formally confirm routes of the Metro Taipei System.

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After the “Department of Rapid Transit Systems, TCG” was founded in 1987, the “Depot Beitou” project, the first project of the Metro Taipei System, commenced on December 1988. On March 28 1996, the transport service of the Muzha Line, the first route of the Metro Taipei System and in , started. To commemorate this achievement, the Taipei Rapid Transit Corporation designated March 28 as the anniversary day of the Metro Taipei. The date of starting transport service for each route of the Metro Taipei is listed as Table 1.

Table 1 the date for transport service of each route of the Metro Taipei Route Departure- Destination Date to provide transport service Muzha Line Zhongshan Junior High School -- Mar. 28, 1996 Danshui Line Danshui ─ Zhongshan XinBeitou Branch XinBeitou ─ Beitou Mar. 28, 1997 Line Danshui Line Zhongshan ─ Dec. 25, 1997 Danshui Line Taipei Main Station ─ Chiang Kai-Shek Memorial Hall Dec. 24, 1998 Xindian Line Chiang Kai-Shek Memorial Hall ─ Guting Zhonghe Line Guting ─ Nanshijiao Xindian Line Guting ─ Xindian Nov. 11, 1999 Nangang Line Taipei City Hall ─ Ximen Dec. 24, 1999 Banqiao Line Ximen ─ Lungshan Temple Banqiao Line Lungshan Temple ─ Xinpu Aug. 31, 2000 Xiaonanmen Line Ximen ─ Chiang Kai-Shek Memorial Hall Nangang Line Kunyang ─ Taipei City Hall Dec. 30, 2000 Xiaobitan Branch Qizhang─ Xiaobitan Sep. 29, 2004 Line Banqiao Line Xinpu─ Fuzhong May 31, 2006 Tucheng Line Fuzhong ─ Yongning Data source: the annual report of the Taipei Rapid Transit Corporation in 2006 and reorganization in this study

At the end of 2006, the number of routes and stations for the Metro Taipei System under operation is 8 and 69, respectively; the total distance for transport service is 74.4 kilometers. The accumulated person-time for passenger transportation reached one hundred million on December 1998 and over 2.5 billion on December 2006. The transportation volume for person-time of passengers is shown in Table 1. Notwithstanding the entire transportation network of the Metro Taipei System is not completed after 10 years from the first operation in 1996 to today, the Metro Taipei System has become the major transportation of residences in the Taipei area according to the data of the transportation capacity growth. Because of the huge amount of budgets for hardware facilities of a rapid transit system as well as profound effects on the area development from a route arrangement, the operational efficiency for the routes under the commercial operation is the objective in this study as a reference to improve the operational strategy for business operators and a reference of planning to build the mass transit system by other cities.

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Person百萬-time人次 (Unit: Million) 3,000

2,500

2,000

1,500

1,000

500

0 85 86 87 88 89 90 91 92 93 94 95 年 Fig. 1-1 Accumulation圖1.1 台北 of捷 transportation運系統累 積volumes運量 圖for the Metro Taipei System

Data source: the White paper for Citizen Service of the Taipei Rapid Transit Corporation in 2007

LITERATURE REVIEW

1. Literatures for the rapid transit Chang, Yu-Heng (1994) argued that factors to influence the managerial performance of the mass rapid transit system for a city includes four mutually correlative dimensions, i.e., system, technique, operation and management. Chang, Chih-Jung (1994) deemed that the major subject of mass transportation in a city is how to reach a balance between investments and operations because the operational efficiency of a rapid transit system shows in a high-requirement condition only due to its huge scale & high investment. Employing CCR & BCC models, Chang, Chih-Ching (2002) explored the managerial performance of six transport service sections of the Metro Taipei System in 2001. Dajani & Gilbert (1978) discussed the importance of evaluating performance of mass transportation and distinguished the relationship between efficiency and effect.

2. Literatures for discussions of using DEA As to performance evaluation of various industries, the application of the Data Envelopment Analysis (DEA) is popular and creates many literatures. A summary for essential literatures regarding the traffic transportation at home and abroad is as follows: Gillen and Lall (1997) measured operational performance of 21 airports in the United States from 1989 to 1993. Adopting the BCC model, Martinez et al. (1999) compared the operational efficiency performed by 26 ports in Spain from 1993 to 1997. Sarkis (2000) evaluated the operational and the cross-time efficiency of 44 major airports in the United States from 1990 to 1994. Defining an airport’s quality from airlines’ viewpoints, Adler and Berechman (2001) selected 6 airlines to conduct a questionnaire survey to evaluate quality of 26 airports in Europe, Africa and Asia in 1998. Martin and Roman (2001) analyzed the performance and technical efficiency of 37 airports in Spain in 1997; Kuo, Chien-Nan (2001), employing CCR & BCC models, evaluated the operational performance of 11

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container ports in the Asia Pacific region in 1999. Valentine and Gray (2001), using the CCR model, appraised the operational performance of the first 31 container ports around the world in 1998. Adopting the CCP model, Tongzon (2001) assessed the productive efficiency of 4 international ports in Australia and 12 international ports of other countries in 1996. Fernandes and Pacheco (2002) assayed the efficiency of 35 domestic airports in Brazil using person-time data in 1999. With CCR & BCC models, Wang et al. (2003) evaluated the managerial efficiency of 28 container ports around the world in 2001. Wu, Chung-Yueh (2003), based on the CCR model, assessed the operational performance of the first 30 stations of Taiwan Railways in 2001. Pels et al. (2003) evaluated the operational performance of 33 airports in Europe from 1995 to 1997 by choosing two dimensions such as airport service and operation airside; Pacheco and Fernandes (2003) analyzed the capability for revenue and efficiency of using airport facilities in 35 airports of Brazil in 1999; Bazargan and Vasigh (2003) investigated the operational efficiency of 45 airports in the United States from 1996 to 2000. Chou, Ming-Tao et al. (2004) used the RDEA model to compare the productive efficiency of 11 container ports in Taiwan, Hong Kong, Macau and China from 2000 to 2002; Lin, Li-Chien and Chen, Yi-Chun (2004) measured the operational efficiency of 10 international airports in the Asia area in 2002; Yoshida and Fujimoto (2004) categorized 67 domestic airports of Japan into four groups to evaluate their operational efficiency in 2000; Sarkis and Talluri (2004) selected the first 80 airports of United States published by FAA as objects for a questionnaire survey to evaluate the operational efficiency performed by 44 of them from 1990 to 1994; Yu (2004) judged the operation efficiency of domestic air routes for 15 military-civil airports from 1995 to 2000 by using non-parametric boundary analyses; Huang, Shan-Chieh (2005), employing CCR & BCC models and the Malmquist index, evaluated the competitiveness of the first 10 container ports in the Asia pacific region and discussed the tendency of change in productivity; Yu, Ming-Min (2005) assessed the operation efficiency for 38 DMUs in military-civil airports of Taiwan having operations of domestic air routes and influence of airborne noise control on airports from 1993 to 1999; Lin, Yu, Ming-Min, and Yang, Chi-Hung (2006) adopted the Window Analysis /AR model to explore the operational performance of three ports, , Taichung, and Kaohsiung, from 1995 to 2002; Lin and Hong (2006) evaluated the operational efficiency of 20 major airports around the world in 2003 based on five factors, ownership of an airport, size of an airport, core airport, location of an airport, and economic growth rate, which are major reasons to affect the operational efficiency of an airport.

3. Literatures for DEA theory As to assessment of an organizational efficiency, the traditional method is to build the input/output ratio of resources as an index or to employ the least square method of statistics for estimation based on the parameter concept. Owing to easy confirmation as well as quantification of input/output items and a functional relationship between inputs and outputs for the general profit organizations, the efficiency of an organization can be objectively evaluated through the parameter method. Nevertheless, as for multiple principles and uneasily quantitative features for evaluation of nonprofit organizations, it is hard to evaluate the efficiency of that organization via the parameter method in practice. Data Envelopment Analysis (DEA), a method without parameters, can detect the relative efficiency of a Decision Making Unit through the mathematic programming model, and it can not only solve distribution of weights but also offer integral & single index for performance evaluation without a requirement of predetermined functions. DEA comes from the CCR model, which is offered by Charnes et al. (1978), and its concept originates from the structure of efficiency evaluation of the non-parametric production frontier function

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argued by Farrell. With multiple inputs and outputs of the CCR model via the mathematical programming technique, the relative efficiency of an organization, namely DMU, can be assessed. In addition, the so-called “relative efficiency” is to divide evaluated DMUs into efficient and inefficient portions with a mathematic technique. In this regard, the efficient DMUs belong to the optimal combination of inputs as well as outputs within all DMUs and are able to create the efficient frontier; an inefficient DMU is to evaluate the degree of inefficiency by the relative position of the inefficient DMU and the efficient frontier. Furthermore, the efficient and the inefficient divided are only the relative correlations of evaluated DMUs, and the degree of this relative correlation will be changed in the event of change of ingredients in DMUs. Thus, that is the origin for the name of the “relative correlation”. For the evaluation for the relative efficiency of a DMU, we take the sum of weighted outputs divided by the sum of weighted inputs to acquire a maximal ratio called the efficiency score. In the mathematic model, the weights of various inputs and outputs of that DMU are regarded as variables to solve a set of weighted values that maximizes the efficiency value of an objective function. With this set of weights substituted into the efficiency evaluation equation of each DMU, the restrictions will make the efficiency value less than 1 for each DMU. Because this procedure for resolutions is executed once for each DMU, we can acquire n sets of weights from n DMUs and the efficiency value for each DMU. As to the fractional programming problem of the original model, we can transfer it to a linear programming for a resolution. Meanwhile, we can also solve a dual problem to get the slack variable and the envelopment surface. With the CCR model published, many scholars continuously join research of DEA for development of efficiency evaluation of various models. Among them, the BCC model of Banker et al. (1984) is the most famous and the application of empirical research in DEA is based on CCR and BCC models in chief.

Mathematical model of DEA (1) CCR model As the efficient frontier of Constant Return to Scale (CRS), the CCR model is to decide reduction of inputs to reach an efficient frontier by means of the quantity of inputs when outputs are constants. With

Ek taken as the efficiency value of a DMU, the fractional programming model for the CCR model is: s ur yrk r1 Max Ek  m vi xik i1 s ur yrk (2.1) r1 s.t. Ek  m  1 vi xik i1

ur ,vi    0; i  1,,m ; r  1,, s ; k  1,,n

: Relative efficiency value of DMUk;

ur ,vi : Virtual multiplier of the rth output and the ith input respectively;

xik : The ith input of DMU k ;

yrk : The rth output of ; r: Output, r 1,,s ;

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i: Input, i  1,,m ; k: Decision Making Unit ( DMU ), k 1,,n ;  : Ultra-micro positive quantity (non-Archinidean quantity). Because of the non-convex and non-linearity of the above equation that leads to uneasy calculation, a linear programming question can be transferred via the following equation. For a DMU k with

xk , yk  as its input and output, the input efficiency can is expressed as: s Max Ek  ur yrk r1 m s.t. vi xik  1 (2.2) i1 s m ur yrk  vi xik  0 r1 i1

ur ,vi    0 ; i  1,,m ; r  1,, s ; k  1,,n Owing to the number of restrictions greater than variables in the original question, it is convenient to solve this question via the dual problem and realize the space of improvement that has an important meaning in the strategy of management. The dual problem is as follow: m s     Min Ek     Sik   Srk   i1 r1  n  (2.3) s.t. k xik X ik  Sik  0 k1 n  k xik  Srk  Yrk , k1   k , Sik , Srk  0; i  1,,m; r  1,, s; k  1,,n   where Sik , Srk are slack variables. With =0 as well as  =1, DMU is efficient; otherwise, with < 1, DMU is inefficient.

(2) BCC model After the CCR model is developed, Banke et al. (1984) expanded the CCR model with introduction of four axioms for the production set as well as the distance function of Shephard (1970) and assumptions of production techniques meeting convex & variable returns to scale (VRS), and divided the total technical efficiency as a product of Pure Technical Efficiency (PTE) and Scale Efficiency (SE). In Figure

2,  u0 is an intercept of the x-axis. With a positive  u0 (a negative u0 ), the corresponding segment, e.g. BC, of the production frontier belongs to increasing returns to scale (IRS); with u0 =0, the corresponding segment, e.g. CD, of the production frontier belongs to constant returns to scale (CRS); with a negative  u0 (a positive ), the corresponding segment, e.g. DE, of the production frontier belongs to decreasing returns to scale (DRS). In addition, other deserving to be noticed is points C & D in the boundary of two regions that can be categorized to the returns to scale of either type. For these points, multiple solutions can be acquired from the resolution model. Based on a reverse inference from this perception, we are not able to decide the returns to scale regarding by a positive or negative

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only with the efficiency value of either DMU evaluated; thus, a further analysis is necessary.

OI 0 OI * As regards the efficiency evaluation of Unit A by the CCR model, the result is A less than A ,

OI A OI A the evaluated result through BCC, and the difference comes from different assumptions in returns to scale.

OI * In general, the academic commodity calls A as the technical efficiency, as the productive

OI A

OI 0 efficiency, and the ratio of these two, A , as the scale efficiency. In other words, the productive

OI * A efficiency equals to a product of the technical efficiency and the scale efficiency.

Y

E

D

A

C v A0 0 A A*

B

X  u 0  u I 0 I * I 0 0 A A A

v0

Fig. 2 Measurement by Pure Technical Efficiency and Scale Efficiency 圖.2 純技術效率與規模效率之衡量

The original question for the BCC model of the input oriented model can be written as follows: s Max Ek  ur yrk  0 r1 m s.t. vi xik  1 (2.4) i1 s m ur yrk  vi xik  0  0 r1 i1

ur ,vi  0 ; i  1,,m ; r  1,, s ; k  1,,n

0 : No restriction in plus or minus sign. Similarly, as for convenience of computation and increase of information in explanation, the original question can be transferred to a dual problem.

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m s     Min Ek   k   Sik   S rk   i1 r1  n  s.t. k yrk  S rk  yrk k 1 (2.5) n  x   S   0  k ik kXik ik i1 n k  1 k1   k , Sik , S rk  0; r  1,, s; i  1,,m; k  1,,n n The added restriction, , is the index as for returns to scale.  k  1 k 1 If n , that unit is at the stage of decreasing returns to scale;  k  1 k 1 n If , that unit is at the stage of increasing returns to scale;  k  1 k 1 n If , that unit is at the stage of the optimal productive scale  k  1 k 1 e : No restriction in plus or minus sign. Under an assumption of constant returns to scale, SE = l signifies a scale efficiency; on the contrary, SE < 1 (or SE > 1) means that DMU is at the inefficient stage of decreasing (increasing) returns to scale, which can be taken as a reference of modifying the productive scale by a policy maker. The situation of returns to scale can be decided through 0 of the equation. If 0 ＞0, the returns to scale of that DMU is gradually increasing in general; contrarily, if ＜0 , the returns to scale of that DMU is gradually decreasing in general; in case ＝0, the returns to scale of that DMU is a constant in general. (3) Window Analysis: Because of failure of executing the conventional DEA model in case of insufficient DMUs, the major objective of this Window Analysis provided by Charnes et al. (1985) is to regard the efficiency of an identical DMU in different periods as the efficiency of another DMU to increase the number of samples and stability in the efficiency of DMUs. The four major functions of the Window Analysis are listed as follows (Hsun Sun, 2004): 1. Determine an adequate length and a number of times of the window. 2. Explore the tendency and effects on DMUs at different periods. 3. Detection of error data 4. Discover efficient DMUs by consistency of the efficiency values. (4) Sensitivity analyses: Charnes et al. (1985) mentioned the effect from change regarding items and values of inputs & outputs on the efficiency value of DMUs.

RESEARCH METHODOLOGY

In this study, we employ Data Envelopment Analysis (DEA) and the input oriented window model to explore the managerial performance of six routes of the Metro Taipei from 1999 to 2006. (Owing to their small scales of Tucheng Line, Xinpu to Yongning beginning transport service on May 31, 2006, and Xiaonanmen Branch Line with one station only & a length of 1.6 kilometers compared with other routes,

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these two routes are excluded from the scope of the study. As to Banqiao Line, the section from Lungshan Temple to Xinpu is selected as the object of evaluation only due to the newly available service of Tucheng on May 31, 2006.) Roll and Gollany (1989) mentioned that the execution of efficiency analysis could depend on multiple inputs and outputs but different items may affect its result; furthermore, a plethora of inputs and outputs will reduce the segmentation effect of DMUs. For establishment of an evaluated model in this study, four items (length of a route, number of stations, parking space, and shops) and two items (person-time of passengers entering and leaving a station) are selected as the inputs and outputs respectively from various data disclosed on websites of the Taipei City Government and the Taipei Rapid Transit Corporation from 1999 to 2006. The performance evaluation model and the definitions for input & output variables are shown in Fig. 3.1 and Table 3.1 respectively.

投入Input項 產Output出項 Length of a route Length路 of長 a route 進Number站人數 of passengers entering a station 車站數 Number of stations Transfer轉換 停車位 Parking space 出Number站人數 of passengers leaving a station

販Shops售店 Fig.圖 33-.1 1Appraisal 評估模 model式圖

Table 3.1 definitions for input and output variables Variable Definition Total length of a route (Unit: kilometer) Length of a route x1  Number of stations A place for loading and unloading passengers (Unit: x station) Input item  2  Parking space x  Space for parking a motorcycle or a motor vehicle (Unit: 3 site) Stores in a station for commodity trading (Unit: shop) Shops x4  Number of passengers Number of passengers entering the platform of this station entering a station y  (Unit: person-time) Output Item 1 Number of passengers Number of passengers leaving the platform of this station (Unit: person-time) leaving a station y2 

Bowlin (1987) mentioned that the number of ideal DMUs should be twice at least as many as the sum of numbers of input and output variables. In this study, the total number for variables with four input items and two output items is six. However, six routes only in the Metro Taipei system do not match this empirical principle; thus, the Window Analysis model is employed for evaluation of the operational efficiency in this study. The data of descriptive statistics for variables is shown in Table 3.2.

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Table 3.2 data of descriptive statistics for variables Variable Maximum Minimum Average Standard deviation

Length of a route x1  23.5 5.4 10.9 6.1 22.0 3.0 10.3 6.3 Number of stations x2  5876.0 636.0 1705.5 1891.4 Parking space x3  36.0 4.0 15.2 10.7 Shops x4  Number of passengers entering a 155201403 10273406 61459664 46235329 station y1  Number of passengers leaving a 154732314 10519083 61400744 46507448 station y2 

The objective of conducting analyses for correlative coefficients is to realize if the input and output variables is able to match a correlation of Isotonicity. The analyzed results indicate significant correlations among variables. The results are shown in Table 3.3.

Table 3.3 analytic table of relevant coefficients

(x1) (x2) (x3) (x4) (y1) (y2) (x1) 1 (x2) 0.965** 1 (x3) 0.934** 0.827** 1 (x4) 0.961** 0.958** 0.861** 1 (y1) 0.822** 0.834** 0.740** 0.929** 1 (y2) 0.817** 0.831** 0.735** 0.926** 1.000** 1 Remark: ** signifies a significant correlation when the statistical significance level is 0.01 (two tail). * signifies a significant correlation when the statistical significance level is 0.05 (two tail).

In this study, the data during eight years from 1999 to 2006 is taken as a reference to make an evaluation. After considering the scale and technical change potentially created in each year, we modify it to every four years as one window so there are five windows evolved in succession for a further analysis. Through the process of evolution of windows, the yearly efficiency change for routes of the Metro Taipei can be observed. The schematic diagram for window analyses is shown in Table 2.1.

Table 2.1 the schematic diagram for window analyses in this study DMU Window 1999 2000 2001 2002 2003 2004 2005 2006 Average

W1 A11 A12 A13 A14

W2 A22 A23 A24 A25

DMU A W3 A33 A34 A35 A36 M A

W4 A44 A45 A46 A47

W5 A55 A56 A57 A58 Data source: Compiled in this study

For realization of effects on efficiency because of input variables, one of four input items in this study will be screened out respectively for performance evaluation as exploration of the sensitivity analyses.

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EMPIRICAL ANALYSES

1. Efficiency analyses for the Window Analysis-I-C model: The general average efficiency is 0.706 where the managerial performance of Zhonghe Line with an efficiency value of 0.959 is the best; the second one is Nangang Line with an efficiency value of 0.912; the third one is Banqiao Line with an efficiency value of 0.782. The general average efficiency of Muzha Line with an efficiency value of 0.432 is the worst. The statistic table for efficiency analyses is shown in Table 4.1.

Table 4.1 statistic table for efficiency analyses 1999 2000 2001 2002 2003 2004 2005 2006 Average 0.334 0.482 0.506 0.523 0.436 0.457 0.473 0.435 Muzha 0.440 0.455 0.418 0.434 0.432 Line 0.430 0.395 0.410 0.403 0.395 0.410 0.403 0.402 0.652 0.657 0.711 0.692 0.593 0.640 0.623 0.688 Danshui 0.616 0.599 0.661 0.679 0.644 Line 0.564 0.623 0.639 0.663 0.623 0.639 0.663 0.664 0.931 0.943 1.000 1.000 0.883 0.934 0.957 1.000 Zhonghe 0.907 0.940 0.981 1.000 0.959 Line 0.901 0.942 0.969 0.993 0.942 0.969 0.993 0.985 0.552 0.575 0.614 0.613 0.518 0.556 0.553 0.591 Xindian 0.535 0.533 0.569 0.585 0.560 Line 0.503 0.538 0.553 0.571 0.538 0.553 0.571 0.572 0.382 0.670 0.852 0.875 0.602 0.766 0.787 0.899 Banqiao 0.736 0.756 0.864 0.932 0.782 Line 0.710 0.812 0.876 0.813 0.812 0.876 0.813 0.813 0.760 0.812 1.000 0.990 0.730 0.899 0.884 1.000 Nangang 0.863 0.849 0.961 1.000 0.912 Line 0.799 0.905 0.942 1.000 0.905 0.942 1.000 1.000 Average 0.602 0.658 0.724 0.709 0.729 0.745 0.741 0.739 0.706

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2. Tendency of change for the cross-time efficiency: Based on analyses of the cross-time efficiency, the general average efficiency displays an undulated variation. A tendency with a gradual increment year by year can be detected at Banqiao Line only; a tendency with a gradual decrease year by year appears at Muzha Line; a tendency of slight fluctuation can be discovered at other routes. Except Muzha Line of the medium capacity, a tendency of a stable growth can be detected at other routes in the recent four years. Analyses for the cross-time efficiency are shown in Table 4.2.

Table 4.2 analytic table for the cross-time efficiency 1999--2002 2000--2003 2001--2004 2002--2005 2003--2006 Muzha 0.461 0.450 0.437 0.409 0.402 Danshui 0.678 0.636 0.639 0.622 0.647 Zhonghe 0.969 0.944 0.957 0.951 0.972 Xindian 0.589 0.555 0.555 0.541 0.558 Banqiao 0.695 0.763 0.822 0.803 0.828 Nangang 0.891 0.878 0.918 0.911 0.962

3. Managerial efficiency in each year: The results of efficiency analyses for all routes of the Metro Taipei system in each year display: The average efficiency for six routes within eight years is 0.706 wherein Zhonghe Line with an efficiency value of 0.958 has an optimum performance; Nangang Line with an efficient value of 0.904 and 1 in 2005 & 2006 is the runner-up; the third one is Banqiao Line with an average efficiency value of 0.744; the worst is Muzha Line with an average efficiency value of 0.421. The statistics for efficiency analyses in each year is shown in Table 4.3.

Table 4.3 statistics for the efficient analyses in each year 1999 2000 2001 2002 2003 2004 2005 2006 Average Muzha 0.334 0.459 0.468 0.470 0.411 0.418 0.403 0.402 0.421 Danshui 0.652 0.625 0.656 0.619 0.649 0.653 0.663 0.664 0.648 Zhonghe 0.931 0.913 0.947 0.949 0.966 0.980 0.993 0.985 0.958 Xindian 0.552 0.547 0.568 0.551 0.559 0.563 0.571 0.572 0.560 Banqiao 0.382 0.636 0.784 0.782 0.847 0.895 0.813 0.813 0.744 Nangang 0.760 0.771 0.921 0.881 0.943 0.961 1 1 0.905

4. Sensitivity analyses: With two input variables such as length of a route & parking space screened out, the general average efficiency will ascend; with number of stations as well as shops eliminated, the general average efficiency will descend; in particular, the managerial efficiency of Muzha Line and Zhonghe Line is the most significantly affected by shops in a station. The sensitivity analyses are shown in Table 4.4.

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Table 4.4 sensitivity analyses Elimination of input variables General DMU Number of efficiency Length of a route Parking space Shops stations Muzha 0.432 0.432 0.432 0.428 0.251 Danshui 0.644 0.644 0.642 0.644 0.612 Zhonghe 0.959 0.959 0.959 0.959 0.573 Xindian 0.560 0.560 0.559 0.559 0.481 Banqiao 0.782 0.782 0.668 0.782 0.782 Nangang 0.912 0.912 0.912 0.912 0.912 Average 0.706 0.715 0.695 0.714 0.602

CONCLUSIONS AND SUGGESTIONS

In general, the average efficiency with a value of 0.706 is desirable wherein Zhonghe Line with an efficiency value of 0.959 has the best managerial performance; Nangang Line with a value of 0.915 is the second one; Banqiao Line with a value of 0.782 is ranked the third; Muzha Line of the medium capacity is the poorest and its efficiency value is 0.432. The general average efficiency displays an undulated tendency: Banqiao Line is the only one that displays a gradual increment year by year; Muzha Line is an example of gradual decline year by year. With two input variables such as length of a route and parking space screened out, the general average efficiency will ascend; with number of stations and shops eliminated, the general average efficiency will descend; in particular, the managerial efficiency of Muzha Line and Zhonghe Line is the most significantly affected by the factor of shops.

Generally speaking, the fact that shops significantly influence performance of the Metro Taipei signifies the Taipei Rapid Transit Corporation ought to plan appropriate points of sales or shops in a station without affecting security of routes and a station’s appearance as the short-term proposal; and incorporate with specific views or industries around a station to reach the goal of expanding the managerial efficiency as a long-term strategy.

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