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TECHNICAL EFFICIENCY AND SERVICE EFFECTIVENESS FOR RAILWAYS INDUSTRY: DEA APPROACHES Lawrence W. LAN Professor Institute of Traffic and Transportation National Chiao Tung University 4F, 114 Sec.1, Chung-Hsiao W. Rd. Taipei, Taiwan 10012 Fax: +886-2-2349-4953 E-mail:[email protected]

Erwin T. J. LIN Ph.D. Student Institute of Traffic and Transportation National Chiao Tung University 4F, 114 Sec.1, Chung-Hsiao W. Rd. Taipei, Taiwan 10012 Fax: +886-2-2349-4953 E-mail: [email protected]

Abstract: This paper adopts various data envelopment analysis (DEA) approaches to investigate the technical efficiency and service effectiveness for some selected 76 railways (DMUs) in the world during the period 1999-2001. We estimate technical efficiency by the input-oriented DEA models and service effectiveness by the output-oriented DEA models. The technical effectiveness scores estimated by one-stage (hyperbolic) DEA are shown somewhat higher than the product of technical efficiency and service effectiveness scores estimated by two-stage DEA. The Kruskal-Wallis rank tests show that railways efficiency and effectiveness vary among regions but the frontiers do not shift during the study period. Most railways reveal variable returns to scale. We also carry out outlier detection and sensitivity analysis for the efficient and/or effective DMUs. To compare the relative efficiency and effectiveness of the 76 rails in a more homogeneous environment, the exogenously fixed inputs DEA and categorical DEA models are further attempted. Key Words: railways industry, data envelopment analysis (DEA), technical efficiency, service effectiveness, technical effectiveness 1. INTRODUCTION Over the past several decades, rail industry in many countries has been facing keen competition from other modes such as highway and air carriers. Most railways have suffered a major decline in the market share and failed to adopt a strategy to improve the decline situation. Take U.S.A. as an example, in intercity passenger transport, the modal share of railroads from 0.9% in 1970 dropped to 0.5% in 1997 (Pucher, 1999). Same situation has been occurred in Europe, rail’s share of the EU freight market declined from 32% in 1970 to 12% by 1999 (Lewis, et al. 2001). China Railway (CR) is another example. The market share (ton-km) of CR freight has declined from 40.53% (1990) to 32.54% (1998) (Xie, et al. 2002). As Fleming (1999) mentioned, truckers can deliver furniture from Lyon, France to Milan, Italy in eight hours, while railways need forty-eight hours. Enhancing the technical efficiency and service effectiveness has become an important issue for this industry to remain competitive and sustainable under such a decline situation. To do so, one must identify and estimate the indexes of efficiency and effectiveness, investigate the sources of inefficiency and ineffectiveness, and propose guidance to direct the poorly performed rail systems toward a more healthy way. Unlike ordinary commodities that are produced and then stockpiled for sale, a transportation service is non-storable. Once the transportation service outputs (vehicle-miles, vehicle-hours, etc.) are transformed from the input factors (labor, fleet, energy, etc.), the service must be Journal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003

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consumed right away. Otherwise, it can be completely wasted or ineffectively utilized. Many indicators for measuring performance of transportation systems have been presented in literature. The most popular one is the transit performance measurement proposed by Fielding, et al. (1985). They provide three measures: cost-efficiency, service-effectiveness, and cost-effectiveness. The cost-efficiency measurement is the ratio of service outputs to service inputs. The service-effectiveness measurement is the ratio of service consumption (passenger-miles, ton-miles, etc.) to service outputs, and the cost-effectiveness measurement is the ratio of service consumption to service input. However, if the input factor prices are not available we cannot estimate the “cost” efficiency (effectiveness) of firms; we estimate the “technical” efficiency (effectiveness) instead. In this paper technical efficiency (effectiveness) rather than cost efficiency (effectiveness) will be used for railway performance evaluation. Previous studies related to railway performance evaluation mainly focused on the cost efficiency (in fact, technical efficiency, as input-factor prices not known) and cost (technical) effectiveness. Little has been devoted to service effectiveness. For example, McGreehan (1993) used passenger-kilometers and ton-kilometers as output measures to analyze the performance of Ireland Railway, while Gathon and Perelman (1992) used train-kilometers as output measures to compare the relative efficiency of 19 European railways. Following the concept of Fielding, et al. (1985), the former paper in effect measured the technical effectiveness, while the later one measured the technical efficiency. In this paper, we estimate both technical efficiency and service effectiveness for 76 worldwide rail systems (called decision making units; DMUs) by employing two-stage data envelopment analysis (DEA), under the assumption of constant returns to scale (CRS) and variable returns to scale (VRS) technologies. At the first-stage, we use input orientation DEA (measuring the maximum possible proportional reduction in all inputs, keeping all outputs fixed) by selecting length of lines, number of locomotives and cars, and number of employees as inputs and train-kilometer as output. At the second-stage, we use output orientation DEA (measuring the maximum possible proportional expansion in all outputs while all inputs remaining unchanged) by selecting train-kilometers as input and passenger-kilometers and ton-kilometers as outputs. In addition, we also perform a technical-effectiveness analysis by one-stage DEA (also called hyperbolic DEA), which seeks the maximum possible proportional changes in all variables, i.e. increase in outputs and decrease in inputs simultaneously (Färe, et al. 1985). Note that the performance of railways may also be influenced by some internal factors as well as external variables that are not controllable by the firms. To investigate the potentially influential sources of inefficiency and ineffectiveness, we further conduct Tobit regression analyses. The efficiency score is regressed on percentage of electrified line, density of line, ownership (private or public), population density, and per capita gross national income. The effectiveness score is regressed on population density, per capita gross national income, utilized rate of route, average length of passenger trip (km) and average length of haul per ton carried (km). It has been argued that the comparison of performance by DEA approaches should be made in a homogeneous environment; thus we further use categorical DEA to estimate the relative efficiency and effectiveness of the DMUs under the same category. The 76 DMUs are clustered into appropriate categories based on the important external factors resulted from the Tobit regression analyses. Based on the categorical DEA results, we can construct a performance matrix in which each firm’s relative efficiency and effectiveness scores are properly allocated. Various strategies to enhance the performance of less efficient and/or less effective rail systems in different sub-matrixes are then proposed.

Journal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003

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The paper is organized as follows. Section 2 describes various DEA models, including basic CCR and BCC models, hyperbolic model, exogenously fixed inputs model, and categorical models. The empirical application to world’s railways and major findings are reported in Section 3. Based on the results of categorical DEA models, section 4 demonstrates a performance matrix where each rail system is allocated. Some brief concluding remarks are presented in Section 5. 2. METHODOLOGY 2.1 The CCR and BCC DEA Models In 1978, Charnes, Cooper and Rhodes (CCR) introduced a mathematical programming method to measure the relative efficiency for organizations or firms and termed as data envelopment analysis (DEA). The advantage of DEA is that no explicit functional forms need to be imposed on the data. Thus, the use of DEA has become increasingly widespread since then. The CCR DEA model is a fractional programming, which can be transformed to linear programming (LP) as follows: Minθ ,λθ s.t. - yi + Y ⋅ λ ≥ 0,

(1)

θ ⋅ xi − X ⋅ λ ≥ 0, λ ≥ 0 where X and Y are the K×N input matrix and the M×N output matrix (for the ith firm these are represented by the vector xi and yi), respectively. is a N×1 vector of constant and is a scalar, which stands for efficiency of ith firm. Solve this LP for each of the N firms; one obtains the efficiency score for each firm. Note that model (1) is an input orientation DEA model under the assumption of constant returns to scale (CRS) technology. In 1984, Banker, Charnes and Cooper (BCC) relaxed the restriction of CRS to account for variable returns to scale (VRS) technology by adding convexity constraint to model (1). The BCC input orientation DEA model then becomes: Minθ ,λθ

s.t. - yi + Y ⋅ ≥ 0,

θ ⋅ xi − X ⋅ ≥ 0, = 1,

(2)

≥0

One can easily transform model (1) and model (2) to output orientation DEA forms as shown in model (3) and (4), respectively. Maxφ ,λ φ s.t. − φ ⋅ y i + Y ⋅ λ ≥ 0 xi − X ⋅ λ ≥ 0

(3)

λ≥0 Maxφ ,λ φ s.t. − φ ⋅ y i + Y ⋅ λ ≥ 0 xi − X ⋅ λ ≥ 0

(4)

λ = 1, λ ≥ 0


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are defined as previous; φ denotes proportional increase in output, which ranges from one to infinity; 1 defines the service effectiveness of firm, which varies

where Y, X, xi, yi and

φ

between zero and one.

2.2 The HYP DEA Model The basic DEA models described in previous section can be based upon input orientation and output orientation. The former measures the maximum possible proportional reduction in all inputs, keeping all outputs fixed. The later measures the maximum possible proportional expansion in all outputs provided all inputs remain unchanged. Färe, et al. (1985) proposed the hyperbolic graph efficiency measures, which seek the maximum possible proportional change in all variables, i.e. increase all outputs and decrease all inputs simultaneously. Assume all outputs to be increased by and all inputs to be decreased by . Because we seek the maximum possible proportional change simultaneously in all variables, we let =1/ , then the model (called HYP DEA model) can be defined as follows: Min θ s.t. -

yi

θ

+ Y ⋅ λ ≥ 0,

(5)

θ ⋅ xi − X ⋅ λ ≥ 0, λ ≥ 0 This is a nonlinear programming (NLP) problem. It can be transformed into a simple linear programming (LP) to solve for .

2.3 The EXO and CAT DEA Models When we attempt to estimate relative technical efficiency and service effectiveness of railways, there might be some environmental variables that are not controlled by the DMUs. To account for these variables, Banker and Morey (1986a) proposed the following exogenously fixed inputs model (or called EXO DEA model). Minθ ,λθ

s.t. - yi + Y ⋅ λ ≥ 0,

θ ⋅ xi − X ⋅ λ ≥ 0, (i = 1,2,..., m' ) xi − X ⋅ λ ≥ 0, (i = m' +1, m' +2,..., m)

(6)

λ = 1, λ ≥ 0 where xm’+1, xm’+2,…, xm denote non-controllable input variables. The constraints xi − X ⋅ λ ≥ 0 limit that DMUs with the same or similar environments should be compared. Some of the non-controllable inputs in model (6) may be categorical variables; for example, xm is further classified into four distinct levels--none, low, average and high, where “high” denotes the most favorable situation. Banker and Morey (1986b) further introduced the descriptor binary variables into model (6) and termed as categorical DEA model as following:


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Minθ ,λθ s.t. - yi + Y ⋅ λ ≥ 0,

θ ⋅ xi − X ⋅ λ ≥ 0, (i = 1,2,...,m' ) N j=1

λ j d m1 , j ≤ d m1 , j 0 ,

N j=1

λ j d m2 , j ≤ d m2 , j 0 ,

(7) N j=1

λ j d m3 , j ≤ d m3 , j 0 ,

λ = 1, λ ≥ 0 where d m1 , j = d m2 , j = d m3 , j = 0 , for none level; d m1 , j = 1, d m2 , j = d m3 , j = 0 , for low level;

d m1 , j = d m2 , j = 1, d m3 , j = 0 , for average level; d m1 , j = d m2 , j = d m3 , j = 1 for high level. To compare the performance measurements in a homogeneous environment, various types of model (7), called CAT DEA models, can be formulated according to appropriate categorical variables. 3. EMPIRICAL ANALYSIS 3.1 Data Sources In economics, factors of production can be classified into two categories: capital and labor. In transportation economics, it is useful to make a further distinction between two types of capital: fixed facilities and vehicles (Boyer, 1998). On the output side, in general, railways produce two kinds of service: passenger and freight. Two output indices were considered in previous literature: train-kilometer for supply side measures and passenger-kilometer and ton-kilometer for demand side measures. Coelli and Perelman (1999) choose staff level, number of rolling stock and length of lines as input factors and passenger-kilometer and ton-kilometer as outputs to estimate the technical efficiency (more accurate, technical effectiveness) of 17 European railways. In this paper, we attempt to estimate both of the technical efficiency and service effectiveness for worldwide rail systems by employing two-stage DEA. At the technical efficiency analysis stage, we use input orientation DEA by selecting length of lines, number of locomotives and cars, and number of employees as inputs and train-kilometer as output. At the service effectiveness analysis stage, we use output orientation DEA by selecting train-kilometer as input and passenger-kilometer and ton-kilometer as outputs. In addition, we perform a technical effectiveness analysis with one-stage (hyperbolic) DEA by choosing the same input factors and outputs as what were used by Coelli and Perelman (1999). Our data set comes from International Union of Railways (UIC) statistical data. There are more than a hundred railways reported in the UIC data set. Some of them produce only passenger or freight service. Because we attempt to compare performance of the multiple-input and multiple-output railways, therefore, we delete all the single output firms (only passenger or freight) and let the remaining 76 railways be included in the sample set. The sample set covers three years from 1999 to 2001 and includes railways in America, Africa, Asia, Europe and Oceania. Table 1 shows the descriptive statistics of output, input and environmental variables. One may argue that there might exist some environmental differences among samples. Truly, samples are distributed among developed countries, developing countries and the third world, respectively. Besides, some of them are large scale with length of line more than ten-thousand kilometers, while some others are small networking less than a hundred kilometers. As Golany and Roll (1989) mentioned, selection of DMUs can be a contradictory consideration. On one hand, one looks for a homogeneous Journal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003

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set of units where comparison makes more sense; on the other hand, one tries to identify the differences between them. Thus, we further identify the influential factors by using Tobit regression techniques. Table 1. Descriptive Statistics of the Selected 76 Rails Description statistics

Consumption Pass-km Ton-km ( 106 ) ( 106 )

Output Train-km ( 106 )

Input Lines (km)

Cars

Environment Labors

GNI

Max. 240,658 1,249,166 1,289 85,835 582,006 1,239,800 41,770 Min. 12 10 0.4 97 114 500 170 Mean 11,220 27,217 85 6,477 25,651 46,986 9,793 Std. Dev. 33,409 145,332 212 12,023 73,503 149,724 11,722 Note: GNI denotes per capita gross national income (US dollar) and POP denotes population density per square kilometer) of the country to which the railway belongs.

POP 615.4 1.5 99.3 107.9 (persons

3.2 Important Findings We estimate efficiency and effectiveness scores by different DEA approaches utilizing the software GAMS 2.50. The detailed analysis results for each DMU are presented in Appendix. Table 2 reports the distribution of efficiency and effectiveness scores. It should be noted that since technology does not change during the three-year sampling period (1999-2001), we only explain the results for 2001. Based on the results and extended analysis, some important findings are summarized and discussed as follows. Table 2. Distribution of Efficiency and Effectiveness Scores by Different DEA Approaches

No. of DMUs for Efficiency Measures No. of DMUs for Effectiveness Measures HYP CCR BCC EXO CAT1 CAT2 CAT3 CCR BCC EXO CAT1 CAT2 CAT3 < 0.500 62 52 22 28 27 42 54 54 43 42 48 48 24 0.500~0.599 0 5 7 10 9 7 5 5 5 6 5 7 12 0.600~0.699 4 5 9 7 7 9 6 4 6 5 6 4 13 0.700~0.799 3 1 2 4 3 2 3 2 1 2 3 3 5 0.800~0.899 2 2 4 4 3 1 1 2 3 3 2 2 4 0.900~0.999 0 1 2 1 1 0 4 2 2 2 2 2 9 1.000 5 10 30 22 26 15 3 7 16 16 10 10 9 Max. 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Min. 0.020 0.039 0.232 0.106 0.117 0.039 0.081 0.081 0.081 0.081 0.081 0.081 0.245 Mean 0.318 0.407 0.725 0.631 0.662 0.479 0.421 0.448 0.535 0.533 0.490 0.485 0.650 Std. Dev. 0.284 0.311 0.268 0.300 0.293 0.325 0.247 0.263 0.311 0.311 0.280 0.281 0.226 Note: CCR denotes the model proposed by Charnes, Cooper and Rhodes (1978), BCC stands for the model proposed by Banker, Charnes and Cooper (1984), EXO represents the exogenously fixed inputs DEA model, CAT1, CAT2, and CAT3 denote that samples are categorized by region, GNI and POP, respectively. HYP is one-stage hyperbolic DEA model. Scores

Finding 1. Efficiency and effectiveness scores are relative low and vary among regions From Table 2 we note that, in general, low efficiency and effectiveness scores are found in the rail industry with few exceptions. The average efficiency is 0.407, while average effectiveness is 0.448 (both in BCC model). This partly reflects that most railways have been facing a decline situation. We adopt Kruskal-Wallis rank test (Sueyoshi and Aoki, 2001) to examine whether scores vary among regions or not. The samples are divided into four regions, which are West Europe and America, East Europe, Asia (Oceania and Mid-East included), and Africa. The test statistic given by Hays (1973) is expressed as:


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H=

12 N ( N + 1)

T j2 j

nj

− 3( N + 1)

where Tj is sum of ranks for group j, nj is number of group j and N is total number of samples. After eliminating the effect of ties, we obtain Heffi = 26.6 and Heffe = 51.54, both greater than the critical value of 2 (=7.815, with dof=3 and Pr=0.05). Therefore, we reject the null hypothesis of scores invariance among regions; that is, both efficiency and effectiveness scores vary among these four regions. On average, railways in Africa explore less efficient and less effective than those in West Europe and America. In the later analysis, we will further construct a region-specific categorical DEA model in order to compare the efficiency and effectiveness of DMUs within the same region.

Finding 2. Technical changes do not occur during the sampling period 1999-2001 Our data cover the years from 1999 to 2001, it thus needs to examine whether frontier shifts during this period. Kruskal-Wallis rank analysis can also be used to test whether a frontier shifts or not (Sueyoshi and Aoki, 2001). Firstly, we estimate the efficiency and effectiveness by using model (2) and (4) with the three-year samples (i.e. N=3×76=228), respectively. Secondly, same models are applied with the samples of 2001. All scores are ranked in a single series and Kruskal-Wallis rank analysis is then applied. By eliminating the effect of ties, the efficiency and effectiveness statistics (H) are 0.092 and 0.873, respectively, both less than the critical value of 2 (=5.99, with dof=2 and Pr=0.05). The null hypothesis (technical changes do not occur during the observed period) cannot be rejected; thus, the findings from 2001 also interpret those resulted from three-year sampling period.

Finding 3. VRS is prevailing in the rail industry The results denoted above are based both on the assumptions of constant returns to scale (CRS) and variable returns to scale (VRS). To investigate which scale is more appropriate to rail systems, Banker (1996) proposed the following method. Assume that is half-normally distributed, we evaluate the statistic THN =

N j =1

(θ Cj − 1) 2 / (θ jB − 1) 2 . If THN is greater than

Fcritical (N,N), reject the null hypothesis of CRS. Firstly, we test for normality by applying the kurtosis method (Thode, 2002), b2=m4 / (m2)2, where m4 and m2 are the fourth and second moments, respectively. Since b2 is 2.827, for two-sided 0.05 test, 2.20

technical efficiency and service effectiveness for ... - Semantic Scholar

technical efficiency and service effectiveness for ... - Semantic Scholar

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