China’s Traffic and Transportation System
Based on Data Envelopment Analysis1
Yu Senfa Chen
Weifeng
School of Economics and Management School of Economics and Management
Southeast University Southeast University
Nanjing, PRC 210096 Nanjing, PRC 210096
chensenfa@163.com y_weifeng@126.com
Yu Yang
School of Economics and Management
Southeast University
Nanjing, PRC 210096
yangyu.seu@gmail.com
Abstract
This paper evaluates the relative efficiency of decade’s development of traffic and
transportation system in China and present regional development based on data
envelopment analysis. The result concludes that the input and output efficiency of
China has not promoted significantly, and the unbalance development between
regions exists. Some regions have a relatively low efficiency and little correlation
with their developing levels, so great attention should be paid to promote the
efficiency of regional traffic and transportation productivity.
Keywords:traffic and transportation; DEA; relative effectiveness; evaluation
1Introduction
Traffic and transportation is the infrastructure and mainstay industry of national economy, and the level of transportation could promote or restrict the scale and speed of national economy to a large extent, so they have a very important effect on national economy. The transportation is not only an issue of society, but also related with economics that the high-efficiency and low-cost transportation is considered as the foundation of a success economy [1]. The traffic and transportation industry is less developed in China, and putting traffic and transportation in the first place has become a great strategic decision in our country at present. Investment on traffic and transportation has been gradually increased these years, and the whole industry has been growing at a high speed. However, it is not clarity about the trend of the efficiency in traffic and transportation. We also want to know whether the unbalance among areas can be blamed to the developing level of the economy. The Data Envelope Analysis[2] (DEA) would be applied in this paper to
1Support by the Doctoral Discipline Fund Project of China Education Ministry (license number：20060286005).
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study the relative efficiency in our country these decades as well as the regional development, which could be a reference for the promoting of transportation benefits and policy making in a macro view.
2 Brief introduction of DEA model and its economic meaning
DEA (Data Envelopment Analysis) was initially proposed by Charnes, Cooper and Rhodes in 1978[2]. Suppose there are n organizations (or entities) which are responsible for converting inputs into outputs and whose performances are to be evaluated. In DEA, each organization (or entity) likes what is called a DMU (Decision Making Unit). For each DMUs, m input items and s output items are selected with properties that numerical data are available for each input and output, with the data assumed to be positive for all DMUs. Let the input and output data for DMU j be 12(, ,,
)j j mj x x x "and ()12,
,,j j sj y y y "respectively, and let
12 (,,,)1,2,, T j j j mj x x x x j n ==""， (1)
12 (,,,),1,2,,T j j j sj y y y y j n ==""
(2)
Given the data, we measure the efficiency of each DMU once and hence need n optimizations, one for each DMU j to be evaluated. Let the DMU j to be evaluated on any trial be designated as DMU 0 where 0 ranges over 1, 2… n . We solve the following fractional programming problem to obtain values for the input “weight”12
((,,,))T
m v v v v =" and the output “weight”12((,,,))T
s u u u u ="as variables [2].
max 1,1,2,,,0,0.T T
T j
T j
u y v x u y j n v x u v ⎧⎪⎪⎪⎪≤=⎨⎪⎪≥≥⎪⎪⎩
" (3)
The objective is to obtain weights v and u that maximize the ratio of DMU 0, the DMU being evaluated. The above fractional program (3) is equivalent to the following linear program (4), and now we replace (1) by (2).
200max ,
0,1,2,,,()1,0,0.T T
T
j j C R T
y x y j n P x μωμωωμ⎧⎪−≥=⎪⎨
=⎪⎪≥≥⎩" (4)
In the above linear program (4), row vector μfor input multipliers and row vector ωfor input multipliers are treated as variables.
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The dual program of 2()C R P is expressed with a real variable θand the transpose, T, of a nonnegative vector 1(,,)T n λ
λλ=
201
011min ,(),0,1,2,,,.n
j j j n
C R j j j j x x
D y y j n
E θ
λθλλθ==⎧⎪⎪≤⎪⎪⎨⎪≥⎪⎪≥=∈⎪⎩∑∑" (5)
Introducing non Archimedean infinitesimal vector ε
[3]
, a standard linear program model can be given as
follows:
20101
1min [()],0,()0,0,1,2,,,,0,0.T T m s n j j j n j j C R
j j
e S e S x x s D y y s j n E s s ε
θελθλλθ−+−=+=−+⎧−+⎪⎪−+=⎪⎪⎪−−=⎨⎪⎪≥=⎪⎪∈≥≥⎪⎩∑∑" (6)
Here m s
R −
∈and s s R +∈are defined the input excesses and output shortfalls respectively, and identify
them as “slack” vectors. Let the optimal objective value be *
θ. The meaning of
*θ is the degree of that 0x
reduce by the same proportion while 0y is fixed in production possibility sets. 0DMU is called weakly CCR-efficiency if 0x can not be reduced ，
i.e. *1θ=. 0DMU is called CCR-efficiency if 0DMU is
weakly CCR-efficiency and at the same time the “slack” vectors are all zero. Base on nature of CCR-efficiency, DEA efficient Decision Making Unit is scale efficient and technique efficient. A Decision Making Unit is not scale efficient and technique efficient if 0x can be reduced by the same proportion ，i.e.
*1θ<. The economic meanings of the value of *
θ
is relative efficiency of input and output, and is the
least input proportion for a fixed output comparing to the most efficient Decision Making Unit.
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For returns to scale ，*
1
1
n
i i αλθ
==
∑can characterize its change , 1α 1α= means returns to scale is invariable. If a DMU is not CCR-efficiency judged by (5), the following model, linear program 22C GS D ε , can be used further to evaluate its scale efficient and technique efficient. Reasons of why a Decision Making Unit is not technique efficient can clearly be seen from the value of s −and s + [4]. 220101 1 1min [()], 0,0,()1,0,1,2,,,,0,0.T T m s n j j j n j j j C GS n j j j e S e S x x s y y s D j n E s s ε θελθλλλθ−+−=+ ==−+⎧−+⎪⎪−+=⎪⎪⎪−−=⎪⎨⎪⎪=⎪⎪≥=⎪⎪∈≥≥⎩∑∑∑" (7) 3 Evaluation on relative efficiency of China traffic and transportation system based on DEA 3.1 E valu a t io n on in pu t an d ou tpu t eff ici en cy of Ch in a t raff ic an d t r an s po r t at i on sys t e m i n t he p as t 50 yea r s b as e d on DEA 3.1.1 I n d exe s ch oos in g an d d at a pr oce ss in g According to theory of production factors, input can divided into labor and capital, and quantity of employee can be considered as labor input index and fixed assets investment as capital input index. For output index, this paper chooses passenger volume, passenger transportation volume, freight volume and freight turnover volume [5] because they embody transport capability quite well. Considering relevant data from the year 1956 to 2005[6] *, we can get the results given in table I: TABLE I: Input and Output of Chinese Transportation System YEAR CAPITA L INPUT (HUNDR QUANTITY OF EMPLOYE E PASSENG ER VOLUME PASSENGE R TRANSPOR TATION FREIGH T VOLUM E FREIGHT TURNOVER VOLUME THOUSAN D MEN) (TEN THOUSAN D MEN) VOLUME(H UNDRED MILLION PERSON KILOMETE RS) (TEN THOUS AND TONS) (HUNDRED MILLION TONS KILOMETE RS) 1956 6.74 50621 465.30 82002 1602 1957 5.50 129.06 63821 496.60 990 1826 1958 13.12 156.28 75136 572.30 132377 2480 1959 16.12 188.50 91138 711.70 206050 3347 1960 17.93 211.10 106700 883.60 223052 3740 1961 4.17 187.53 119835 1105.30 132477 2665 1962 2.22 134.92 122154 1085.60 92185 2252 1963 3.44 130.92 97538 726.60 94062 2363 19 6.42 136.15 94300 685.80 114168 2769 1965 8.74 149.24 96334 697.00 133253 3485 1966 9.37 145.29 108656 778.80 1442 3920 1967 8.13 144.55 114067 863.80 123804 3069 1968 6.13 146.04 111182 936.30 115053 3126 1969 10.92 152.66 123859 1070.70 138238 38 1970 15.30 163.80 130056 1031.10 167913 4590 1971 14.19 178.30 142931 1106.50 194469 5236 1972 16.82 194.31 160828 1235.70 211877 5685 1973 23.83 193. 174805 1325.20 225473 6342 1974 29.99 198.45 182146 1376.60 223860 6367 1975 32.21 212.62 192969 1434.60 251593 7594 1976 25.13 225.44 201411 1469.60 253967 6979 1977 21.54 234.06 225007 1586.70 290254 8063 1978 24.85 271.00 253993 1743.10 319431 9928 1979 25.50 488.34 2665 1968.50 318258 11014 1980 24.39 493.32 341785 2281.30 310841 11629 1981 19.82 496.88 384844 2499.60 2982 11747 1982 25.74 499.96 42 2742.80 311974 12540 1983 29.98 498.63 470614 3095.00 323956 13466 1984 52.42 503.03 530217 3620.40 339995 14920 1985 69. 509.30 620206 4436.40 745763 18365 1986 106.46 518.06 688212 46.80 853557 20147 1987 122.71 520.28 7422 5411.50 948229 22228 1988 138.57 518.66 809592 6209.40 982195 23826 19 156.05 516.35 791376 6074.60 988435 25591 1990 180.53 521.28 772682 5628.30 970602 26207 1991 215. 530.26 806048 6178.40 985793 27986 1992 360.24 529.00 860855 6949.40 10459 29218 1993 604. 523.15 996634 7858.10 1115902 30525 1994 791.43 521.35 1092881 8591.40 1180396 33275 -5-1995 1124.78 538.90 1172596 9001.90 1234937 35909 517.80 1245356 91.80 1298421 36590 1996 1287.25 510.30 1326094 10055.50 1278218 38385 1997 1530.43 398.70 1378717 10636.70 1267427 380 1998 2460.41 373.90 1394413 11299.80 1293008 40568 1999 2460.52 359.80 1478573 12261.00 1358682 44321 2000 31.94 2001 4116.43 482.42 1534122 13155.13 1401786 47710 465.50 1608150 14125.70 1483446 50686 2002 4393.98 528.90 1587497 13810.50 1561422 53859 2003 42.70 2004 7091.50 520.29 1767453 16309.10 17012 69445 80258 17466.74 1862066 2005 8860.40 508.90 1847018 * data after year 2000 root in: China statistic yearbook(2000～2005). Beijing: China statistic press. To simplify operations and obtain overall development trend of transportation system efficiency, Let each five-year operation of Chinese transportation as one DMU, so there are 10 DMUs. In each DMUs, the value of each index is come from the average of five years’ corresponding data. According to model (6), there build 10 linear program problems. solving these problems by Lingo software, the results are given in table II. From table II it can be seen that efficiency is rising gradually from DMU1956~1960 to DMU 1966～1970. All DMUs are weakly CCR-efficient after 1966～1970, and DMU1986～1990 is CCR-efficient. Figure 1 depicts the changes of relative efficiency of all DMUs. Table II: Value of Each DMU’s Efficiency θ DMU * 1956～1960 0.95246 1961～1965 0.99476 1966～1970 1 1971～1975 1 1976～1980 1 1981～1985 1 1986～1990 1 1991～1995 1 1996～2000 1 2001～2005 1 -6- -7- Fig. 1. Trend of efficiency for each DMUs: DMU1955~1960 ~ DMU2000~2005. 3.1.2 E valu at io n on t he ef f ic ien cy of Ch in a ’s t r an sp o rtat ion From Figure 1, we can see that the efficiency of traffic and transportation in our country is relatively low, but the efficiency is increasing. In the early stage of liberation, the national economy is less developed, and the traffic and transportation laid particular stress on the eastern coast region, had an inconsequential structure with backwardness in transportation technical equipment. With the development of national economy, the transportation industry has enlarged not only in scale, but also in efficiency. While from the 1970s, each optimal solution of all DMUs ,* θ,are all equal to 1，which does not indicate that the economic benefit is in an “optimal” estate at all times for the reason that the * θ is a relative efficiency and the efficiency of our transportation is stagnating for a long time. There are some reasons for this. The traffic and transportation system is divided and administrated by transport modes, keeping unchanged after several reforms and the adjustment of enterprises. Although administration sectors separated and integrated many times, the function did not change at all and were kept intersected. Because of the dividedly administration by several sectors, administration as an entire industry lacked. It is limited for the corresponding adjustment among different transporting ways so that an integrated transportation system can hardly established all round this country, which is also the reason why the operation efficiency could not be promoted for long. In the condition of dispersive decision making, the phenomena of “many departments in a government” and do in own ways is inevitably. Investment in different transporting ways can not receive their reasonable distribution proportion and the establishment can not be allocated reasonably. Cargo transported in different ways can not be carried out fast and economically. These backwards are all against the rules of economics, leading to waste to different extents, and make it difficult to solve the problem of overall arrangement of traffic and transportation. In addition, the non separation between the government and the enterprises would weaken the function of governments’ macro administration; excessively centralize the power of communication departments, while enterprises are lack of freedom for their own operation, so it is difficult to activate the enthusiasm of enterprises and employees, all of which are the important factors restricting the promotion of efficiency. 1.01 0.95 0.96 0.97 0.98 0.99 1 t ran s p ort at i on b as ed on DEA The current Chinese economy and region development is imbalanced. Transportation, as the foundation of national economy, which promotes mutually with economy, also performance similarly, this imbalance displays in two aspects, and one displays heterogeneity in the transportation scale in the region space; the other is the regional disparity on the investment-benefit. Generally, the existence of the first difference is reasonable and essential, or at least it can be a strategic decision during a certain time, which is the result of transports layout or the adjustment according to the natural resource distribution, the local economical characteristic, the productive forces layout and so on. As for the second difference, this article uses evaluation model (6), and applies the statistical data in 2005. Its input indexes are still fixed assets and employee. Passenger volume, passenger transportation volume, freight volume and freight turnover volume are to be as the output indexes, relevant data of 31 provinces in China are given in Table III. Table IV: Input and Output of 31 Provinces in China PROVINCE FIXED ASSETS (HUND RED MILLIO N YUAN) EMPLO YEE (PERSO NS) PASSENGE R VOLUME (TEN THOUSAND MEN) PASSEN GER TRANSP ORTATI ON VOLUME (HUNDR ED MILLION PERSON KMS) FREIGH T VOLUM E(TEN THOUSA ND TONS) FREIGHT TURNOVE R VOLUME (HUNDRE D MILLION TONS KMS) Beijing 240.9 133393 8040 137.1 32113 582.1 Tianjin 151.7 74216 4514 117.5 39219 12593.0 Hebei 420.5 200158 804 9.8 88342 5068.1 Shanxi 217.6 152987 39975 2.4 133662 1690.9 Neimenggu 362.2 124170 31776 287.3 69187 1437.1 Liaoning 301.6 234440 60100 599.9 95558 3350.5 Jilin 175.1 127384 27601 244.7 34162 605.9 Heilongjiang 182.7 213142 55408 432.2 61800 1167.4 Shanghai 416.2 130030 7985 128.4 68636 12128.1 Jiangsu 585.5 235031 145121 1193.6 111233 2993.2 Zhejiang 723.7 127705 161115 848.5 126903 3417.0 Anhui 246.5 1070 72657 782.4 67125 1566.1 Fujian 270.9 97153 55121 397.1 41200 1573.1 Jiangxi 310.3 117800 41586 592.4 33996 885.2 Shandong 405.7 211823 98506 827.8 144701 5551.0 Hennan 541.4 248209 976 998.3 78699 2352.5 Hubei 292.7 210155 70497 663.0 46766 1415.7 Hunan 216.6 157743 116091 1011.5 77534 1628.6 Gangdong 635.0 312985 1496 1448.4 119287 3860.3 Guangxi 195.7 131795 51396 557.7 38226 1098.3 Hainan 32.5 36074 26785 .5 10182 448.8 -8-Chongqing 228.3 98268 63308 280.0 39329 625.5 Sichuan 278.0 160728 168505 682.3 67351 916.6 Guizhou 144.7 61746 450 312.4 21770 6.5 Yunnan 337.5 96157 40792 291.0 62015 680.6 Xizang 62.8 3927 385 18.4 356 40.7 Shan’xi 241.3 157855 38725 486.2 41551 1028.8 Gansu 137.4 87025 17804 302.9 26653 983.2 Qinghai 58.8 25026 4886 43.3 6816 147.1 Ningxia 44.0 25019 7066 62.4 8529 255.2 Xinjiang 211.6 76352 24309 306.2 30041 806.6 * data root in：China statistic yearbook 2006 According to model (6), 31 linear program problems are established respectively for 31 provinces of China. Use the computer to solve these problems, and get results in table V. From table V, Transportation investment-production efficiency and relative efficiency of 31provinces are huge different, weak CCR-efficiency provinces include Tianjin, Hebei, Shanxi, Heilongjiang, Zhejiang, Anhui, Hunan, Hainan, Sichuan and Guizhou, and Shanxi is CCR-efficiency. Relatively the lowest efficiency provinces are Beijing, Jilin, Hubei, Shaanxi and Qinghai. Figure 2 is the broken line drawings of 31 provinces relative efficiency (value *θ). From table V it can be seen that there is no necessary relation between transportation efficiency and the developing level of economy in various provinces. There is a universal viewpoint that in economic developed area transportation efficiency is also inevitably high, but actually this viewpoint is one-sided, or even wrong. It can be seen clearly from the table V for economical developed provinces like Beijing, Guangdong, Chongqing and so on, their transportation efficiencies are not high, but in some economical backwardness areas like Anhui, Hunan, Guizhou, their traffic and transportation operates very efficiently. For not CCR-efficiency DMUs, using followed model (7) and having further analysis, input excesses and output shortfalls are the two primary reasons of why relative efficiencies of these provinces are low. Table V: Relative efficiency of each province PROVINCE*θPROVINCE*θ Hainan 1 Henan 0.628612 Tianjin 1 Xinjiang 0.571569 Hebei 1 Shandong 0.946797 Anhui 1 Shanghai 0.771402 Zhejiang 1 Jiangsu 0.761572 -9-Hunan 1 Yunnan 0.757529 Shanxi 1 Liaoning 0.7291 Heilongjiang 1 Guangdong 0.700799 Sichuan 1 Gansu 0.570799 Guizhou 1 Ningxia 0.5121 Neimenggu 0.696512Hubei 0.493 Jiangxi 0.684338Shan'xi 0.493123 Chongqing 0.67808 Jilin 0.426011 Fujian 0.658162Qinghai 0.351744 0.2971 Guangxi 0.655382Beijing Xizang 0.2943 Fig. 2. Relative efficiency of each province. At abscissa in this figure, 1 to 31 respectively represent 1Hainan, 2Tianjin, 3Hebei, 4Anhui, 5Zhejiang, 6Hunan, 7Shanxi, 8Heilongjiang, 9Sichuan, 10Guizhou, 11Shandong, 12Shanghai, 13Jiangsu, 14Yunnan, 15Liaoning, 16Guangdong, 17Neimenggu, 18Jiangxi, 19Chongqing, 20Fujian, 21Guangxi, 22Xizang, 23Henan, 24Xinjiang, 25Gansu, 26Ningxia , 27Hubei, 28Shan'xi, 29Jilin, 30Qinghai, 31Beijing. The evaluation results are mainly caused by their own reasons, besides some relationship with the choosing of indexes in this paper [7]. The same as other production industries, the transportation industry seeks for the benefit as well as the amount of output, while the repeated low-level construction of infrastructure, myopic investment on fixed assets and despising the administration take place frequently. Therefore, the regional development can not be blamed to governments’ investment or the developing level of a certain region. Although the macroeconomic control has a significant meaning, currently in our country, as resources are scarce and short of transportation capacity, more attention should be paid to the efficiency of transportation, improving management and quicken the steps to the integration of transportation in appropriate ways. 4 Conclusion China’s traffic and transportation has been gotten great achievements. In the year 2005, China passenger -10-volume reached 18.5 billion, and passenger transportation volume, freight volume and freight turnover volume reached 1747 billion person kilometers, 186 trillion tons, and 8026 billion ton kilometers respectively. These numbers are dozens times of that in decades ago. Generally, scale efficiency exists in traffic and transportation industry, while in this paper, the input and output efficiency of traffic and transportation industry during the last 50 years is studied using DEA methods, and quantitative comparative analysis in different periods is also carried out. The result concludes that the efficiency has not promoted in the last 30 years expect the first periods. Besides, this paper studies the difference of efficiency among regions in a quantitative way, and the result indicates that there exists an unbalance and significant difference among regions. And there is no necessary relation between transportation efficiency and the developing level of economy (see Figure 2). In the periods of high-speed developing, each sectors of traffic and transportation industry should pay enough attention to the promotion of their efficiency, deepen the reform of the system, and optimize the resource allocation of transportation. In further research, we will consider the change in price level of the capital, which is ignored in this paper. References [1]Cai Qinglin, Zhang Xiuzhi and Liu Yanqin. Subject of Transportation Layout. Beijing: Science Press, 2004, ch. 1. [2]William W. Cooper, Lawrence M. Seiford and Kaoru Tone, Introduction to Data Envelopment Analysis and Its Uses. New York: Springer Science+Business Media, 2006, ch. 2. [3]Wei Quanling. Data Envelopment Analysis. Beijing: Science Press, 2004. 2－30. [4]M. Khodabakhshi, “A super-efficiency model based on improved outputs in data envelopment analysis”. Applied Mathematics and Computation, 184 (2007): 695–700. [5]Xiong Chongjun, Ding Zhaoxuan, and Pan Ying, “Research on the correspond development of Chinese integration transportation ways”. System Rngineering, 2006, (6): 1-5. [6]Integration Layout Department of Ministry of Communications, Compile of Statistic Dada of New Chinese Fifty Years’ Traffic.Beijing: public traffic press, 2000. [7] Mette Asmild, Joseph C.Paradi, David N.Reese and Fai Tam, “Measuring overall efficiency and effectiveness using DEA”. European Journal of Operational Research, 178 (2007): 305–321. -11-下载本文
