THE ASSESSMENT OF TURKISH RAILWAY TRANSPORTATION SYSTEM AT THE FIRST DECADE OF THE 21TH CENTURY BY APPLYING MULTI-CRITERIA DECISION MAKING METHODS

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1 . Uluslar arası Raylı Sistemler Mühendisliği Sempozyumu (ISERSE 3), 9 Ekim 03, Karabük, Türkiye THE ASSESSMET OF TURKISH RAILWAY TRASPORTATIO SYSTEM AT THE FIRST DECADE OF THE TH CETURY BY APPLYIG MULTICRITERIA DECISIO MAKIG METHODS Muharrem ÜVER a, Esra Kurt TEKEZ b, Ercüment eşet DİZDAR a a Karabük University, Engineering Faculty, Department Of Industrial Engineering, 7800 Karabük, Turkey b Sakarya University, Engineering Faculty, Department Of Industrial Engineering,Esentepe Campus, 5487 Sakarya, Turkey Abstract In this paper, Turkish railway transport system is evaluated throughout 00 0 by applying multi criteria decision making methods. Each year are considered as a decisionmaking unit called DMU. The assessment of the efficiency of railway transportation is made by applying the methods of Multi Obective Optimization by Ratio Analysis plus the Full Multiplicative Form (MULTIMOORA) and Data Envelopment Analysis (DEA). For this purpose, two inputs namely energy consumption and labour in railway transport are considered in the conducted analysis. On the other hand, two forms of transport passenger and freight transport are distinguished, and each of them is measured using indicators of passenger and milliontonne kilometres respectively. As a conclusion, the final ranks provided by MULTIMOORA and DEA methods are compared according to performance efficiency of each year. The proposed evaluation in this study would help to decisions in the railway transport. Keywords: MultiObective Decision Making, MCDM, MULTIMOORA, DEA, Efficiency, Railway Transport System.. Introduction The assessment of the efficiency of a certain economic sector as railway transportation has high importance when making strategic decisions at any management level. This study, hence, is aimed at evaluating Turkish railway transport sector by applying multicriteria decision making (MCDM) method MULTIMOORA (Multi Obective Optimization plus the Full Multiplicative Form) and Data Envelopment Analysis (DEA). Due to limited data availability, we analyzed the railway transport sector as a whole, i. e. it was not decomposed into that of land, air, railway or water. Although every production factor, including, capital and land is required for developing the railway transport sector, due to limited data availability, it is not possible to tackle them all when performing analysis (Baležentis, A. and Baležentis, T., 0). Consequently, one input, namely energy consumption in railway transport, was considered in the conducted analysis. Indeed, relatively high energy intensity and labor is peculiar for economy (Streimikienė et al. 007 Klevas, Minkstimas 004 Baležentis et al. 00). Therefore, the identification of energy inefficient sectors is an important issue. On the other hand, two forms of railway transport passenger and freight transport may be distinguished, and each of them was measured using composite indicators of passenger kilometres (PKM) and freight tonnekilometres (FKM) respectively (Ramanathan 000). These two indices were considered as the outputs of transport sector activity. Moreover, two methods, namely MULTIMOORA and DEA, were employed in the performed analysis. MCDM methods are becoming more and more actual nowadays. The widening spectrum of multi criteria problems encompasses business decision making, ranking schools, public procurements etc. (Peldschus, Zavadskas 005 Peldschus et al. 00 Kahraman 008 Roy 005 Ananda, Herath 009 Zavadskas, Turskis0). In this study, the MULTIMOORA method will be applied when estimating the efficiency of Turkish railway transport sector. This method was introduced and developed by Brauers and Zavadskas (006, 00a). MULTIMOORA summarizes three methods thus offering robust ranking options. Hence, the MULTIMOORA method will be employed when evaluating the efficiency of the railway transport sector. However, MCDM methods provide ranking without any additional information. Therefore, the use of additional methods becomes an actual issue (Baležentis, A. and Baležentis, T., 0).

2 The DEA, it is a nonparametric method of measuring the relative efficiency of a decision making unit such as a firm or public sector agency, which results in estimating actual as well as potential efficiency. Ranking based on such efficiency is usually not very robust (Jaržemskienė 009). evertheless, DEA offers some additional information that soundly supports multi criteria optimization. The modern DEA was first introduced by Charnes et al. (978). DEA is a relative, technical efficiency measurement tool that uses operations and research techniques to automatically calculate the weights assigned to the inputs and outputs of the production units being assessed (Kahraman 008). DEA was applied in many studies like the studies of agriculture (Alvarez, Arias 004), transport (Hermans et al. 008 Jaržemskienė 009 MarkovitsSomogyi 0), healthcare (Ró 00) and business performance (Halkos, Salamouris 004 Chen, Ali 004 Sufian 00). Recently, many improvements to DEA have been offered (Shetty, Pakkala 00 Zerafat Angiz et al. 00 Wang et al. 009). The DEA method will be applied in this study in order to evaluate the efficiency of Turkish railway transport sector. This research was carried out on the basis of data provided by Turkish State Railways Annual Statistics (accessible online ( and covers the period of This paper is organized as follows: Section deals with MULTIMOORA, the following Section 3 describes DEA and finally, the empirical application of the latter methods is discussed in Section 4.. MULTIMOORA Method The MODM methods start with a decision matrix of different alternatives or DMUs on different obectives (Brauers et al., 008) which are obtained from the raw data as in Table : Table. Initial decision matrix of MODM Ob. Ob. Ob.i Ob.n DMU X X X i X n DMU X X X i X n X X X i X n DMU X X X i X n X X X i X n DMU m X m X m X im X nm DMU: Decision Making Unit. where: xi is the response of DMU on obective or criteria i i =,,, n is the number of obectives or criteria =,,, m is the number of DMU. An obective and a correspondent criterion are always together. Eventually, when the text mentions each column as obective, the correspondent criterion is also meant. (Brauers et al., 008). If each column is translated in ratios dimensionless measures can be generated and the columns become comparable to each other. Indeed they are no more expressed in a unit. There can be possibility for different kind of ratios, but (Brauers and Zavadskas, 006) proved that the best one is based on the square root in the denominator. The Ratio System which forms the basis of the MOORA method follows the vertical reading of the initial decision matrix. The exact relation between the methods of MOORA with MULTIMOORA is given in Fig..

3 .. The MOORA Method Fig.. Diagram of MULTIMOORA Method Multiobective optimization, also known as multicriteria optimization, is the process of simultaneously optimizing two or more conflicting criteria (obectives) subect to certain constraints (Gadakh, 00). The MOORA (MultiObective Optimization by Ratio Analysis) is one of the new approaches in MODM which assesses the alternatives by ranking. MOORA, eventually assisted with the Ameliorated ominal Group Technique, is indeed composed of two methods: a Ratio System and a Reference Point Approach. (Brauers and Zavadskas, 0)... The Ratio System The Ratio System of MOORA defines data normalization by comparing a DMU of an obective to all values of the obective using Equation :, () where: denotes the ith DMU of the th obective (in this case, the th structural indicator of the ith state). Usually these numbers belong to interval [0 ]. These indicators are added with a maximization (for beneficial criterias) or subtracted with minimization (for non beneficial criterias) and a summary index of the state is derived in this way using Equation :, () where: g =,.,n denotes the number of obectives to be maximized. Then, every ratio is given the rank: the higher is the index, the higher is the rank.... The Reference Point Approach The reference point approach is based on the ratio system. The Maximal Obective Reference Point (vector) is found according to the ratios found in Equation. The th coordinate of the reference point can be described as in case of maximization. Every coordinate of this vector represents the maxima or minima of a certain obective (indicator). Then, every element of the normalized response matrix is recalculated and the final rank is given according to deviation from the reference point and the Min Max Metric of Tchebycheff as in Equation 3:, (3) 3

4 .. The Full Multiplicative Form and MULTIMOORA Brauers and Zavadskas (00) proposed MOORA to be updated by the Full Multiplicative Form method embodying the maximization and minimization of a purely multiplicative utility function. The overall utility of the ith DMU can be expressed as a dimensionless number:, (4) where:, i =,,, m denotes the outcome of the obectives of the ith DMU to be maximized with g =,,, n is the number of obectives (indicators) to be maximized and denotes the product of the obectives of the ith DMU to be minimized with n g is the number of obectives (indicators) to be minimized. Thus, MULTIMOORA concludes MOORA (i. e. the Ratio System and Reference point) and the Full Multiplicative Form as in Equation 4.. The Reference Point prevents MULTIMOORA from becoming a fully compensatory technique. Although the Ratio System and the Full Multiplicative Form are fully compensatory methods, the Reference Point is the method based on the Min Max metric of Tchebycheff and thus identifies certain DMUs peculiar with relative backwardness in either of criteria. Hence, MULTIMOORA is a quite effective method under the MODM Methods for assessing the sustainability of different phenomena resulting in the unbiased ranking of DMUs. 3. The Modern Version of Data Envelopment Analysis (DEA) The modern version of DEA originated in studies by Charnes et al. (978, 98). Hence, these DEA models are called CCR models. Initially, the fractional form of DEA was offered. However, this model was transformed into inputoutputoriented multiplier models, which could be solved by means of linear programming (LP). In addition, the dual CCR model (i.e. envelopment program) can be described for each of the primal programs (Cooper et al. 006 Ramanathan 003). In a revision of their original model Charnes, Cooper, and Rhodes (979) introduced penalties in the obective function for strictly positive input and output slacks. Their revised outputoriented model was as in Equation 5: max ~ = ( s s s s ) s. t. = y s = y t = = y = x x s s s = y = x = x t t t 0 ( =,,..., ) s, s, s, s 0 free. (5) Here is an infinitesimally small positive number (selected by the researcher). By including input and ~ * output slacks in the obective function, we ensure that > whenever any of slack variables is strictly positive at the optimal solution. Thus a firm will be rated as fully efficient only when * equals and all the slacks are equal to 0 at the optimal solution. Otherwise, its efficiency will be less than unity even when * equals. Consider the revised form of the inputoriented model as in Equation 6: 4

5 min ~ = ( s s s s ) s. t. = y s = y t = y s = y t = x s = x t = x s = x t 0 ( =,,..., ) s, s, s, s 0 free. (6) At present, the overall consensus in the literature is that presence of positive slacks in the optimal solution should be interpreted as merely signifying that the efficient radial proection of ( x t, y t ) is not Pareto efficient. Beyond that, the revised obective function value should not be used to obtain a scalar measure of technical efficiency. One should rather report the slacks separately along with the radial efficiency measure. In a later chapter we will return to the question of incorporating slacks in a scalar measure of efficiency. 4. Results The initial data are given in Table. One can notice that in this study each investigated year is treated as a separate DMU peculiar with a respective technological and economic environment. First, some general trends were observed during the period of YEARS Table. Inputs and outputs of the railway transport sector, 00 0 IPUT Energy Consumption (Tonne Of Oil Equivalent) (EC) 5 OUTPUT MI MI MAX MAX Labor (L) Volume Of Passenger Transport (Million PassengerKilometers) (PKM) Volume Of Freight Transport (Million TonneKilometers) (FKM) Energy consumption in the transport sector grew by 5% from 374 Tonne of Oil Equivalent (TOE) in 00 up to 7065 TOE in 0 with an average annual growth rate of %. The very peak of energy consumption was achieved in 0, too. The volume of railway passenger transport shrunk by 6,5% from 773 million PKM in 00 down to 6806 million PKM in 0 exhibiting an annual decrease rate in 0,5 %. In addition, the volume of passenger transport reached its low and peak in 00 and 006

6 respectively. Meanwhile, the volume of freight transport grew by some 8,3% from 476 FKM up to 8933 FKM in 0 with an annual growth rate of,3 %. Moreover, freight transport reached its peak in 0. The application of MULTIMOORA began with normalization (Table 3) according to Eq. (), see Table 3a. Subsequently, Eq. () was used in order to obtain the summarizing ratios of the Ratio System of MOORA(Table 3b). Eq. (3) was applied (Table 4) for the ratios obtained according to Eq. () therefore providing the ratios of the Reference Point of MOORA. Finally, the initial data were computed according to Formula (4) thus providing the ratios of the Full Multiplicative Form (Table 3a). The results of the Full Multiplicative Form and the Ratio System are shown in Figs respectively It is obvious that both methods suggest the railway transport sector operating the most effectively during the period of in terms of the indicators considered. Table 3. The Ratio System of MOORA and the Full Multiplicative Form (MF) Table 3a. The sum of squares and their square roots the Full Multiplicative Form YEARS EC L PKM FKM MF , , , , , , , , , , ,04 SUM OF SQUARES ROOT SUM OF SQUARES Table 3b. ormalized values of responses and the Ratio System (RS) YEARS EC L PKM FKM RS 00 0,793 0,3693 0,3083 0,599 0, ,743 0,3478 0,894 0,639 0, ,855 0,304 0,305 0,946 0, ,767 0,308 0,3043 0,3006 0, ,857 0,847 0,360 0,987 0, ,854 0,7 0,387 0,38 0, ,3089 0,306 0,35 0,303 0, ,398 0,9 0,973 0,39 0, ,350 0,776 0,307 0,30 0, ,384 0,648 0,745 0,39 0, ,3476 0,649 0,885 0,3333 0,009 6

7 The Reference Point approach, hence, will be used as a control method for obtaining more robust results. The Reference Point approach, therefore, provided additional information on measuring the relative efficiency of the railway transport sector in Turkey. According to Eq. (3), the summarizing ratio for a certain time period is the maximum deviation (distance) from the reference values of each criterion. As Fig. shows, these maximal values were defined according to different criteria during certain periods. Table 4. The Reference Point of MOORA Table 4a. Coordinates of The Reference Point EC L PKM FKM REFERECE POIT 0,743 0,648 0,387 0,3333 Table 4b. Deviations from The Reference Point YEARS EC L PKM FKM RP (MIIMAX) ,0050 0,045 0,004 0,0734 0,0000 0,0830 0,093 0,0694 0,0 0,0556 0,06 0,0387 0,004 0,0370 0,044 0,037 0,05 0,099 0,007 0,0346 0,0 0,0063 0,0000 0,05 0,0346 0,0378 0,006 0,030 0,0455 0,073 0,04 0,004 0,0407 0,08 0,070 0,03 0,054 0,0000 0,044 0,04 0,0734 0,000 0,030 0,0000 0,045 0,0830 0,0556 0,0370 0,0346 0,05 0,0378 0,0455 0,0407 0,054 0,0734 The ranks were given by maximizing the ratios of the Ratio System and the Full Multiplicative Form and minimizing ratios (distances) from the Reference Point. Finally, the results of the three parts of MULTIMOORA are summarized in Table 5. 7

8 Table 5. The efficiency of the transport sector according to MULTIMOORA YEARS RATIO SYSTEM REFERECE POIT APPROACH MULTIPLICATIVE FORM of MULTIMOORA RATIO SYSTEM REFERECE POIT APPROACH MULTIPLICATIVE FORM of MULTIMOORA Fig.. The efficiency of Turkish Railway Transport sector according to the Full Multiplicative Form, The ranks provided by different parts of MULTIMOORA were summarized according to the dominance theory (Brauers, Zavadskas 0). However, in this particular case, the final ranks coincided with those provided by the Full Multiplicative Form. To conclude, the final ranks provided by MULTIMOORA indicate that the railway transport sector was operating most effectively during , whereas it exhibited relative inefficiency throughout

9 Table 6. Potential outputs of the transport sector according to DEA, 00 0 YEARS (%) Slack For PKM (Ө) (%) Slack For FKM (Ө) 00 9, 7,8 00 6,7, ,4 6, ,0 0, ,0 0, ,0 0, ,4 3, , 4, 009 0,0,4 00 3,3 5, 0 3, 3,0 DEA was performed by employing the LIDO programme. The relative efficiency of the railway transport sector was estimated by employing Equation (6). As Table 6 shows, the volume of both passenger and freight transport could have been increased by some 9.4% to reach the efficiency frontier given the observed energy consumption. More specifically, the largest slack was observed in 00 (9, %). Moreover, the application enabled to identify pure technical and scale efficiency (Fig. ). (%) Efficiency For PKM (Ө) (%) Efficiency For FKM (Ө) Fig.. Technical and scale efficiency of Turkish railway transport sector, Indeed, the technical modernization of the railway transport sector and the resolution of resource allocation problems might have lead to an increase in technical efficiency. Meanwhile, economic downturn prevents the transport system from working at full capacity, hence scale efficiency is still observed. For instance, having observed the previous trends in operation efficiency, one can easily forecast the need of inputs. 5. Conclusions The assessment of the efficiency of a certain economic sector is of high importance when making strategic decisions at any management level. Hence, the efficiency of Turkish railway transport sector was evaluated by applying multi criteria decision making method MULTIMOORA (MultiObective Optimization plus the Full Multiplicative Form) and data envelopment analysis. 9

10 The final ranks provided by MULTIMOORA indicate that the railway transport sector was operating most effectively during , whereas it exhibited relative inefficiency throughout Indeed, the technical modernization of the railway transport sector in Turkey and the resolution of resource allocation problems might have lead to an increase in technical efficiency. Meanwhile, economic downturn prevents the transport system from working at full capacity, hence scale efficiency is still observed. In addition, DEA with minimum weight restriction as well as other improvements might be applied for more robust results in further studies. Hence, other economic sectors can be evaluated on the basis of the proposed analytical framework. In addition, the indicator system can be expanded by adding more indicators identifying certain inputs and outputs. The findings of such studies might be important when making strategic decisions at various management levels. References [] Alvarez, A. Arias, C Technical efficiency and farm size: a conditional analysis, Agricultural Economics 30(3): [] Ananda, J. Herath, G A critical review of multicriteria decision making methods with special reference to forest management and planning, Ecological Economics 68(0): [3] Baležentis, A. Baležentis, T. Valkauskas, R. 00. Evaluating situation of Lithuania in the European Union: structural indicators and MULTIMOORA method, Technological and Economic Development of Economy 6(4): [4] Baležentis, A., Baležentis, T., 0. Assessing the efficiency of Lithuanian transport sector by applying the methods of MULTIMOORA And Data Envelopment Analysis, Transport, 6(3): [5] Banker, R. D. Charnes, A. Cooper, W. W Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science 30(9): [6] Brauers, W. K Optimization Methods for a Stakeholder Society: A Revolution in Economic Thinking by Multiobective Optimization. st edition. Springer. 35 p. [7] Brauers, W. K. M. Zavadskas, E. K. Turskis, Z. Vilutienė, T. 008a. Multiobective contractor s ranking by applying the MOORA method, Journal of Business Economics and Management 9(4): [8] Brauers, W. K. M. Zavadskas, E. K. Peldschus, F. Turskis, Z. 008b. Multiobective decisionmaking for road design, Transport 3(3): [9] Brauers, W. K. M. Ginevičius, R. 00. The economy of the Belgian regions tested with MULTIMOORA, Journal of Business Economics and Management (): [0] Brauers, W. K. M. Ginevičius, R Robustness in regional development studies. The case of Lithuania, Journal of Business Economics and Management 0(): 40. [] Brauers, W. K. M. Ginevičius, R. Podvezko, V. 00. Regional development in Lithuania considering multiple obectives by the MOORA method, Technological and Economic Development of Economy 6(4): [] Brauers, W. K. M. Zavadskas, E. K The MOORA method and its application to privatization in a transition economy, Control and Cybernetics 35(): [3] Brauers, W. K. Zavadskas, E. K Robustness of the multiobective MOORA method with a test for the facilities sector, Technological and Economic Development of Economy 5(): [4] Brauers, W. K. M. Zavadskas, E. K. 00a. Proect management by MULTIMOORA as an instrument for transition economies, Technological and Economic Development of Economy 6(): 5 4. [5] Brauers, W. K. M. Zavadskas, E. K. 00b. Robustness in the MULTIMOORA model: the example of Tanzania, Transformations in Business and Economics 9(3): [6] Brauers, W. K. M. Zavadskas, E. K. 0. MULTIMOORA optimization used to decide on a bank loan to buy property, Technological and Economic Development of Economy 7(): [7] Brauers, W. K. M. Ginevičius, R. Zavadskas, E. K. Antuchevičienė, J The European Union in a transition economy, Transformation in Business and Economics 6(): 37. [8] Charnes, A. Cooper, W. W. Rhodes, E Measuring the efficiency of decision making units, European Journal of Operational Research (6):

11 [9] Charnes, A. Cooper, W. W. Rhodes, E. 98. Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through, Management Science 7(6): [0] Chen, Y. Ali, A. I DEA Malmquist productivity measure: ew insights with an application to computer industry, European Journal of Operational Research 59(): [] Cooper, W. W. Seiford, L. M. Tone, K Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEASolver Software. nd edition. Springer. 58 p. [] Debreu, G. 95. The coefficient of resource utilization, Econometrica 9(3): ]3] Halkos, G. E. Salamouris, D. S Efficiency measurement of the Greek commercial banks with the use of financial ratios: a data envelopment analysis approach, Management Accounting Research 5(): 0 4. [4] Hermans, E. Van den Bossche, F. Wets, G Combining road safety information in a performance index, Accident Analysis and Prevention 40(4): [5] Jaržemskienė, I Research into the methods of analysing the productivity indicators of transport terminals, Transport 4(3): [6] Kahraman, C Multicriteria decision making methods and fuzzy sets, Springer Optimization and Its Applications 6(): 8. [7] Kalibatas, D. Turskis, Z Multicriteria evaluation of inner climate by using MOORA method, Information Technology and Control 37(): [8] Klevas, V. Minkstimas, R The guidelines for state policy of energy efficiency in Lithuania, Energy Policy 3(3): [9] MarkovitsSomogyi, R. 0. Measuring efficiency in transport: the state of the art of applying data envelopment analysis, Transport 6(): 9. [30] Peldschus, F. Zavadskas, E. K Fuzzy matrix games multicriteria model for decisionmaking in engineering, Informatica 6(): [3] Peldschus, F. Zavadskas, E. K. Turskis, Z. Tamošaitienė, J. 00. Sustainable assessment of construction site by applying game theory, Inzinerine Ekonomika Engineering Economics (3): [3] Ramanathan, R A holistic approach to compare energy efficiencies of different transport modes, Energy Policy 8(): [33] Ramanathan, R An Introduction to Data Envelopment Analysis: A Tool for Performance Measurement. Sage Publications Pvt. Ltd. 0 p. [34] Ray, S. C Data Envelopment Analysis: Theory and Techniques for Economics and Operations Research. Cambridge University Press. 366 p. [35] Ró, J. 00. Productivity of university hospitals in Poland: a Malmquistindex approach, Ekonomika 89(4): 3 4. [36] Roy B Paradigms and challenges, International Series in Operations Research and Management Science Vol. 78. [37] Multiple Criteria Decision Analysis: State of the Art Surveys, Figueira, J. Greco, S. Ehrgott, M. (Eds.), 3 4. [38] Shetty, U. Pakkala, T. P. M. 00. Ranking efficient DMUs based on single virtual inefficient DMU in DEA, OP. RESEARCH 47(): [39] Streimikienė, D. Čiegis, R. Grundey, D Energy indicators for sustainable development in Baltic States, Renewable and Sustainable Energy Reviews (5): [40] Sufian, F. 00. Modelling banking sector efficiency: a DEA and time series approach, Ekonomika 89(): 9. [4] İnternet: TCDD, Turkish State Railways Annual Statistics, 00005, , 0070 Yearbooks. (0). [4] Wang, Y.M. Luo, Y. Liang, L Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis, Journal of Computational and Applied Mathematics 3(): [43] Zavadskas, E. K. Turskis, Z. 0. Multiple criteria decision making (MCDM) methods in economics: an overview, Technological and Economic Development of Economy 7(): [44] Zerafat Angiz, L. M. Mustafa, A. Emrouznead, A. 00. Ranking efficient decisionmaking units in data envelopment analysis using fuzzy concept, Computers and Industrial Engineering 59(4): 7 79.