Measuring performance by integrating k-medoids with DEA: Mongolian case
Abstract
Performance measurement encourages Decision Making Units (DMUs) to improve their level of performance by comparing their current financial positions with that of their peers. Data Envelopment Analysis (DEA) is a widely used approach to performance measurement, though it is susceptible when the data is heterogeneous. The main objective of this study is to examine the performance of Mongolian listed companies by combining DEA and a k-medoid clustering method. Clustering facilitates the characterization and patterns of data and identification of homogenous groups. This study applies the integration of k-medoids and performance measurement. The research used 89 Mongolian companies’ financial statements from 2012 to 2015 - obtained from the Mongolian Stock Exchange website. The companies are grouped by k-medoids clustering, and efficiency of each cluster is evaluated by DEA. According to the silhouette method, the companies are classified into two clusters which are considered first cluster as small and medium-sized (80), and second cluster as big (9) companies. Both clusters are analyzed and compared by financial ratios. The mean efficiency score of big companies’ is much higher than that of small and medium-sized companies. Integrated results show that cluster-specific efficiency provides better performance than pre-clustering efficiency results.
Keyword : financial performance, k-medoids clustering, data envelopment analysis, input efficiency, variable return to scale, decision making unit
How to Cite
Bayaraa, B., Tarnoczi, T., & Fenyves, V. (2019). Measuring performance by integrating k-medoids with DEA: Mongolian case. Journal of Business Economics and Management, 20(6), 1238-1257. https://doi.org/10.3846/jbem.2019.11237
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Gandrud, C. (2015). Reproducible research with R and R studio (2nd ed.). New York: Chapman & Hall/CRC. https://doi.org/10.1201/b18546
Griffin, J. E. J. P. A. (2011). Bayesian clustering of distributions in stochastic frontier analysis. Journal of Productivity Analysis, 36(3), 275-283. https://doi.org/10.1007/s11123-011-0213-7
Hartigan, J. A. (1989). Clustering algorithms (pp. 331-335). John Wiley & Sons, Inc. https://doi.org/10.1002/0471725382.scard
Ho-Kieu, D., Vo-Van, T., & Nguyen-Trang, T. (2018). Clustering for probability density functions by new k-Medoids Method. Scientific Programming, 2018, 7. https://doi.org/10.1155/2018/2764016
Jahangoshai Rezaee, M., Jozmaleki, M., & Valipour, M. (2018). Integrating dynamic fuzzy C-means, data envelopment analysis and artificial neural network to online prediction performance of companies in stock exchange. Physica A: Statistical Mechanics and Its Applications, 489, 78-93. https://doi.org/10.1016/j.physa.2017.07.017
Kassambara, A. (2017). Practical guide to cluster analysis in R: unsupervised machine learning. STHDA.
Kaufman, L., & Rousseeuw, P. J. (1987). Clustering by means of medoids. In Y. Dodge (Ed.), Statistical Data Analysis Based on the L 1-Norm and Related Methods. First International Conference. Elsevier Science Ltd.
Kianfar, K., Ahadzadeh Namin, M., Alam Tabriz, A., Najafi, E., & Hosseinzadeh Lotfi, F. (2017). Hybrid cluster analyzing and data envelopment analysis with interval data. Scientia Iranica, 25(5), 2904-2911. https://doi.org/10.24200/sci.2017.4482
Kim, B., Lee, H., & Kang, P. (2018). Integrating cluster validity indices based on data envelopment analysis. Applied Soft Computing, 64, 94-108. https://doi.org/10.1016/j.asoc.2017.11.052
Lemos, C. A. A., Lins, M. P. E., & Ebecken, N. F. F. (2005). DEA implementation and clustering analysis using the K-Means algorithm. WIT Transactions on Information and Communication Technologies, 35, 321-329.
Masri, M. H. (2013). Performance measurement systems in service SME: A Brunei case study (PhD Thesis). The University of Manchester, United Kingdom.
Mei, J. P., & Chen, L. (2011). Fuzzy relational clustering around medoids: A unified view. Fuzzy Sets and Systems, 183(1), 44-56. https://doi.org/10.1016/j.fss.2011.06.009
Mohammad, S., Zadegan, R., Mirzaie, M., & Sadoughi, F. (2013). Ranked k-medoids: A fast and accurate rank-based partitioning algorithm for clustering large datasets. Knowledge-Based Systems, 39, 133-143. https://doi.org/10.1016/j.knosys.2012.10.012
Munisamy-Doraisamy, S. (2004). Benchmarking the performance of UK electricity distribution network operators: A study of quality, efficiency and productivity. Quality. Warwick Business School.
Narayana, G. S., & Vasumathi, D. (2018). An Attributes similarity-based K-Medoids clustering technique in data mining. Arabian Journal for Science and Engineering, 43(8), 3979-3992. https://doi.org/10.1007/s13369-017-2761-2
Neely, A., Gregory, M., & Platts, K. (1995). Performance measurement system design. International Journal of Operations & Production Management, 15(4), 80-116. https://doi.org/10.1108/01443579510083622
Omrani, H., Shafaat, K., & Emrouznejad, A. (2018). An integrated fuzzy clustering cooperative game data envelopment analysis model with application in hospital efficiency. Expert Systems with Applications, 114, 615-628. https://doi.org/10.1016/j.eswa.2018.07.074
Park, H. S., & Jun, C. H. (2009). A simple and fast algorithm for K-medoids clustering. Expert Systems with Applications, 36(2), 3336-3341. https://doi.org/10.1016/j.eswa.2008.01.039
Patel, A., & Singh, P. (2013). New Approach for K-mean and K-medoids Algorithm. International Journal of Computer Applications Technology and Research, 2(1), 1-5. https://doi.org/10.7753/IJ-CATR0201.1001
Po, R.-W., Guh, Y.-Y., & Yang, M.-S. (2009). A new clustering approach using data envelopment analysis. European Journal of Operational Research, 1. https://doi.org/10.1016/j.ejor.2008.10.022
Rokach, L., & Maimon, O. (2010). Chapter 15 – Clustering methods. In The data mining and knowledge discovery handbook (pp. 321-352). Springer. https://doi.org/10.1007/0-387-25465-X_15
Sood, M., & Bansal, S. (2013). K-Medoids clustering technique using bat algorithm. International Journal of Applied Information Systems, 5(8), 20-22. https://doi.org/10.5120/ijais13-450965
Sudit, E. F. (1996). Effectiveness, quality and efficiency: a management oriented approach. Springer. https://doi.org/10.1007/978-94-009-1828-3
Thakare, S. Y., & Bagal, S. B. (2015). Performance evaluation of K-means clustering algorithm with various distance metrics. International Journal of Computer Applications, 110(11), 975-8887. https://doi.org/10.5120/19360-0929
Ueasin, N., Liao, S. Y., & Wongchai, A. (2015). The technical efficiency of rice husk power generation in Thailand: comparing data envelopment analysis and stochastic frontier analysis. Energy Procedia, 75, 2757-2763. https://doi.org/10.1016/j.egypro.2015.07.518
Vincová, I. K. (2005). Using dea models to measure efficiency. Biatec, (1), 24-28.
Wu, J. (2012). Springer Theses: recognizing outstanding (Phd Research). Advances in K-means Clustering: a data mining thinking. Springer. https://doi.org/10.1007/978-3-642-29807-3
Xu, R., & Wunsch, D. C. (2008). Clustering. Wiley. https://doi.org/10.1002/9780470382776
Zhang, Q., & Couloigner, I. (2005). A new and efficient K-Medoid algorithm for spatial clustering. In O. Gervasi, et al. (Eds.), Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science (vol. 3482, pp. 181-189). Springer. https://doi.org/10.1007/11424857_20
Amin, M., Wan-Ismail, W.-K., Abdul-Rasid, S. Z., & Selemani, R. D. A. (2014). The impact of human resource management practices on performance: Evidence from a Public University. The TQM Journal, 26(2), 125-142. https://doi.org/10.1108/TQM-10-2011-0062
Arbin, N., Suhaimi, N. S., Mokhtar, N. Z., & Othman, Z. (2016). Comparative analysis between k-means and k-medoids for statistical clustering. In Proceedings – AIMS 2015, 3rd International Conference on Artificial Intelligence, Modelling and Simulation (pp. 117-121). https://doi.org/10.1109/AIMS.2015.82
Arora, P., & Varshney, S. (2016). Analysis of K-means and K-Medoids algorithm for big data. Procedia – Procedia Computer Science, 78, 507-512. https://doi.org/10.1016/j.procs.2016.02.095
Azadeh, A., Ghaderi, S. F., Miran, Y. P., Ebrahimipour, V., & Suzuki, K. (2007). An integrated framework for continuous assessment and improvement of manufacturing systems. Applied Mathematics and Computation, 186(2), 1216-1233. https://doi.org/10.1016/j.amc.2006.07.152
Bi, G., Song, W., & Wu, J. (2014). A clustering method for evaluating the environmental performance based on slacks-based measure. Computers & Industrial Engineering, 72, 169-177. https://doi.org/10.1016/j.cie.2014.03.016
Bogetoft, P., & Otto, L. (2011). International Series in Operations Research & Management Science: Vol. 157. Benchmarking with DEA, SFA, and R. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1900-6
Boussofiane, A., Dyson, R. G., & Thanassoulis, E. (1991). Applied data envelopment analysis. European Journal of Operational Research, 52(1), 1-15. https://doi.org/10.1016/0377-2217(91)90331-O
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444. https://doi.org/10.1016/0377-2217(78)90138-8
Cooper, W., Seiford, L., & Tone, K. (2006). Introduction to data envelopment analysis and its uses. Retrieved from http://link.springer.com/content/pdf/10.1007/0-387-29122-9.pdf
Dai, X., & Kuosmanen, T. (2014). Best-practice benchmarking using clustering methods: Application to energy regulation. Omega, 42(1), 179-188. https://doi.org/10.1016/j.omega.2013.05.007
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society. Series A (General), 120(3), 253. https://doi.org/10.2307/2343100
Fenyves, V., Tarnóczi, T., & Zsidó, K. (2015). Financial performance evaluation of agricultural enterprises with DEA method. Procedia Economics and Finance, 32(15), 423-431. https://doi.org/10.1016/S2212-5671(15)01413-6
Gandhi, G., & Srivastava, R. (2014). Analysis and implementation of modified K-medoids algorithm to increase scalability and efficiency for large dataset. IJRET: International Journal of Research in Engineering and Technology, 3(6), 150-153. https://doi.org/10.15623/ijret.2014.0306027
Gandrud, C. (2015). Reproducible research with R and R studio (2nd ed.). New York: Chapman & Hall/CRC. https://doi.org/10.1201/b18546
Griffin, J. E. J. P. A. (2011). Bayesian clustering of distributions in stochastic frontier analysis. Journal of Productivity Analysis, 36(3), 275-283. https://doi.org/10.1007/s11123-011-0213-7
Hartigan, J. A. (1989). Clustering algorithms (pp. 331-335). John Wiley & Sons, Inc. https://doi.org/10.1002/0471725382.scard
Ho-Kieu, D., Vo-Van, T., & Nguyen-Trang, T. (2018). Clustering for probability density functions by new k-Medoids Method. Scientific Programming, 2018, 7. https://doi.org/10.1155/2018/2764016
Jahangoshai Rezaee, M., Jozmaleki, M., & Valipour, M. (2018). Integrating dynamic fuzzy C-means, data envelopment analysis and artificial neural network to online prediction performance of companies in stock exchange. Physica A: Statistical Mechanics and Its Applications, 489, 78-93. https://doi.org/10.1016/j.physa.2017.07.017
Kassambara, A. (2017). Practical guide to cluster analysis in R: unsupervised machine learning. STHDA.
Kaufman, L., & Rousseeuw, P. J. (1987). Clustering by means of medoids. In Y. Dodge (Ed.), Statistical Data Analysis Based on the L 1-Norm and Related Methods. First International Conference. Elsevier Science Ltd.
Kianfar, K., Ahadzadeh Namin, M., Alam Tabriz, A., Najafi, E., & Hosseinzadeh Lotfi, F. (2017). Hybrid cluster analyzing and data envelopment analysis with interval data. Scientia Iranica, 25(5), 2904-2911. https://doi.org/10.24200/sci.2017.4482
Kim, B., Lee, H., & Kang, P. (2018). Integrating cluster validity indices based on data envelopment analysis. Applied Soft Computing, 64, 94-108. https://doi.org/10.1016/j.asoc.2017.11.052
Lemos, C. A. A., Lins, M. P. E., & Ebecken, N. F. F. (2005). DEA implementation and clustering analysis using the K-Means algorithm. WIT Transactions on Information and Communication Technologies, 35, 321-329.
Masri, M. H. (2013). Performance measurement systems in service SME: A Brunei case study (PhD Thesis). The University of Manchester, United Kingdom.
Mei, J. P., & Chen, L. (2011). Fuzzy relational clustering around medoids: A unified view. Fuzzy Sets and Systems, 183(1), 44-56. https://doi.org/10.1016/j.fss.2011.06.009
Mohammad, S., Zadegan, R., Mirzaie, M., & Sadoughi, F. (2013). Ranked k-medoids: A fast and accurate rank-based partitioning algorithm for clustering large datasets. Knowledge-Based Systems, 39, 133-143. https://doi.org/10.1016/j.knosys.2012.10.012
Munisamy-Doraisamy, S. (2004). Benchmarking the performance of UK electricity distribution network operators: A study of quality, efficiency and productivity. Quality. Warwick Business School.
Narayana, G. S., & Vasumathi, D. (2018). An Attributes similarity-based K-Medoids clustering technique in data mining. Arabian Journal for Science and Engineering, 43(8), 3979-3992. https://doi.org/10.1007/s13369-017-2761-2
Neely, A., Gregory, M., & Platts, K. (1995). Performance measurement system design. International Journal of Operations & Production Management, 15(4), 80-116. https://doi.org/10.1108/01443579510083622
Omrani, H., Shafaat, K., & Emrouznejad, A. (2018). An integrated fuzzy clustering cooperative game data envelopment analysis model with application in hospital efficiency. Expert Systems with Applications, 114, 615-628. https://doi.org/10.1016/j.eswa.2018.07.074
Park, H. S., & Jun, C. H. (2009). A simple and fast algorithm for K-medoids clustering. Expert Systems with Applications, 36(2), 3336-3341. https://doi.org/10.1016/j.eswa.2008.01.039
Patel, A., & Singh, P. (2013). New Approach for K-mean and K-medoids Algorithm. International Journal of Computer Applications Technology and Research, 2(1), 1-5. https://doi.org/10.7753/IJ-CATR0201.1001
Po, R.-W., Guh, Y.-Y., & Yang, M.-S. (2009). A new clustering approach using data envelopment analysis. European Journal of Operational Research, 1. https://doi.org/10.1016/j.ejor.2008.10.022
Rokach, L., & Maimon, O. (2010). Chapter 15 – Clustering methods. In The data mining and knowledge discovery handbook (pp. 321-352). Springer. https://doi.org/10.1007/0-387-25465-X_15
Sood, M., & Bansal, S. (2013). K-Medoids clustering technique using bat algorithm. International Journal of Applied Information Systems, 5(8), 20-22. https://doi.org/10.5120/ijais13-450965
Sudit, E. F. (1996). Effectiveness, quality and efficiency: a management oriented approach. Springer. https://doi.org/10.1007/978-94-009-1828-3
Thakare, S. Y., & Bagal, S. B. (2015). Performance evaluation of K-means clustering algorithm with various distance metrics. International Journal of Computer Applications, 110(11), 975-8887. https://doi.org/10.5120/19360-0929
Ueasin, N., Liao, S. Y., & Wongchai, A. (2015). The technical efficiency of rice husk power generation in Thailand: comparing data envelopment analysis and stochastic frontier analysis. Energy Procedia, 75, 2757-2763. https://doi.org/10.1016/j.egypro.2015.07.518
Vincová, I. K. (2005). Using dea models to measure efficiency. Biatec, (1), 24-28.
Wu, J. (2012). Springer Theses: recognizing outstanding (Phd Research). Advances in K-means Clustering: a data mining thinking. Springer. https://doi.org/10.1007/978-3-642-29807-3
Xu, R., & Wunsch, D. C. (2008). Clustering. Wiley. https://doi.org/10.1002/9780470382776
Zhang, Q., & Couloigner, I. (2005). A new and efficient K-Medoid algorithm for spatial clustering. In O. Gervasi, et al. (Eds.), Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science (vol. 3482, pp. 181-189). Springer. https://doi.org/10.1007/11424857_20