Performance Measurement with Stochastic Data Envelopment Analysis: Comparative Analysis of Turkish Electricity Distribution Companies

Yıl 2021, Cilt: 24 Sayı: 1, 87 - 101, 01.03.2021

Zühre Aydın Yenioğlu , Bilal Toklu

https://doi.org/10.2339/politeknik.621397

Cited By: 3

Öz

In this study, performance measurement and efficiency benchmarking of Turkey’s 21 electricity distribution companies were aimed. Random input and output variables of distribution companies are included in the stochastic input and output oriented chance constrained Banker, Charnes and Cooper (BCC) Data Envelopment Analysis (DEA) models within the symmetric error structure. Deterministic input and output oriented BCC DEA models were compared with the stochastic models and stochastic measurement values were verified with the deterministic measurement values. The chance-constrained problems were created by uncertain data for stochastic DEA, then stochastic models were converted to deterministic equivalents and were linearized. Turkey's 21 electricity distribution companies have been accepted as decision-making units (DMUs) of DEA models. According to the efficiency results of deterministic and stochastic models, efficient and inefficient electricity distribution companies were determined. The objective is to add statistical noise to DEA models in the analyzed data and to obtain performance measurement in this direction. Noise element was included into the models within the scope of single factor symmetric error structure and the models were examined separately for each error level in order to examine the different results between the models. This study is the first approach that was performed to evaluate the power distribution companies to incorporate stochastic data into DEA within a symmetric error structure in Turkey.

Anahtar Kelimeler

Stochastic data envelopment analysis, chance constrained stochastic programming, symmetric error structure

Stokastik Veri Zarflama Analizi ile Etkinlik Ölçümü : Türkiye Elektrik Dağıtım Şirketlerinin Karşılaştırmalı Analizi

Öz

Bu çalışmada, Türkiye’de bulunan 21 elektrik dağıtım şirketinin performans ölçümü ve etkinlik çerçevesinde kıyaslanması amaçlamıştır. Dağıtım şirketlerinin rasgele girdi ve çıktı değişkenleri, stokastik girdiye ve çıktıya yönelimli şans kısıtlı Banker, Charnes ve Cooper (BCC) Veri Zarflama Analizi (VZA) modellerine simetrik hata yapısı ile dâhil edilmiştir. Deterministik girdiye ve çıktıya yönelimli BCC VZA modelleriyle stokastik modeller karşılaştırılmış, stokastik ölçüm değerleri, deterministik ölçüm değerleriyle doğrulanmıştır. Çalışmada, belirsiz verilerle çalışan stokastik VZA için şans kısıtlı problemler oluşturulmuş, stokastik modeller deterministik eşdeğerlerine dönüştürülmüş ve doğrusallaştırılmıştır. VZA modellerinde Türkiye’nin 21 elektrik dağıtım şirketi karar verme birimleri (KVB) olarak kabul edilmiştir. Elde edilen sonuçlarla, deterministik ve stokastik modellerin etkinlik sonuçlarına göre, etkin ve etkin olmayan elektrik dağıtım şirketleri belirlenmiştir. Amaç, analiz edilen verilerde istatistiksel gürültüyü VZA modellerine ekleyip, performans ölçümünü bu doğrultuda gerçekleştirmektir. Modellere gürültü unsuru tek faktörlü simetrik hata yapısı kapsamında dâhil edilmiş, modeller arasındaki farklı sonuçları incelemek amacıyla her hata seviyesi için modeller ayrı ayrı ele alınmıştır. Çalışma, Türkiye'de elektrik dağıtım şirketlerinin değerlendirilmesinde, simetrik hata yapısı ile stokastik verileri VZA’ya dâhil eden ilk yaklaşımdır.

Anahtar Kelimeler

Stokastik veri zarflama analizi, şans kısıtlı stokastik programlama, simetrik hata yapısı

Kaynakça

• KAYNAKLAR (REFERENCES)[1] Azadeh,A., Motevali, Haghighi, S., Zarrin, M., Khaefi, S.,. Performance evaluation of Iranian electricity distribution units by using stochastic data envelopment analysis. Electrical Power and Energy Systems 73, 919–931, (2015)[2] Jamasb, T., Pollitt, M.,. Benchmarking and Regulation: International Electricity Experience. Utilities Policy, 9, 107–130,(2001).[3] Farrell MJ.,. The measurement of productive efficiency. J R Stat Soc Ser A. Gen,120,253-90,( 1957). [4] Charnes, A., Cooper, W. W.. Chance-Constrained Programming. Management Science, 6, 1, 73-79, (1959).[5] Charnes, A., Cooper, WW., Rhodes, E.. Measuring the efficiency of decision making units. European Journal of Operational Research 2 , 429-444, (1978).[6] Banker, R.D., Charnes, A., Cooper, W.W.. Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Management Science, 30, 1078– 1092, , (1984).[7] Behzadi, MH., Mirbolouki, M., . Symmetric Error Structure in Stochastic DEA. Int. J. Industrial Mathematics 4 , 335-343,(2012).[8] Mirbolouki, M., Behzadi, MH., Korzaledin, M.. Multiplier ,models in stochastic DEA. Data Envelopment Analysis and Decision Science Volume 2014 , Article ID: dea-00044,(2014). [9] Brazdik, F.. Stochastic Data Envelopment Analysis: Oriented and Linearized Models. joint workplace of the Center for Economic Research and Graduate Education, Charles University, Prague, and the Economics Institute of the Academy of Sciences of the Czech Republic,(2004).[10] Land, C. K., Lovell, C. A. K.,Thore, S.. Productive Efficiency under Capitalism and State Socialism: An Empirical Inquiry Using Chance-Constrained Data Envelopment Analysis. Technological Forecast Social Change, 46, 139-152,(1994).[11] Land, C. K., Lovell, C. A. K., Thore, S.. Chance-Constrained Data Envelopment Analysis. Managerial and Decision Economics, Vol. 14, 541-554,(1993).[13] Cooper, WW., Deng, H., Huang, Z., Li, SX.. Chance constrained programming approaches to congestion in stochastic data envelopment analysis. European Journal of Operational Research 155, 487-501,(2004).[14] Sengupta, JK.. Efficiency analysis by stochastic data envelopment analysis. Applied Economics Letters 7, 379-383,(2002).[15] Huang, Z., Li, SX.. Stochastic DEA models with different types of input-output disturbances. Journal of Productivity Analysis 15, 95-113,(2001).[16] Olesen, OB.. Comparing and Combining Two Approaches for Chance Constrained DEA. Discussion paper, The University of Southern Denmark,(2002).[17] Khodabakhshi, M.. An Output Oriented Super-Efficiency Measure in Stochastic Data Envelopment Analysis: Considering Iranian Electricity Distribution Companies. Computers & Industrial Engineering 58 , 663–671,(2010).[18] Khodabakhshi, M., Asgharian, M.. An input relaxation measure of efficiency in stochastic data envelopment analysis. Applied Mathematical Modelling 33, 2010-2023,(2008).[19] Khodabakhshi, M., Kheirollahi, H.. Measuring technical efficiency of Iranian electricity distribution units with stochastic data envelopment analysis. Iranian Conference on Applied Mathematical Modelling,(2010).[20] Jahanshahloo, GR., Behzadi, MH., Mirbolouki, M.. Ranking Stochastic Efficient DMUs based on Reliability. International Journal of Industrial Mathematics 2, 263-270,(2010).[21] Omrani, H., Azadeh, A., Ghaderi, SF., Abdollahzadeh, S.. A Consistent Approach for Performance Measurement Of Electricity Distribution Companies. Int J Energy Sect Manage 4, 399–416,(2010).[22] Azadeh, A., Ghaderi, SF., Omrani, H., Eivazy, H.. An integrated DEA–COLS–SFA algorithm for optimization and policy making of electricity distribution units. Energy Policy 37, 2605–2618,(2009).[23] Mullarkey, S., Caulfield, B., McCormack, S., Basu, B.. A framework for establishing the technical efficiency of Electricity Distribution Counties (EDCs) using Data Envelopment Analysis. Energy Conversion and Management, 94, 112-123,(2015). [24]Gouveia, M.C., Dias, L.C., Antunes, C.H., Boucinha, J., Inácio, C.F.. Benchmarking of maintenance and outage repair in an electricity distribution company using the value-based DEA method. Omega, 53, 104-114,(2015).[25]Arcos-Vargas, A., Núñez-Hernández, F., Villa-Caro G.. A DEA analysis of electricity distribution in Spain: An industrial policy recommendation. Energy Policy, 102, 583–592,(2017).[26] Talluri, S., Narasimhan, R., Nair, A.. Vendor performance with supply risk: a chance-constrained DEA approach. International Journal of Production Economics 100, No. 2, 212–222,(2006). [27] Sueyoshi, T.. Stochastic DEA for restructure strategy: an application to a Japanese petroleum company. Omega 28, 385–98,(2000).[28] Sadjadi, SJ., Omrani, H., Makui, A., Shahanaghi, K.. An interactive robust data envelopment analysis model for determining alternative targets in Iranian electricity distribution companies. Expert Syst Appl 38, 9830–9,(2011).[29] Sadjadi, S.J., Omrani, H.. Data Envelopment Analysis With Uncertain Data: An Application For Iranian Electricity Distribution Companies. Energy Policy 36, 4247–4254. [30] Gstach, D., 1998. Another approach to data envelopment analysis in noisy environments: DEA+. Journal of Productivity Analysis 9, 161-176, (2008). [31] Brockett PL , Golany B.. Using Rank Statistics for Determining Programmatic Efficiency Differences in Data Envelopment Analysis. Management Science 42(3), 466-472,(1996). [32] Omrani, H., Beiragh, R.G., Kaleibari, S.S.. Performance assessment of Iranian electricity distribution companies by an integrated cooperative game data envelopment analysis principal component analysis approach. Electrical Power and Energy Systems, 64, 617-625,(2015).