American Institute of Mathematical Sciences

Advanced
October  2016, 12(4): 1311-1322. doi: 10.3934/jimo.2016.12.1311

Revenue congestion: An application of data envelopment analysis

Habibe Zare Haghighi 1, , Sajad Adeli 2, , Farhad Hosseinzadeh Lotfi 3, and  Gholam Reza Jahanshahloo 3,

1. 

Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran
2. 

Department of Financial Engineering, Faculty of Engineering, University of Science and Culture, Tehran, Iran
3. 

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran, Iran

Received  November 2013 Revised  October 2015 Published  January 2016

Congestion is generally used in the economics and indicates a situation where a decrease (increase) in one or more inputs can increase (decrease) one or more outputs. In this paper, we introduce a new concept using data envelopment analysis, and call it revenue congestion. The new concept implies a situation where reduction in some inputs may result in an increase in revenue. This improvement in revenue is rather possible by a simultaneous increase and decrease in outputs due to a reduction in inputs. Then, we try to propose a method to distinguish the revenue congestion and identify its sources and amounts. To illustrate the use of the proposed method, an empirical application corresponding to 30 Iranian bank branches is provided. 16 branches evidence revenue congestion via the proposed approach. This identification is very significant because these branches can increase the revenue of their outputs by eliminating the amounts of revenue congestion in each of their inputs. Moreover, it is found that an increase in all outputs is not always profitable, but rather in some cases a decrease in some outputs and an increase in some other outputs can help the firms to make more profits.
Keywords: Data envelopment analysis, revenue efficiency, congestion, output price, bank branches..
Mathematics Subject Classification: Primary: 90B50, 91B06; Secondary: 90C9.
Citation: Habibe Zare Haghighi, Sajad Adeli, Farhad Hosseinzadeh Lotfi, Gholam Reza Jahanshahloo. Revenue congestion: An application of data envelopment analysis. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1311-1322. doi: 10.3934/jimo.2016.12.1311
References:
[1]

G. R. Amin and M. Toloo, Finding the most efficient DMUs in DEA: An improved integrated model,, Computers and Industrial Engineering, 52 (2007), 71.  doi: 10.1016/j.cie.2006.10.003.  Google Scholar

[2]

J. Aparicio, F. Borras, J. T. Pastor and F. Vidal, Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA,, European Journal of Operational Research, 231 (2013), 443.  doi: 10.1016/j.ejor.2013.05.047.  Google Scholar

[3]

J. Aparicio, F. Borras, J. T. Pastor and F. Vidal, Measuring and decomposing firm's revenue and cost efficiency: The Russell measures revisited,, International Journal of Production Economics, 165 (2015), 19.  doi: 10.1016/j.ijpe.2015.03.018.  Google Scholar

[4]

P. L. Brocket, W. W. Cooper, H. C. Shin and Y. Wang, Inefficiency and congestion in Chinese production before and after the 1978 economic reforms,, Socio-Economic Planning Sciences, 32 (1998), 1.  doi: 10.1016/S0038-0121(97)00020-7.  Google Scholar

[5]

W. Cook, Y. Roll and A. Kazakov, A DEA model for measuring the relative efficiencies of highway maintenance patrols,, Information Systems and Operational Research, 28 (1990), 113.   Google Scholar

[6]

W. W. Cooper, R. G. Thompson and R. M. Thrall, Intoduction: Extensions and new developments in DEA,, Annals of Operations Research, 66 (1996), 3.  doi: 10.1007/BF02125451.  Google Scholar

[7]

W. W. Cooper, L. M. Seiford and J. Zhu, A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA,, Socio-Economic Planning Sciences, 34 (2000), 1.  doi: 10.1016/S0038-0121(99)00010-5.  Google Scholar

[8]

W. W. Cooper, B. Gu and S. Li, Comparisons and evaluations of alternative approaches to the treatment of congestion in DEA,, European Journal of Operational Research, 132 (2001), 62.  doi: 10.1016/S0377-2217(00)00113-2.  Google Scholar

[9]

G. Debreu, The coefficient of resource utilization,, Econometrica, 19 (1951), 273.   Google Scholar

[10]

R. Färe and L. Svensson, Congestion of production factors,, Econometrica, 48 (1980), 1745.   Google Scholar

[11]

R. Färe and S. Grosskopf, Measuring congestion in production,, Zeitschrift für Nationalökonomie, 43 (1983), 257.  doi: 10.1007/BF01283574.  Google Scholar

[12]

R. Färe, S. Grosskopf and C. A. K. Lovell, The Measurement of Efficiency of Production,, Boston: Kluwer Nijhoff, (1985).   Google Scholar

[13]

M. J. Farrell, The measurement of productive efficiency,, Journal of the Royal Statistical Society, 120 (1957), 253.  doi: 10.2307/2343100.  Google Scholar

[14]

G. R. Jahanshahloo and M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion considering textile industry of China,, Applied Mathematics and computation, 151 (2004), 263.  doi: 10.1016/S0096-3003(03)00337-0.  Google Scholar

[15]

G. R. Jahanshahloo, F. Hosseinzadeh Lotfi and M. Moradi, A DEA approach for fair allocation of common revenue,, Applied Mathematics and Computation, 160 (2005), 719.  doi: 10.1016/j.amc.2003.11.027.  Google Scholar

[16]

G. R. Jahanshahloo, A. Memariani, F. Hosseinzadeh Lotfi and H. Z. Rezai, A note on some of DEA models and finding efficiency and complete ranking using common Set of weights,, Applied Mathematics and computation, 166 (2005), 265.  doi: 10.1016/j.amc.2004.04.088.  Google Scholar

[17]

T. Kuosmanen and T. Post, Measuring economic efficiency with incomplete price information: With an application to European commercial banks,, European Journal of Operational Research, 134 (2001), 43.  doi: 10.1016/S0377-2217(00)00237-X.  Google Scholar

[18]

T. Kuosmanen and T. Post, Measuring economic efficiency with incomplete price information,, European Journal of Operational Research, 144 (2003), 454.  doi: 10.1016/S0377-2217(01)00398-8.  Google Scholar

[19]

R. Lin, Allocating fixed costs and common revenue via data envelopment analysis,, Applied Mathematics and computation, 218 (2011), 3680.  doi: 10.1016/j.amc.2011.09.011.  Google Scholar

[20]

F. F. Liu and H. H. Peng, Ranking of units on the DEA frontier with common weights,, Computers and Opreations Research, 35 (2008), 1624.  doi: 10.1016/j.cor.2006.09.006.  Google Scholar

[21]

A. A. Noura, F. Hosseinzadeh Lotfi, G. R. Jahanshahloo, S. Fanati Rashidi and B. R. Parker, A new method for measuring congestion in data envelopment analysis,, Socio-Economic Planning Sciences, 44 (2010), 240.  doi: 10.1016/j.seps.2010.06.003.  Google Scholar

[22]

Y. Roll, W. Cook and B. Golany, Controlling factor weights in data envelopment analysis,, IIE Transactions, 23 (1991), 2.  doi: 10.1080/07408179108963835.  Google Scholar

[23]

B. K. Sahoo, M. Mehdiloozad and K. Tone, Cost, revenue and profit efficiency measurement in DEA: A directional distance function approach,, European Journal of Operational Research, 237 (2014), 921.  doi: 10.1016/j.ejor.2014.02.017.  Google Scholar

[24]

Z. Sinuany-Stern and L. Friedman, DEA and discriminant analysis of ratios for ranking units,, European Journal of Operational Research, 111 (1998), 470.  doi: 10.1016/S0377-2217(97)00313-5.  Google Scholar

[25]

T. Sueyoshi and K. Sekitani, DEA congestion and returns to scale under an occurrence of multiple optimal projections,, European Journal of Operational Research, 194 (2009), 592.  doi: 10.1016/j.ejor.2007.12.022.  Google Scholar

[26]

K. Tone and B. K. Sahoo, Degree of scale economies and congestion: A unified DEA approach,, European Journal of Operational Research, 158 (2004), 755.  doi: 10.1016/S0377-2217(03)00370-9.  Google Scholar

[27]

Q. L. Wei and H. Yan, Congestion and returns to scale in data envelopment analysis,, European Journal of Operational Research, 153 (2004), 641.  doi: 10.1016/S0377-2217(02)00799-3.  Google Scholar

[28]

H. Zare-Haghighi, M. Rostamy-Malkhalifeh and G. R. Jahanshahloo, Measurement of congestion in the simultaneous presence of desirable and undesirable outputs,, Journal of Applied Mathematics, 2014 (2014), 1.  doi: 10.1155/2014/512157.  Google Scholar

show all references

References:
[1]

G. R. Amin and M. Toloo, Finding the most efficient DMUs in DEA: An improved integrated model,, Computers and Industrial Engineering, 52 (2007), 71.  doi: 10.1016/j.cie.2006.10.003.  Google Scholar

[2]

J. Aparicio, F. Borras, J. T. Pastor and F. Vidal, Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA,, European Journal of Operational Research, 231 (2013), 443.  doi: 10.1016/j.ejor.2013.05.047.  Google Scholar

[3]

J. Aparicio, F. Borras, J. T. Pastor and F. Vidal, Measuring and decomposing firm's revenue and cost efficiency: The Russell measures revisited,, International Journal of Production Economics, 165 (2015), 19.  doi: 10.1016/j.ijpe.2015.03.018.  Google Scholar

[4]

P. L. Brocket, W. W. Cooper, H. C. Shin and Y. Wang, Inefficiency and congestion in Chinese production before and after the 1978 economic reforms,, Socio-Economic Planning Sciences, 32 (1998), 1.  doi: 10.1016/S0038-0121(97)00020-7.  Google Scholar

[5]

W. Cook, Y. Roll and A. Kazakov, A DEA model for measuring the relative efficiencies of highway maintenance patrols,, Information Systems and Operational Research, 28 (1990), 113.   Google Scholar

[6]

W. W. Cooper, R. G. Thompson and R. M. Thrall, Intoduction: Extensions and new developments in DEA,, Annals of Operations Research, 66 (1996), 3.  doi: 10.1007/BF02125451.  Google Scholar

[7]

W. W. Cooper, L. M. Seiford and J. Zhu, A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA,, Socio-Economic Planning Sciences, 34 (2000), 1.  doi: 10.1016/S0038-0121(99)00010-5.  Google Scholar

[8]

W. W. Cooper, B. Gu and S. Li, Comparisons and evaluations of alternative approaches to the treatment of congestion in DEA,, European Journal of Operational Research, 132 (2001), 62.  doi: 10.1016/S0377-2217(00)00113-2.  Google Scholar

[9]

G. Debreu, The coefficient of resource utilization,, Econometrica, 19 (1951), 273.   Google Scholar

[10]

R. Färe and L. Svensson, Congestion of production factors,, Econometrica, 48 (1980), 1745.   Google Scholar

[11]

R. Färe and S. Grosskopf, Measuring congestion in production,, Zeitschrift für Nationalökonomie, 43 (1983), 257.  doi: 10.1007/BF01283574.  Google Scholar

[12]

R. Färe, S. Grosskopf and C. A. K. Lovell, The Measurement of Efficiency of Production,, Boston: Kluwer Nijhoff, (1985).   Google Scholar

[13]

M. J. Farrell, The measurement of productive efficiency,, Journal of the Royal Statistical Society, 120 (1957), 253.  doi: 10.2307/2343100.  Google Scholar

[14]

G. R. Jahanshahloo and M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion considering textile industry of China,, Applied Mathematics and computation, 151 (2004), 263.  doi: 10.1016/S0096-3003(03)00337-0.  Google Scholar

[15]

G. R. Jahanshahloo, F. Hosseinzadeh Lotfi and M. Moradi, A DEA approach for fair allocation of common revenue,, Applied Mathematics and Computation, 160 (2005), 719.  doi: 10.1016/j.amc.2003.11.027.  Google Scholar

[16]

G. R. Jahanshahloo, A. Memariani, F. Hosseinzadeh Lotfi and H. Z. Rezai, A note on some of DEA models and finding efficiency and complete ranking using common Set of weights,, Applied Mathematics and computation, 166 (2005), 265.  doi: 10.1016/j.amc.2004.04.088.  Google Scholar

[17]

T. Kuosmanen and T. Post, Measuring economic efficiency with incomplete price information: With an application to European commercial banks,, European Journal of Operational Research, 134 (2001), 43.  doi: 10.1016/S0377-2217(00)00237-X.  Google Scholar

[18]

T. Kuosmanen and T. Post, Measuring economic efficiency with incomplete price information,, European Journal of Operational Research, 144 (2003), 454.  doi: 10.1016/S0377-2217(01)00398-8.  Google Scholar

[19]

R. Lin, Allocating fixed costs and common revenue via data envelopment analysis,, Applied Mathematics and computation, 218 (2011), 3680.  doi: 10.1016/j.amc.2011.09.011.  Google Scholar

[20]

F. F. Liu and H. H. Peng, Ranking of units on the DEA frontier with common weights,, Computers and Opreations Research, 35 (2008), 1624.  doi: 10.1016/j.cor.2006.09.006.  Google Scholar

[21]

A. A. Noura, F. Hosseinzadeh Lotfi, G. R. Jahanshahloo, S. Fanati Rashidi and B. R. Parker, A new method for measuring congestion in data envelopment analysis,, Socio-Economic Planning Sciences, 44 (2010), 240.  doi: 10.1016/j.seps.2010.06.003.  Google Scholar

[22]

Y. Roll, W. Cook and B. Golany, Controlling factor weights in data envelopment analysis,, IIE Transactions, 23 (1991), 2.  doi: 10.1080/07408179108963835.  Google Scholar

[23]

B. K. Sahoo, M. Mehdiloozad and K. Tone, Cost, revenue and profit efficiency measurement in DEA: A directional distance function approach,, European Journal of Operational Research, 237 (2014), 921.  doi: 10.1016/j.ejor.2014.02.017.  Google Scholar

[24]

Z. Sinuany-Stern and L. Friedman, DEA and discriminant analysis of ratios for ranking units,, European Journal of Operational Research, 111 (1998), 470.  doi: 10.1016/S0377-2217(97)00313-5.  Google Scholar

[25]

T. Sueyoshi and K. Sekitani, DEA congestion and returns to scale under an occurrence of multiple optimal projections,, European Journal of Operational Research, 194 (2009), 592.  doi: 10.1016/j.ejor.2007.12.022.  Google Scholar

[26]

K. Tone and B. K. Sahoo, Degree of scale economies and congestion: A unified DEA approach,, European Journal of Operational Research, 158 (2004), 755.  doi: 10.1016/S0377-2217(03)00370-9.  Google Scholar

[27]

Q. L. Wei and H. Yan, Congestion and returns to scale in data envelopment analysis,, European Journal of Operational Research, 153 (2004), 641.  doi: 10.1016/S0377-2217(02)00799-3.  Google Scholar

[28]

H. Zare-Haghighi, M. Rostamy-Malkhalifeh and G. R. Jahanshahloo, Measurement of congestion in the simultaneous presence of desirable and undesirable outputs,, Journal of Applied Mathematics, 2014 (2014), 1.  doi: 10.1155/2014/512157.  Google Scholar

[1]

Cheng-Kai Hu, Fung-Bao Liu, Cheng-Feng Hu. Efficiency measures in fuzzy data envelopment analysis with common weights. Journal of Industrial & Management Optimization, 2017, 13 (1) : 237-249. doi: 10.3934/jimo.2016014
[2]

Mahdi Mahdiloo, Abdollah Noorizadeh, Reza Farzipoor Saen. Developing a new data envelopment analysis model for customer value analysis. Journal of Industrial & Management Optimization, 2011, 7 (3) : 531-558. doi: 10.3934/jimo.2011.7.531
[3]

Runqin Hao, Guanwen Zhang, Dong Li, Jie Zhang. Data modeling analysis on removal efficiency of hexavalent chromium. Mathematical Foundations of Computing, 2019, 2 (3) : 203-213. doi: 10.3934/mfc.2019014
[4]

Mohammad Afzalinejad, Zahra Abbasi. A slacks-based model for dynamic data envelopment analysis. Journal of Industrial & Management Optimization, 2019, 15 (1) : 275-291. doi: 10.3934/jimo.2018043
[5]

Jingmei Zhou, Xiangmo Zhao, Xin Cheng, Zhigang Xu. Visualization analysis of traffic congestion based on floating car data. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1423-1433. doi: 10.3934/dcdss.2015.8.1423
[6]

Saber Saati, Adel Hatami-Marbini, Per J. Agrell, Madjid Tavana. A common set of weight approach using an ideal decision making unit in data envelopment analysis. Journal of Industrial & Management Optimization, 2012, 8 (3) : 623-637. doi: 10.3934/jimo.2012.8.623
[7]

Angela Cadena, Adriana Marcucci, Juan F. Pérez, Hernando Durán, Hernando Mutis, Camilo Taútiva, Fernando Palacios. Efficiency analysis in electricity transmission utilities. Journal of Industrial & Management Optimization, 2009, 5 (2) : 253-274. doi: 10.3934/jimo.2009.5.253
[8]

Wu Chanti, Qiu Youzhen. A nonlinear empirical analysis on influence factor of circulation efficiency. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 929-940. doi: 10.3934/dcdss.2019062
[9]

Deren Han, Xiaoming Yuan. Existence of anonymous link tolls for decentralizing an oligopolistic game and the efficiency analysis. Journal of Industrial & Management Optimization, 2011, 7 (2) : 347-364. doi: 10.3934/jimo.2011.7.347
[10]

Zhenhua Peng, Zhongping Wan, Weizhi Xiong. Sensitivity analysis in set-valued optimization under strictly minimal efficiency. Evolution Equations & Control Theory, 2017, 6 (3) : 427-436. doi: 10.3934/eect.2017022
[11]

Bart Feyaerts, Stijn De Vuyst, Herwig Bruneel, Sabine Wittevrongel. Performance analysis of buffers with train arrivals and correlated output interruptions. Journal of Industrial & Management Optimization, 2015, 11 (3) : 829-848. doi: 10.3934/jimo.2015.11.829
[12]

Shouyu Ma, Zied Jemai, Evren Sahin, Yves Dallery. Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts. Journal of Industrial & Management Optimization, 2018, 14 (3) : 931-951. doi: 10.3934/jimo.2017083
[13]

Jian Chen, Lei Guan, Xiaoqiang Cai. Analysis on Buyers' cooperative strategy under group-buying price mechanism. Journal of Industrial & Management Optimization, 2013, 9 (2) : 291-304. doi: 10.3934/jimo.2013.9.291
[14]

Xiao-Qian Jiang, Lun-Chuan Zhang. Stock price fluctuation prediction method based on time series analysis. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 915-927. doi: 10.3934/dcdss.2019061
[15]

Zuray Melgarejo, Francisco J. Arcelus, Katrin Simon-Elorz. A three-stage DEA-SFA efficiency analysis of labour-owned and mercantile firms. Journal of Industrial & Management Optimization, 2011, 7 (3) : 573-592. doi: 10.3934/jimo.2011.7.573
[16]

Yihong Xu, Zhenhua Peng. Higher-order sensitivity analysis in set-valued optimization under Henig efficiency. Journal of Industrial & Management Optimization, 2017, 13 (1) : 313-327. doi: 10.3934/jimo.2016019
[17]

Claude Carlet, Khoongming Khoo, Chu-Wee Lim, Chuan-Wen Loe. On an improved correlation analysis of stream ciphers using multi-output Boolean functions and the related generalized notion of nonlinearity. Advances in Mathematics of Communications, 2008, 2 (2) : 201-221. doi: 10.3934/amc.2008.2.201
[18]

Toufik Bakir, Bernard Bonnard, Jérémy Rouot. A case study of optimal input-output system with sampled-data control: Ding et al. force and fatigue muscular control model. Networks & Heterogeneous Media, 2019, 14 (1) : 79-100. doi: 10.3934/nhm.2019005
[19]

Julien Dambrine, Nicolas Meunier, Bertrand Maury, Aude Roudneff-Chupin. A congestion model for cell migration. Communications on Pure & Applied Analysis, 2012, 11 (1) : 243-260. doi: 10.3934/cpaa.2012.11.243
[20]

Zhouchen Lin. A review on low-rank models in data analysis. Big Data & Information Analytics, 2016, 1 (2&3) : 139-161. doi: 10.3934/bdia.2016001

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (25)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences