A New Decomposition of Cost Efficiency based on the Price and Cost based Production Possibility Sets in non-competitive space in DEA

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

R. Fallahnejad ¹ (Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran.)
E. Rezaei hezaveh ² (Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran.)

تاریخ دریافت : 1399/01/09 تاریخ پذیرش : 1400/08/28 تاریخ انتشار : 1400/10/11

کلید واژه: non-competitive space, Data Envelopment Analysis, Different Prices, competitive space, cost efficiency,

چکیده مقاله :

Identification of various sources of inefficiency plays an important role in the performance analysis aimed at developing plans for the improvement of decision making. In this regard, not only technical, cost, and allocative efficiency can be estimated by information on inputs and outputs and their prices, but losses due to the lack of profit and revenue and optimal cost can also be calculated based on the relevant inefficiency. The present paper aimed at providing new estimation of cost efficiency and sources of losses in the total efficiency in a non-competitive environment where there is the possibility of change in prices of inputs and outputs from one DMU to another. In line with studies (Tone .K, "A Strange Case of the Cost and Allocative Efficiencies in DEA". Journal of the Operational Research Society 53, (2002), pp.1225-1231) and (Tone. K., Tsutsui, M. "Decomposition of Cost Efficiency and its Application to Japanese-Us Electric Utility Comparisons". Socio-Economic Planning Sciences 47 (2007), pp.91-106), the present study sought to introduce new sources of inefficiency and related losses by presenting new price-based and cost-based production possibility sets.

چکیده انگلیسی:

شناسایی منابع مختلف ناکارایی، نقش مهمی در تحلیل عملکرد با هدف توسعه برنامه‌هایی برای بهبود تصمیم‌گیری ایفا می‌کند. در این راستا نه تنها کارایی فنی، هزینه ای و تخصیصی را می توان با اطلاعات ورودی ها و خروجی ها و قیمت آنها تخمین زد، بلکه می توان زیان های ناشی از عدم سود، درآمد و هزینه بهینه را نیز بر اساس ناکارای های مربوطه محاسبه کرد.  مقاله حاضر قصد دارد تخمین جدیدی از کارایی هزینه و منابع تلفات در کارایی کل در یک محیط غیر رقابتی که امکان تغییر قیمت ورودی ها و خروجی ها از یک واحد تصمیم گیری وجود دارد، را ارائه دهد. در راستای مطالعات(Tone. K., Tsutsui, M. "Decomposition of Cost Efficiency and its Application to Japanese-Us Electric Utility Comparisons". Socio-Economic Planning Sciences 47 (2007), pp.91-106)و(Tone .K, "A Strange Case of the Cost and Allocative Efficiencies in DEA". Journal of the Operational Research Society 53, (2002), pp.1225-1231)مطالعه حاضر به دنبال معرفی منابع جدید ناکارایی و زیان های مرتبط با آنها توسط ارائه مجموعه های امکان تولید جدید مبتنی بر قیمت و هزینه می باشد. 

منابع و مأخذ:

 [1] A. Agha Iqbal, C. S. Lerme, L. M. Seiford, Components of efficiency evaluation in data envelopment analysis, European Journal of Operational Research 80 (1995) 462-473. https://doi.org/10.1016/0377-2217(94)00131-U.

[2] A.	Amirteimoori,	S.	Kordrostami,	A.
Rezaitabar, An improvement to the cost
efficiency	interval:	a	DEA-based	ap

proach, Applied mathematics and computation 181 (2006) 775-781. https://doi.org/10.1016/J.AMC.2006.02.005.

[3] A.	Mostafaee,	F.	H. in	Saljooghi,	Cost
efficiency	measures	data	envelop
ment	analysis	with	data	uncertainty,
European	Journal	of	Operational	Re
search	202	(2010)	595-603.	https:

//doi.org/10.1016/J.EJOR.2009.06.007.
[4] A. S. Camanho, R. G. Dyson, Cost efficiency measurement with price uncertainty: a DEA application to bank branch assessments, European journal of operational research 161 (2005) 432-446. https://doi.org/10.1016/J.EJOR.2003.07.018.
[5] A. S. Camanho, R.G. Dyson, A generalization of the Farrell cost efficiency measure applicable to non-fully competitive settings, Omega 36 (2008) 147-162. https://doi.org/10.1016/J.OMEGA.2005.12.004.
[6] B. Sahoo, K. Biresh, Cost, revenue and profit efficiency measurement in DEA: Adirectional distance function approach, European Journal Of Opreational Research 237 (2014) 921-31. https://doi.org/10.1016/j.ejor.2014.02.017.
[7] H. Bagherzadeh Valami, Cost efficiency with triangular fuzzy number input prices: An application of DEA. Chaos, Solitons and Fractals 42 (2009) 1631-1637. https://doi.org/10.1016/J.CHAOS.2009.03.066.
[8] H. Fukuyama, W. Weber, E CONOMIC Inefficiency Measurement Of Input Spending When Decision Making Units Face Different Input Prices, Journal Of The Opreational Research Society 55 (2004) 1102-1110. https://doi.org/10.1057/PALGRAVE.JORS.2601750
[9] J. J. D´ıaz-Hern´andez, E. Mart´ınez-Budr´ıa, J. J. Salazar-Gonz´alez, Measuring cost efficiency in the presence of quasi-fixed inputs using dynamic Data Envelopment Analysis: The case of port infrastructure, Maritime Economics & Logistics 16 (2014) 111-126. https://doi.org/10.1057/MEL.2013.28.
[10] J, Puri, SH. Prasad Yadav, A Fully Fuzzy DEA Approach For Cost And Revenue Efficiency Measurement In The Presence Of Undesirable Outputs And Its Application To The Banking Sector In India, International Journal Of Fuzzy System 18 (2016) 212-226. https://doi.org/10.1007/S40815-015-0031-6.
[11] K. Tone, A slacks-based measure of efficiency in data envelopment analysis, European journal of operational research 130 (2001) 498-509. https://doi.org/10.1016/S0377-2217(99)00407-5.
[12] K. Tone, A StrangeCase Of the Cost and Allocative Efficiencies in DEA, Journal of the Operational Research Society 53 (2002) 1225-1231. https://doi.org/10.1057/palgrave.jors.2601438
[13] K. Tone, M. Tsutsui, Decomposition Of Cost Efficiency And Its Application To Jupaness-Us Electric Utility Comparisons, Socio-Economic Planning Sciences 47 (2007) 91-106. https://doi.org/10.1016/J.SEPS.2005.10.007.
[14] L. Fang, Centralized resource allocation based on efficiency analysis for step-bystep improvement paths, Omega 51 (2015) 24-28. https://doi.org/http://dx.doi.org/10.1016/j
[15] L. Fang, H. Li, Cost efficiency in data envelopment analysis under the law of

one price,	European Journal of Oper
ational	Research	240	(2015)	488-492.

https://doi.org/http://dx.doi.org/ 10.1016/j.ejor.2014.07.017.
[16] M. J. Farrell, The measurement of productive efficiency, Journal of the Royal Statistical Society, Series A (General) 120 (1957) 253-290. https://doi.org/10.2307/2343100.
[17] M. R. Mozaffari, P. Kamyab, J. Jablonsky, J. Gerami, Cost and revenue efficiency in DEA-R models, Computers and Industrial Engineering 78 (2014) 188-94. http:/dx.doi.org/1001016/j.cje. (2014).2014.10.001.
[18] M. V. P. De Souza, R. C. Souza, J. F. M. Pessanha, C. H. da Costa Oliveira, M. Diallo, An application of data envelopment analysis to evaluate the efficiency level of the operational cost of Brazilian electricity distribution utilities, Socio-Economic Planning Sciences 48 (2014) 169-174. https://doi.org/10.1016/J.SEPS.2014.03.002.
[19] P. Ralevic, M. Dobrodlac, D. Markovic, Using a Nonparametric Technique To Measure The Cost Efficiency Of Postal Delivery Branches, Central European Journal Of Operations Research 24 (2016) 637-657. https: //doi.org/10.1007/S10100-014-0369-0.
[20] R. F¨are, S. Grosskopf, S. CAK Lovell The Measurement of Efficiency of Production, Dordrecht: Springer Netherlands (1985). https://doi.org/10.1007/978-94-015-7721-2_1.
[21] R. F¨are, S. Grosskopf, Measuring shadow price efficiency. In Applications of Modern Production Theory, Efficiency and Productivity, Springer, Dordrecht 3 (1988) 223-234. https://doi.org/10.1007/978-94-009-3253-1_9.

[22] R. K. Shiraz, Emrouznejad,	A. Hatami-Marbini,	A.
H.	Fukuyama,	Chance
constrained cost efficiency in data en
velopment	analysis and	model outputs,	with	ran
dom	inputs	Operational
Research	20	(2018)	1863-98.	https:

//doi.org/10.1007/S12351-018-0378-1.
[23] S. C. Ray, L. Chen, K. Mukherjee, In

put	price	variation	across	locations
and a generalized measure of cost ef
ficiency,	International	Journal	of Pro

duction Economics 116 (2008) 208-218. https://ideas.repec.org/a/eee/proeco/v116y2008i2p208-218.html.
[24] S. C. Ray, H. J. Kim, Cost efficiency in the US steel industry: A nonparametric analysis using data envelopment analysis, European Journal of Operational Research 80 (1995) 654-671. https://doi.org/10.1016/0377-2217(94)00143-Z.
[25] S. Thor, G. Kozmetsky, F. Phillips, DEAof Financial Statements Data: The U.S. Computer Industry, Journal of  Productivity 5 (1994) 229-248. https://doi.org/10. 1007/BF01073909.
[26] T. Kuosmanen, T. Post, Measuring economic efficiency with incomplete price information: with an application to European commercial banks, European journal of operational research 134 (2001) 43-58. https://doi.org/10.1016/S0377-2217(00)00237-X.
[27] T. Kuosmanen, T. Post, Nonparametric efficiency analysis underprice uncertainty: a first-order stochastic dominance approach, Journal of Productivity Analysis 17 (2002) 183-200. https://doi.org/10.1023/A:1015037719942.
[28] T. Kuosmanen, T. Post, Measuring economic efficiency with incomplete price information, European Journal of Operational Research 144 (2003) 454-457. https://doi.org/10.1016/S0377-2217(01)00398-858

[29] W. W. Cooper, L. M. Seiford, K. Tone, DATA ENVELOPMENT ANALYSIS A Comprehensive Text With Models Applications, Springer Science + Business Media, LLC. Library Of Congress Control Number: (2007).

[30] W. W. Cooper, R. G. Thompson, R. M. Thrall, Extensions and new developments in DEA, Annals of Operations Research 66 (1996) 3-45. https://doi.org/10.1007/BF02125451.