Introducing a new inefficiency source due to inappropriate price selection in a Non-Competitive Environment in Data Envelopment Analysis (a case study in the Imam Khomeini Oil Refinery Company of Shazand in Iran)

Subject Areas : Statistics

Elham Rezaei hezaveh ¹ (Department of Mathematics, Khorramabad branch, Islamic Azad University, Khorramabad, Iran)
Reza Fallahnejad ² (Department of Mathematics, Khorramabad branch, Islamic Azad University, Khorramabad, Iran)
Masoud Sanei ³ (Department of Mathematics,Tehran center branch, Islamic Azad University, tehran, Iran)
Mohammad Izadikhah ⁴ (Department of Mathematics,Arak branch, Islamic Azad University, Arak, Iran)

Received: 2019-06-26 Accepted : 2020-01-19 Published : 2020-10-22

Keywords: کارایی هزینه, تحلیل پوششی داده ها, قیمت های غیریکسان, فضای غیررقابتی,

Abstract :

Data Envelopment Analysis (DEA) is an appropriate tool for estimating various types of efficiency including Cost Efficiency (CE). Identifying and identifying inefficiency resources plays an important role in analyzing unit performance in order to plan for improving the status of Decision Making Units (DMUs). Now , if information on the inputs and outputs and pricing information of the evaluated units is available, we can calculate the lack of profit and revenue and cost optimization with respect to their inefficiencies. In this paper, we intend to determine the production possibility set (PPS) a new price and a new cost, based on which a new inefficient source and a new source selection of price vectors in a non competitive environment (that is , in the event of a possible change of loss due to the incorrect in Input prices And outputs from the Decision Making Unit to other Decision Making Units (DMUs)).

References:

[1] Barzegarinegad A, Jahanshahloo G, Rostamy-Malkhalifeh M. A full ranking for decision making units using ideal and anti-ideal points in DEA. The Scientific World Journal (2014).

 

[2] Blank JL, Eggink E. The decomposition of cost efficiency: an empirical application of the shadow cost function model to Dutch general hospitals. Health Care Management Science. May 1;7(2):79-88(2004).

 

[3] Chambers RG, Färe R. Additive decomposition of profit efficiency. Economics Letters. Sep 1;84(3):329-34 (2004).

 

[4] Cheng YS, Li SK. Income inequality and efficiency: A decomposition approach and applications to China. Economics Letters. Apr 1;91(1):8-14 (2006).

 

[5] Chen Y, Du J, Sherman HD, Zhu J. DEA model with shared resources and efficiency decomposition. European Journal of Operational Research. Nov 16;207(1):339-49(2010).

 

[6] Cooper WW, Thompson RG, Thrall RM. Introduction: Extensions and new developments in DEA. Annals of operations Research. Feb 1;66(1):1-45 (1996).

 

[7] Cooper WW, Seiford LM, Tone K. Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software. Journal-operational Research Society; 52(12):1408-9(2001).

 

[8] Cook WD, Zhu J, Bi G, Yang F. Network DEA: Additive efficiency decomposition. European journal of operational research. Dec 1; 207(2):1122-9 (2010).

 

[9] Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. European journal of operational research. Nov 1;2(6):429-44 (1978).

 

[10] Farrell MJ. The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A (General). 120(3):253-81(1957).‏

 

[11] Jahanshahloo GR, Hosseinzadeh Lotfi F, Rostamy-Malkhalifeh M, Ghobadi S. Using enhanced Russell model to solve inverse data envelopment analysis problems. The Scientific World Journal (2014).

 

[12] Kao C. Efficiency decomposition in network data envelopment analysis: A relational model. European journal of operational research. Feb 1;192(3):949-62(2009).

 

[13] Liang L, Cook WD, Zhu J. DEA models for two‐stage processes: Game approach and efficiency decomposition. Naval Research Logistics (NRL). Oct;55(7):643-53(2008).

 

[14] Liu ST. A note on efficiency decomposition in two-stage data envelopment analysis. European Journal of Operational Research. Aug 1;212(3): 606-8 (2011).

 

[15] Lotfi FH, Navabakhs M, Tehranian A, Rostamy-Malkhalifeh M, Shahverdi R. Ranking bank branches with interval data the application of DEA. InInternational Mathematical Forum Vol. 2, No. 9, pp. 429-440 (2007).

 

[16] Nemoto J, Goto M. Productivity, efficiency, scale economies and technical change: A new decomposition analysis of TFP applied to the Japanese prefectures. Journal of the Japanese and International Economies. Dec 1;19(4):617-34(2005).

 

[17] Peykani P, Mohammadi E, Emrouznejad A, Pishvaee MS, Rostamy-Malkhalifeh M. Fuzzy data envelopment analysis: An adjustable approach. Expert Systems with Applications. Dec 1; 136: 439-52 (2019).

 

[18] Peykani P, Mohammadi E, Jabbarzadeh A, Jandaghian A. Utilizing robust data envelopment analysis model for measuring efficiency of stock, a case study: Tehran Stock Exchange. Journal of New Researches in Mathematics. Feb 1; 1(4): 15-24 (2016).

 

[19] Peykani P, Mohammadi E, Pishvaee MS, Rostamy-Malkhalifeh M, Jabbarzadeh A. A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches. RAIRO- Operations Research. Oct 1; 52(4-5): 1445-63 (2018).

 

[20] Peykani P, Mohammadi E, Rostamy-Malkhalifeh M, Hosseinzadeh Lotfi F. Fuzzy data envelopment analysis approach for ranking of stocks with an application to Tehran stock exchange. Advances in Mathematical Finance and Applications. Mar 1;4(1):31-43(2019).

 

[21] Peykani P, Mohammadi E, Esmaeili S, Sadat F. Stock evaluation under mixed uncertainties using robust DEA model. Journal of Quality Engineering and Production Optimization. Jun 1;4(1):73-84 (2019).

 

[22] Thor. S, Kozmetsky.G, and Phillips. F. DEAof Financial Statements Deta: The U.S. Computer Industry. Journal of Productivity Analysis 5, pp.229-248 (1994).

[23] Tone K. A strange case of the cost and allocative efficiencies in DEA. Journal of the Operational Research Society. Nov 1; 53(11):1225-31(2002).

 

[24] Tone K, Tsutsui M. Decomposition of cost efficiency and its application to Japanese-US electric utility comparisons. Socio-Economic Planning Sciences. Jun 1;41(2):91-106(2007).

 

[25] Yamamura K, Ushida A, Horiuchi K. Improving the efficiency of interval analysis by Kevorkian's decomposition technique. Electronics and Communications in Japan (Part III: Fundamental Electronic Science). Feb; 75(2): 36-46 (1992).

 

[26] Yang CC. An enhanced DEA model for decomposition of technical efficiency in banking. Annals of Operations Research. Mar 1;214(1):167-85(2014).

 

[27] Zieschang KD. A note on the decomposition of cost efficiency into technical and allocative components. Journal of Econometrics. Dec 1; 23(3): 401-5(1983).