Measuring the Interval industry cost efficiency score in DEA

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Basic Sciences, Central Tehran Branch, Islamic Azad University, Tehran, Iran

10.22034/amfa.2020.1880449.1308

Abstract

In this paper we extend the concept of "cost minimizing industry structure" and develop two DEA models for dealing with imprecise data. The main aim of this study is to propose an approach to compute the industry cost efficiency measure in the presence of interval data. We will see that the value obtained by the proposed approach is an interval value. The lower bound and upper bound of the interval industry cost efficiency measure are computed and then decomposed into three components to examine the relationship between them and the lower and upper bounds of the individual interval cost efficiency measures. We also define the cost efficient organization of the industry as a set of DMUs, which minimizes the total cost of producing the interval industry output vector. In fact, this paper determines the optimal number of DMUs and the reallocation of the industry observed outputs among them. We hereby determine the effects of the optimal number of DMUs and the reallocation of outputs among them on the interval industry cost efficiency measure. Finally, a numerical example will be presented to illustrate the proposed approach.

Keywords


References
[1] Banker, R.D., Charnes, A., Cooper, W.W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 1984, 30, P. 1078-1092. Doi:10.1287/mnsc.30.9.1078.
 
[2] Baumol, W.J., Panzar, J.C., Willig, R.D., Contestable markets and the theory of industry structure, New York: Harcourt Brace Jovanovich 1982.
 
[3] Baumol, W.J., Fisher, D., Cost-minimizing number of firms and determination of industry structure, The Quarterly Journal of Economics, 1978, 92, P. 439-468. Doi:10.2307/1883153.
 
[4] Cesaroni G., Industry cost efficiency in data envelopment analysis, Socio-Economic Planning Sciences, 2017, 16, P.30041-30046. Doi: 10.1016/j.seps.2017.01.001.
[5] Charnes, A., Cooper, W.W., Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 1978, 2(6), P.429–444. Doi: 10.1016/0377-2217(78)90138-8.
 
[6] Cooper, W.W., Park, K.S., Yu, G., IDEA and AR-IDEA: models for dealing with imprecise data in DEA. Management Science, 1999, 45, P.597–607. Doi: 10.1287/mnsc.45.4.597.
 
[7] Despotis, D.K., Smirlis, Y.G., Data envelopment analysis with imprecise data, European Journal of Operational Research, 2002, 140, P.24–36. Doi: 10.1016/S0377-2217(01)00200-4.
 
[8] Farrell, M.G., The measurement of productive efficiency, Journal of the Royal Statistical Society, Series A, 1957, 120, P. 253-281. Doi: 10.2307/2343100.
 
[9] Førsund, F., Hjalmarsson, L., Generalized Farrell measures of efficiency: An application to milk processing in Swedish dairy plants, The Economic Journal, 1979, 89, P. 294-315. Doi: 10.2307/2231603.
 
[10] Hosseinzade Lotfi, F., Jahanshahloo, G.R., Shahverdi, R., Rostamy-Malkhalifeh, M., Cost Efficiency and Cost Malmquist Productivity Index with Interval Data, International Mathematical Forum, 2007, 2(9), P. 441 – 453. Doi: 10.12988/imf.2007.07040.
 
[11] Joulaei, M., Mirbolouki, M., Reduction of DEA-Performance Factors Using Rough Set Theory: An Application of Companies in the Iranian Stock Exchange, Advances in Mathematical Finance and Applications, 2020, 5(1), P.53-67. Doi: 10.22034/amfa.2019.1868389.1223.
 
[12] Li, S.K, Cheng, Y.S., Solving the puzzles of structural efficiency, European Journal of Operational Research, 2007, 180, P. 713-722. Doi: 10.1016/j.ejor.2006.05.010.
 
[13] Navidi, S., Rostamy-Malkhalifeh, M., Banihashemi, S., Using MODEA and MODM with Different Risk Measures for Portfolio Optimization, Advances in Mathematical Finance and Applications, 2020, 5(1), P. 29-51. Doi: 10.22034/amfa.2019.1864620.1200.
 
[14] Peykani, P., Mohammadi E., Interval network data envelopment analysis model for classification of investment companies in the presence of uncertain data, Journal of Industrial and Systems Engineering, 2018, 11(Special issue: 14th International Industrial Engineering Conference), P. 63-72.
 
[15] Peykani, P., Mohammadi E., Window network data envelopment analysis: an application to investment companies, International Journal of Industrial Mathematics, 2020, 12(1), P. 89-99.
 
[16] Peykani, P., Mohammadi E., Emrouznejad, A., Pishvaee, M.S., Rostamy-Malkhalifeh, M., Fuzzy data envelopment analysis: An adjustable approach, Expert Systems with Applications, 2019, 136, P. 439-452
Doi: 10.1016/j.eswa.2019.06.039.
 
[17] Peykani, P., Mohammadi E., Emrouznejad, A., Pishvaee, M.S., 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, 2018, 52(4), P. 1445-1463.
 Doi: 10.1051/ro/2018019.
 
[18] Peykani, P., Mohammadi E., Rostamy-Malkhalifeh, M., Hosseinzade Lotfi, F., Fuzzy Data Envelopment Analysis Approach for Ranking of Stocks with an Application to Tehran Stock Exchange, Advances in Mathematical Finance and Applications, 2019, 4(1), P. 31-43. Doi:10.22034/amfa.2019.581412.1155.
 
[19] 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 Research in Mathematics, 2016, 1(4), P. 15-24.
 
[20] Peykani, P., Mohammadi E., Seyed Esmaeili, F.S., Stock Evaluation under Mixed Uncertainties Using Robust DEA Model, Journal of Quality Engineering and Production Optimization, 2019, 4(1), P. 73-84.
 Doi: 10.22070/jqepo.2019.3652.1080.
 
[21] Poordavoodi, A., Moazami Goudarzi, M.R.,  Haj Seyyed Javadi, H., Rahmani, A.M., Izadikhah, M., Toward a More Accurate Web Service Selection Using Modified Interval DEA Models with Undesirable Outputs, Computer Modeling in Engineering & Sciences, 2020, 123(2), P. 525-570, Doi: 10.32604/cmes.2020.08854
[22] Portela, M.C.A.S. and Thanassoulis, E., Economic efficiency when prices are not fixed: disentangling quantity and price efficiency, Omega, 2014, 47, P. 36-44. Doi: 10.1016/j.omega.2014.03.005.
 
[23] Shahhosseini, M., Hu, G., Pham, H., Optimizing Ensemble Weights for Machine Learning Models: A Case Study for Housing Price Prediction, In INFORMS International Conference on Service Science, Springer, Cham, 2019, P. 87-97.
 
[24] Shahhosseini, M., Martinez-Feria, R.A., Hu, G., Archontoulis, S.V., Maize yield and nitrate loss prediction with machine learning algorithms, Environmental Research Letters, 2019. Doi: 10.1088/1748-9326/ab5268.
 
[25] Sueyoshi, T., Measuring efficiencies and returns to scale of Nippon Telegraph & Telephone in production and cost analyses, Management Science, 1997, 43, P. 779-796. Doi: 10.1287/mnsc.43.6.779.
 
[26] Tagashira, T., Minami C., The Effect of Cross-Channel Integration on Cost Efficiency, Journal of Interactive Marketing, 2019, 47, P. 68-83. Doi: 10.1016/j.intmar.2019.03.002.
 
[27] Tohidi, G., Tohidnia, S., A non-radial approach to improve the interval cost efficiency score in DEA, International Journal of Industrial and Systems Engineering, 2021, 39(2), P. 151-161.
 
[28] Tohidnia, S., Tohidi, G., Measuring productivity change in DEA-R: A ratio-based profit efficiency model, Journal of the Operational Research Society, 2019, 70, P. 1511–1521. Doi: 10.1080/01605682.2018.1506561.
 
[29] Tavana, M., Izadikhah, M., Farzipoor Saen, R., Zare, R., An integrated data envelopment analysis and life cycle assessment method for performance measurement in green construction management. Environ Sci Pollut Res, 2021,  28, P. 664–682. Doi: 10.1007/s11356-020-10353-7
[30] Walheer, B., Disaggreation of the Cost Malmquist Index with joint and output-specific inputs, Omega, 2018, 75, P. 1-12. Doi: 10.1016/j.omega.2017.01.012.
 
[31] Wang, Q., Wu, Z., Chen, X., Decomposition weights and overall efficiency in a two-stage DEA model with shared resources, Computers and Industrial Engineering, 2019, 136, P. 135-148. Doi: 10.1016/j.cie.2019.07.014.
Volume 7, Issue 2
April 2022
Pages 379-390
  • Receive Date: 06 October 2019
  • Revise Date: 31 January 2020
  • Accept Date: 04 February 2020
  • First Publish Date: 01 April 2022