Interval Economic Efficiency Measures in Data Envelopment Analysis

Subject Areas : Applied Mathematics Modeling

Amin Mostafaee ¹

1 - Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

Received: 2022-03-03 Accepted : 2022-02-03 Published : 2020-12-01

Keywords: Price uncertainty, DEA, Revenue Efficiency, economic efficiency, Cost efficiency,

Abstract :

One of the most essential pieces of information given by DEA models is the cost efficiency of decision-making units (DMUs). Cost efficiency (CE) is defined as the ratio of minimum costs to current costs and in fact, evaluates the ability to produce current outputs at a minimal cost. While the traditional cost efficiency models require the values for all data to be known exactly, in real-world problems the exact values of input prices are unknown, and only the maximum and minimum bounds of input prices can be estimated for each DMU. Hence, the main aim of the current paper is to develop a pair of two-level mathematical programming problems, whose optimal values represent the optimistic and pessimistic cost efficiency measures. The two-level nonlinear program for the optimistic cost efficiency measure is then transformed into a one-level linear program. In this regard, we provide an explicit formula for measuring the pessimistic CE measure.

References:

 [1] Arabmaldar A, Kwasi Mensah E, Toloo M. Robust worst-practice interval DEA with non-discretionary factors. Expert Systems with Applications. 2021;182:115256
[2] Bazaraa M.S., J.J. Jarvis, H.D. Sherali. Linear Programming and Network Flows, John Wiley and Sons, 1990.
[3] Blagojević M, Ralević P, Šarac D. An integrated approach to analysing the cost efficiency of postal networks.
Utilities Policy. 2020;62:101002.
[4] Camanho A.S., R.G. Dyson. Cost efficiency measurement with price uncertainty: a DEA application to bank
branch assessments.European J. of Operational Research 161:432-446 (2005). 

 [5] Charnes A., W.W. Cooper, E. Rhodes. Measuring the efficiency of decision making units. European J. of
Operational Research 2:429-444 (1978).
[6] Despotis D.K., Y.G. Smirlis. Data envelopment analysis with imprecise data. European J. of Operational
Research 140:24-36 (2002).
[7] Entani T., M. Yutaka, H. Tanaka. Dual models of interval DEA and its extension interval data. European J.
of Operational Research 136:32-45 (2002).
[8] Esmaeili M. An Enhanced Russell Measure in DEA with interval data. Applied Mathematics and Computation. 2012;219(4):1589-93.
[9] Fa¨re R., S. Grosskopf, C.A.K. Lovell. The measurement of efficiency of production. Kluwer Academic Publishers (1985).
[10] Hatami-Marbini A, Emrouznejad A, Agrell PJ. Interval data without sign restrictions in DEA. Applied Mathematical Modelling. 2014;38(7):2028-36.
[11] Harrington JE. There may be no pass through of a merger-related cost efficiency. Economics Letters.
2021;208:110050.
[12] Izadikhah, M., Roostaee, R., Emrouznejad, A. (2021). Fuzzy Data Envelopment Analysis with Ordinal and
Interval Data. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 29(3), 385-
410. https://doi.org/10.1142/s0218488521500173
[13] Jiang X, Wu L. A Residential Load Scheduling Based on Cost Efficiency and Consumer’s Preference for Demand Response in Smart Grid. Electric Power Systems Research. 2020;186:106410.
[14] Jahanshahloo G.R., M. Soleimani-damaneh, A. Mostafaee. Cost efficiency analysis with ordinal data: a theoretical and computational view. International J. of Computer Mathematics 84 (4):553-562 (2007).
[15] Jahanshahloo G.R., M. Soleimani-damaneh, A. Mostafaee. On the computational complexity of cost efficiency analysis models. Applied Mathematics and Computation 188 (1): 638-640 (2007).
[16] Jahanshahloo G.R., M. Soleimani-damaneh, A. Mostafaee. A Simplified version of the DEA cost efficiency
model, European J. of Operational Research 184:814-815 (2008).
[17] Kao C. Interval efficiency measures in data envelopment analysis with imprecise data. European J. of Operational Research 174:10871099 (2006).
[18] Kuosmanen T., T. Post. Measuring economic efficiency with incomplete price information: With an application to European comerical banks. European J. of Operational Research 134:43-58 (2001).
[19] Kuosmanen T., T. Post. Measuring economic efficiency with incomplete price information. European J. of
Operational Research 144:454-457 (2003).
[20] Mostafaee A, Saljooghi FH. Cost efficiency measures in data envelopment analysis with data uncertainty.
European Journal of Operational Research. 2010;202(2):595-603 

 [21] Obeng K, Sakano R. Effects of government regulations and input subsidies on cost efficiency: A decomposition approach. Transport Policy. 2020;91:95-107.
[22] Pourmohammad-Zia N, Karimi B, Rezaei J. Food supply chain coordination for growing items: A
trade-off between market coverage and cost-efficiency. International Journal of Production Economics.
2021;242:108289.
[23] Schaffnit C., D. Rosen, J.C. Paradi. Best practice analysis of bank branches: an application of DEA in a large
Canadian bank. European Journal of Operational Research 98 (1997) 269-289.
[24] Wang Y.M, R. Greatbanks, J.B. Yang. Interval efficiency assessment using data envelopment analysis. Fuzzy
Sets and System 153:347-370 (2005).
[25] Zhu J. Imprecise data envelopment analysis (IDEA): A review and improvement with an application. European J. of Operational Research 144:513-529(2003).
[26] Zhu J. Efficiency evaluation with strong ordinal input and output measures. European J.of Operational Research 146: 477-485(2003).