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The impossibility of convex constant returns-to-scale production technologies with exogenously fixed factors
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Podinovski, Victor V. and Bouzdine-Chameeva, Tatiana. (2011) The impossibility of convex constant returns-to-scale production technologies with exogenously fixed factors. European Journal of Operational Research, Volume 213 (Number 1). pp. 119-123. ISSN 0377-2217
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Official URL: http://dx.doi.org/10.1016/j.ejor.2011.03.003
Abstract
The extensions to the variable (VRS) and the constant (CRS) returns-to-scale models developed by Banker and Morey are considered among the main approaches to the incorporation of exogenously fixed factors in models of data envelopment analysis (DEA). Recently, Syrjanen showed that the Banker and Morey CRS technology is not convex. Taking into account that its subset VRS technology is explicitly assumed convex, this observation leads to difficulties with explaining the fundamental production assumptions of the CRS extension. Motivated by the example of Syrjanen, the contribution of this paper is twofold. First, we show that the nonconvex Banker and Morey CRS technology is nevertheless a suitable reference technology for the assessment of scale efficiency. Second, we ask if a convex technology could be constructed that would "correct" the nonconvexity of the CRS technology of Banker and Morey. The answer to this is negative: one consequence of assuming both convexity and ray unboundness with fixed exogenous factors is that we can always "mix-and-match" discretionary and nondiscretionary factors taken from different units, arriving at totally unrealistic production plans. This demonstrates that generally there exists no meaningful convex CRS technology with exogenously fixed factors that can be used in its own right, apart from its use as a reference technology in the measurement of scale efficiency. (C) 2011 Elsevier B.V. All rights reserved.
| Item Type: | Journal Article |
|---|---|
| Subjects: | H Social Sciences > HA Statistics H Social Sciences > HB Economic Theory |
| Divisions: | Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School |
| Library of Congress Subject Headings (LCSH): | Data envelopment analysis, Economies of scale, Exogeneity (Econometrics) |
| Journal or Publication Title: | European Journal of Operational Research |
| Publisher: | Elsevier Science BV |
| ISSN: | 0377-2217 |
| Date: | 2011 |
| Volume: | Volume 213 |
| Number: | Number 1 |
| Page Range: | pp. 119-123 |
| Identification Number: | 10.1016/j.ejor.2011.03.003 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| References: | Banker, R.D., 1984. Estimating most productive scale size using data envelopment analysis. European Journal of Operational Research 17, 35–44. Banker, R.D., Charnes, A., Cooper, W.W., 1984. Some models for estimating technical and scale efficiencies in data envelopment analysis. Management Science 30, 1078–1092. Banker, R.D., Morey, R.C., 1986. Efficiency analysis for exogenously fixed inputs and outputs. Operations Research 34, 513–521. Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444. Cooper, W.W., Seiford, L.M., Tone, K., 2000. Data Envelopment Analysis. Kluwer Academic Publishers, Boston. Golany, B., Roll, Y., 1993. Some extensions of techniques to handle nondiscretionary factors in data envelopment analysis. Journal of Productivity Analysis 4, 419–432. Kuosmanen, T., 2005. Weak disposability in nonparametric productivity analysis with undesirable outputs. American Journal of Agricultural Economics 87, 1077–1082. Kuosmanen, T., Podinovski, V.V., 2009. Weak disposability in nonparametric production analysis: Reply to Färe and Grosskopf. American Journal of Agricultural Economics 91, 539–545. Löber, G., Staat, M., 2010. Integrating categorical variables in data envelopment analysis models: A simple solution technique. European Journal of Operational Research 202, 810–818. Lovell, C.A.K., 1994. Linear programming approaches to the measurement and analysis of productive efficiency. TOP 2, 175–248. Muñiz, M., Paradi, J., Ruggiero, J., Yang, Z., 2006. Evaluating alternative DEA models used to control for non-discretionary inputs. Computers and Operations Research 33, 1173–1183. Podinovski, V.V., 2004. Bridging the gap between the constant and variable returnsto- scale models: Selective proportionality in data envelopment analysis. Journal of the Operational Research Society 55, 265–276. Ruggiero, J., 1996. On the measurement of technical efficiency in the public sector. European Journal of Operational Research 90, 553–565. Syrjänen, M.J., 2004. Non-discretionary and discretionary factors and scale in data envelopment analysis. European Journal of Operational Research 158, 20–33. Yang, H., Pollitt, M., 2009. Incorporating both undesirable outputs and uncontrollable variables into DEA: The performance of Chinese coal-fired power plants. European Journal of Operational Research 197, 1095–1105. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/41345 |
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