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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

Official Date:

2011

Dates:

Date	Event
2011	Published

Volume:

Volume 213

Number:

Number 1

Page Range:

pp. 119-123

Identifier:

10.1016/j.ejor.2011.03.003

Status:

Peer Reviewed

Publication Status:

Published

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