Regular Variable Returns to Scale Production Frontier and Efficiency Measurement

Sung Ko Li (), Chun Kei Tsang (), Shu Kam Lee () and Xinju He ()
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Sung Ko Li: Business, Economic and Public Policy Research Centre, Hong Kong Shue Yan University, Hong Kong, China; and School of Economics, Hefei University of Technology, Hefei, China
Chun Kei Tsang: Business, Economic and Public Policy Research Centre, Hong Kong Shue Yan University, Hong Kong, China; and Department of Economics, Hong Kong Baptist University, Hong Kong, China
Shu Kam Lee: Business, Economic and Public Policy Research Centre, Hong Kong Shue Yan University, Hong Kong, China
Xinju He: School of Business, Guangxi University, Nanning, China; and Key Laboratory of Interdisciplinary Science of Statistics and Management (Guangxi University), Education Department of Guangxi, Nanning, China

Operations Research, 2025, vol. 73, issue 5, 2830-2848

Abstract: The most frequently used empirical production frontier in data envelopment analysis, the variable returns to scale frontier, has a convex technology set and displays a special structure in economics, called the regular variable returns to scale in this paper; the production technology exhibits increasing returns to scale at the beginning of the production process followed by constant returns to scale and decreasing returns to scale. When the assumption of convexity is relaxed, modeling regular variable returns to scale becomes difficult, and currently, no satisfactory solution is available in multioutput production. Overcoming these difficulties, this paper adopts a suggestion in literature to incorporate regular variable returns to scale into the free disposal hull frontier under multiple outputs. We establish a framework for analyzing regular variable returns to scale and recommend an empirical production frontier for measuring technical efficiency with such pattern and multiple outputs. In the presence of regular variable returns to scale without convexity, the value of the technical efficiency measure computed from this new frontier is closer to the “true” value than that from the free disposal hull frontier, and the conventional variable returns to scale frontier may cause misleading implications.

Keywords: Optimization; regular variable returns to scale; strong disposability; nonconvex production technology (search for similar items in EconPapers)
Date: 2025
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