Construction of convex three-dimensional sections in DEA models with selective convexity

Vladimir E. Krivonozhko (), Alexandr P. Aphanasyev, Andrey V. Lychev and Pavel D. Khoner
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Vladimir E. Krivonozhko: National University of Science and Technology “MISIS”
Alexandr P. Aphanasyev: Lomonosov Moscow State University
Andrey V. Lychev: National University of Science and Technology “MISIS”
Pavel D. Khoner: National University of Science and Technology “MISIS”

Journal of Productivity Analysis, 2025, vol. 64, issue 3, No 18, 558 pages

Abstract: Abstract The Data Envelopment Analysis (DEA) approach emerged at the end of the last century. This approach is a generalization of simple indicators of production units behavior to a multidimensional case. This approach leads in reality to the solution of large family of optimization problems. The Free Disposal Hull (FDH) models were proposed almost at the same time. However, production possibility set (PPS) of FDH models is non-convex. One can stress that the DEA and FDH technologies are two extreme cases for application and investigation of production unit’s behavior. However, some new models have appeared recently for investigation of complex production units. The models with selective convexity embrace a wide class of DEA models where such variables as percentages, ratios, averages, etc. are considered in order to expand the range of their applications. Any mathematical discipline is trying to use visualization for the interpretation and explanation of its important notions. This is especially important for DEA models, since this scientific instrument was intended also for managers and other practitioners, not only for scientists. However, there exist a small number of papers devoted to the visualization methods in the DEA area. In this paper, methods for constructions of convex three-dimensional sections in DEA models with selective convexity are considered.

Keywords: Data envelopment analysis; Selective convexity; Frontier visualization; Isoquants; Three-dimensional sections (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11123-025-00784-0

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