On value efficiency

• Published in: Optimization Vol. 63; no. 4; pp. 617 - 631
• Main Authors: Soleimani-damaneh, Majid, Korhonen, Pekka J., Wallenius, Jyrki
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis Group 01-04-2014; Taylor & Francis LLC
• Subjects: Constraining; Continuity; Data envelopment analysis; Decision making; Decision making units; Efficiency; Mathematical functions; Measurement techniques; Mordukhovich's subdifferential; nonsmooth analysis; Operations research; Optimization; Recognition; Studies; Tangents; value efficiency analysis
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2012.673126

Value efficiency analysis (VEA) is a data envelopment analysis (DEA)-based approach that measures the efficiency of decision-making units, incorporating the decision maker's preferences explicitly. If the functional form of the value function is assumed pseudoconcave, then a tangent cone where the most preferred point is its vertex can be used to recognize value inefficient points. In this article, we consider the value function assumptions and show that the pseudoconcavity assumption can be extended to also cover nonsmooth value functions in VEA using a known class of limiting subdifferentials in nonsmooth analysis. The focus of this article is to show that the tangent cone approach to recognize value inefficient points is a valid approach even if the value function assumptions are more general than pseudoconcavity. Moreover, we show that continuity is needed in the case of true value efficiency.