Directional scale elasticity considering the management preference of decision-makers

¹ School of Business Administration, Hunan University, Changsha 410082, P.R. China
² Institute of Data Science and Decision Optimization, Hunan University, Changsha 410082, P.R. China
³ Beijing Normal University, Zhuhai, 519087, P.R. China
⁴ DBM, BNU-HKBU United International College, Zhuhai 519087, P.R. China

^* Corresponding author: Z.B.Zhou@hnu.edu.cn; z.b.zhou@163.com

Received: 20 October 2021
Accepted: 14 August 2021

Abstract

Most data envelopment analysis (DEA) studies on scale elasticity (SE) and returns to scale (RTS) of efficient units arise from the traditional definitions of them in economics, which is based on measuring radial changes in outputs caused by the simultaneous change in all inputs. In actual multiple inputs/outputs activities, the goals of expanding inputs are not only to obtain increases in outputs, but also to expect the proportions of such increases consistent with the management preference of decision-makers. However, the management preference is usually not radial changes in outputs. With the latter goal into consideration, this paper proposes the directional SE and RTS in a general formula for multi-output activities, and offers a DEA-based model for the formula of directional SE at any point on the DEA frontier, which is straightforward and requires no simplifying assumptions. Finally, the empirical part employs the data of 16 basic research institutions in Chinese Academy of Sciences (CAS) to illustrate the superiority of the proposed theories and methods.