Combining efficiency and scaling effects in activity analysis: towards an improved best practice criterion

¹ Department of Operations Research, FernUniversität in Hagen, Hagen 58097, Germany
² Chair of Quantitative Methods, Leibniz FH School of Business, Hannover 30539, Germany
³ Department of Parallelism and VLSI, FernUniversität in Hagen, Hagen 58097, Germany

^* Corresponding author: andreas.dellnitz@leibniz-fh.de

Received: 22 July 2021
Accepted: 4 March 2022

Abstract

Efficiency is the main issue in any data envelopment analysis. Realizing output by a minimum of input or reaching a maximum of output by a given input is the credo, scale effects often are only a sort of accessory. In modern economics scale effects play a prominent role, however. What is the right size of a decision making unit (DMU) and how to proceed there. Returns to scale inform a DMU about its hitherto disregard of scale effects and show the way towards its ideal activity size. Combining efficiency aspects and scaling effects leads to a new DEA-best practice criterion of DMUs and gives them a profound orientation of their current position. This combination turns out to be the relation of weighted outputs to weighted inputs – in optimal prices under variable returns to scale (VRS). It is the VRS-productivity. For DMUs with increasing returns to scale the recommended growth path is in accordance with economic rationales, for decreasing returns to scale the recommended shrinking path uncovers severe flaws in VRS-models and needs adjustment. All theoretical considerations are illustrated by little numerical examples. A real world application of 37 Brazilian banks demonstrates the benefits of the new concept.