Bargaining approach for efficiency assessment and target setting with fixed-sum variables

There are many Data Envelopment Analysis (DEA) applications in which an input or output variable is such that the total amount for all the units in the sample is fixed. In this paper, such situations are modelled as a bargaining problem in which the players correspond to each of the variables for each of the units. All the players try to improve their utility as much as possible, where utility improvement implies a reduction in the case of an input variable or an undesirable output and an increase in the case of a desirable output. The Feasible Set of the bargaining problem derives from the corresponding fixed-sum DEA technology. A centralized DEA model is formulated for computing the Nash bargaining solution, which determines the efficient targets of all the units. From these targets, a modified Enhanced Russell Graph efficiency measure (ERM) is proposed to compute the corresponding efficiency scores. The proposed approach has been validated on different datasets corresponding to a variety of situations in-volving fixed-sum variables. (c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

This paper presents a model that combines fixed-sum DEA technology with bargaining methods to deal with input or output variables with fixed total amounts. By computing the Nash bargaining solution and using an enhanced efficiency measure, efficient analysis for all units is achieved.