An Inverse DEA Model for Two-Stage Systems: A Slack-Based Measure

Abstract

Conventional Inverse Data Envelopment Analysis (InvDEA) models estimate the input/output levels of Decision-Making Units (DMUs) in order that the efficiency score of units remain unchanged. They ignore slacks in both the efficiency evaluation and the estimation of input/output levels of DMUs, while the existence of slacks can give more accurate information about inputs/outputs of the under-evaluation DMU and estimate inputs/outputs of DMUs more accurate and real. Moreover, the traditional InvDEA models consider DMUs as a black box and do not consider the internal structure of units. To overcome the aforementioned issues, this paper proposes an Inverse Slack-Based Measure of efficiency (InvSBM) model for input estimation in a two-stage network structure. In the model, the efficiency score of under evaluation DMU with a two-stage network character remains unchanged. Since the model is Non-Linear Multi-Objective Programming (NLMOP), a three-stage method is provided in order to estimate input levels of units. Finally, a real case study in the banking industry is presented to show the abilities of the proposed approach.