A novel two-stage DEA production model with freely distributed initial inputs and shared intermediate outputs

Conventional data envelopment analysis (DEA) models treat the decision-making units (DMUs) as black-boxes: inputs enter the system and outputs exit the system, with no consideration for the intermediate steps characterizing the DMUs. As a result, intermediate measures are lost in the process of changing the inputs to outputs and it becomes difficult, if not impossible, to provide individual DMU managers with specific information on what part of a DMU is responsible for the overall inefficiency. This study defines a two-stage DEA model, where each DMU is composed of two sub-DMUs in series, the intermediate products by the sub-DMU in Stage 1 are partly consumed by the sub-DMU in Stage 2, and the initial inputs of the DMU can be freely allocated in both stages. Also, there are additional inputs directly consumed in Stage 2 while part of the outputs of Stage 1 are final outputs. We develop four new linear models to determine the upper and lower bounds of the efficiencies of the two sub-DMUs in a non-cooperative setting and a linear model to calculate the overall efficiency of DMU in a cooperative setting. That is, the overall efficiency of a DMU is modelled in a cooperative setting via upper and lower bounds obtained in the non-cooperative one. The proposed two-stage DEA method allows for important applications to several management areas. A case study in the banking industry is presented to demonstrate the applicability and exhibit the efficacy of the proposed models. © 2017 Elsevier Ltd. All rights reserved.