A slacks-based measure of efficiency in two-stage data envelopment analysis

As a non-parametric technique, Data Envelopment Analysis (DEA) evaluates the relative efficiency of peer decision making units (DMUs) that have multiple inputs and outputs. In many situations, DMUs have a two-stage structure, where the first stage uses inputs to produce outputs that then become the inputs to the second stage. The first stage outputs are called "intermediate products." In recent years, a great number of DEA studies have focused on developing the two-stage processes, so that researchers, by using radial DEA models, have proposed new models for evaluating the efficiency of two-stage processes. However, because of the existence of intermediate measures, these models do not provide comprehensive information about the efficiency frontier and the projections of inefficient DMUs. This paper introduces a non-radial model in the slacks-based measure (SBM) framework for two-stage production processes that considers the series relationship between two stages. Unlike the radial two-stage DEA models, the new approach enables us to determine efficient projections for inefficient DMUs within the framework of two-stage DEA. An example from the literature is applied to clarify the model.

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