Measuring the performance of two-stage production systems with shared inputs by data envelopment analysis

As a non-parametric technique in Operations Research and Economics, Data Envelopment Analysis (DEA) evaluates the relative efficiency of peer production systems or decision making units (DMUs) that have multiple inputs and outputs. In recent years, a great number of DEA studies have focused on two-stage production systems in series, where all outputs from the first stage are intermediate products that make up the inputs to the second stage. There are, of course, other types of two-stage processes that the inputs of the system can be freely allocated among two stages. For this type of two-stage production system, the conventional two-stage DEA models have some limitations e.g. efficiency formulation and linearizing transformation. In this paper, we introduce a relational DEA model, considering series relationship among two stages, to measure the overall efficiency of two-stage production systems with shared inputs. The linearity of DEA models is preserved in our model. The proposed DEA model not only evaluates the efficiency of the whole process, but also it provides the efficiency for each of the two sub-processes. A numerical example of US commercial banks from literature is used to clarify the model.

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