A single two-stage network DEA model ensuring feasibility and interpretable efficiency measurement

Data envelopment analysis (DEA) is a well-known data-enabled technique to evaluate the relative efficiency of empirical production technology of decision-making units (DMUs) that transform inputs (resources) into outputs (products). Such technologies may consist of two or more internal stages. In a two-stage network (2SN) DEA, the outputs of the first stage serve as inputs for the second stage and are referred to as intermediates. DEA evaluates relative efficiencies based on observed DMUs under a very few assumptions. However, conventional 2SN DEA models may indicate that none of the observed DMUs are overall efficient. To address this issue, a few approaches have been proposed in the literature to ensure that at least one efficient DMU is identified through sequential or iterative processes. In this study, we propose a single model for simultaneously evaluating stage and overall efficiencies. Unlike other existing models, our model ensures that the resulting projections are radially interpretable, remain within the feasible production possibility set, and prevents infeasibility or bias in evaluating stage efficiencies. We demonstrate the model using a real-world numerical example and compare its results to those of existing models.