Classical DEA models typically assume a linear valuation approach in performance assessment. However, in practical applications, many DMU inputs and outputs exhibit nonlinear valuation. A linear valuation may fail to accurately capture the variations in value across different DMUs. One critical challenge in efficiency evaluation is the presence of undesirable outputs, which negatively affects DMU performance. To address this, decision-makers aim to incorporate the impact of undesirable factors into efficiency measurements, enabling them to identify high-performing DMUs under comparable conditions and use them as benchmarks for inefficient ones. In response to this issue, this study introduces a novel approach based on the SBM Network DEA model to enhance airport efficiency within a two-stage framework while accounting for undesirable outputs. By applying piecewise linear theory, the model assigns lower weight to excessive quantities of undesirable outputs, effectively distinguishing DMUs that generate fewer undesirable outputs from those producing higher amounts. Furthermore, this research offers a practical benchmarking strategy for inefficient airports, aiming to improve their efficiency while considering the priority of each stage.

In most production systems, the objective is to minimize input consumption while maximizing the generation of desirable outputs. However, many production processes also generate undesirable outputs as by-products of desirable outputs. In many real-world systems, undesirable outputs are inherently linked to the production of desirable outputs. Several studies in the Data Envelopment Analysis (DEA) literature have addressed performance evaluation of decision-making units (DMUs) in the presence of undesirable outputs. However, most existing models assume that desirable and undesirable outputs are independent, which may not reflect real production environments. The objective of this study is to model the dependency between desirable and undesirable outputs and to develop a novel DEA framework based on an axiomatic approach. Specifically, the classical axiom of output disposability is decomposed into two separate axioms: disposability of desirable outputs and disposability of undesirable outputs. Based on these axioms, a new production possibility set (PPS) is constructed. The proposed DEA model explicitly incorporates the dependency between desirable and undesirable outputs. A case study involving sensor monitoring systems is presented to demonstrate the applicability of the proposed approach.