An Axiomatic DEA Model for Performance Evaluation of Wireless Sensor Networks with Dependent Desirable and Undesirable Outputs

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.