A review of inverse data envelopment analysis: origins, development and future directions

Abstract Data envelopment analysis (DEA) is a widely used mathematical programming approach for assessing the efficiency of decision-making units (DMUs) in various sectors. Inverse DEA is a post-DEA sensitivity analysis approach developed initially for solving resource allocation. The main objective of inverse DEA is to determine the optimal quantity of inputs and/or outputs for each DMU under input and/or output perturbation (s), which would allow them to reach a given efficiency target. Since the early 2000s, inverse DEA has been extended theoretically and applied successfully in different areas including banking, energy, education, sustainability and supply chain management. In recent years, research has demonstrated the potential of inverse DEA for solving novel inverse problems, such as estimating merger gains, minimizing production pollution, optimizing business partnerships and more. This paper provides a comprehensive survey of the latest theoretical and practical advancements in inverse DEA while also highlighting potential areas for future research and development in this field. One such area is exploring the use of heuristic algorithms and optimization techniques in conjunction with inverse DEA models to address issues of infeasibility and nonlinearity. Moreover, applying inverse DEA to new sectors such as healthcare, agriculture and environmental and climate change issues holds great promise for future research. Overall, this paper sets the stage for further advancements in this promising approach.