A Framework for Efficiency Analysis and Resource Allocation Using Inverse DEA under Uncertainty

Abstract

Inverse Data Envelopment Analysis (Inv-DEA) determines the input increase required for a Decision-Making Unit (DMU) to increase its outputs, or the additional outputs attainable when inputs rise to a predetermined level, all while maintaining current efficiency. Traditional Inv-DEA models assume precise (crisp) data. However, real-world applications often involve imprecise inputs and outputs due to inherent complexity and uncertainty. This study introduces a methodological framework that integrates uncertainty theory based on belief degrees into both input-oriented and output-oriented Inv-DEA models. The proposed models are applied to resource allocation problems. We employ uncertain programming techniques to convert the resulting nonlinear uncertain Inv-DEA models into solvable deterministic linear programs. This transformation is achieved through two key approaches: For models with uncertain variables in the objective function, we use the expected value criterion to optimize average performance. For models with uncertain constraints, we apply chance-constrained programming. This framework effectively addresses essential uncertainty, enabling computational solution via standard linear programming techniques. To validate the practical applicability and effectiveness of the proposed inverse DEA methodology for resource allocation, we conduct an efficiency evaluation using a numerical example.