An interval efficiency analysis with dual-role factors

Data envelopment analysis (DEA) is a data-driven and benchmarking tool for evaluating the relative efficiency of production units with multiple outputs and inputs. Conventional DEA models are based on a production system by converting inputs to outputs using input-transformation-output processes. However, in some situations, it is inescapable to think of some assessment factors, referred to as dual-role factors, which can play simultaneously input and output roles in DEA. The observed data are often assumed to be precise although it needs to consider uncertainty as an inherent part of most real-world applications. Dealing with imprecise data is a perpetual challenge in DEA that can be treated by presenting the interval data. This paper develops an imprecise DEA approach with dual-role factors based on revised production possibility sets. The resulting models are a pair of mixed binary linear programming problems that yield the possible relative efficiencies in the form of intervals. In addition, a procedure is presented to assign the optimal designation to a dual-role factor and specify whether the dual-role factor is a nondiscretionary input or output. Given the interval efficiencies, the production units are categorized into the efficient and inefficient sets. Beyond the dichotomized classification, a practical ranking approach is also adopted to achieve incremental discrimination through evaluation analysis. Finally, an application to third-party reverse logistics providers is studied to illustrate the efficacy and applicability of the proposed approach.