Imprecise data envelopment analysis for the two-stage process

The aggregate black-box approach of conventional Data Envelopment Analysis (DEA) limits its usefulness in situations where the observation is the result of independent decision making in sub-units (sub-DMUs), sequentially linked through processes or semi-finished products. The situation is commonly found in e.g supply chain management, health care provision and environmental management (waste water treatment). Alternative approaches for sublevel evaluations include two-stage or multi-stage models, where intermediate outputs or inputs are identified to span local production possibility spaces. However, the reliance upon numeric values for such intermediate inputs or outputs adds an additional difficulty that may lower the value of the assessment. In this paper, we present an approach for two-stage evaluation with interval data to resolve this problem. The results show that ignoring the interval quality of the data leads to distorted evaluations, both for the subunit and the system efficiency. The proposed method obtains an efficiency interval consisting in an upper and a lower bound for the system efficiency and the sub-DMU efficiency. In order to link two stages, we consider the interval intermediate measures that are outputs and inputs for the first stage and the second stage, respectively. The derived interval metric, along with its mean, provides a more informative basis for multi-stage evaluation in the presence of imprecise data. The ranks of DMUs and sub-DMUs are obtained based on their interval efficiencies.