A Mathematical Programming Approach for Measuring Technical Efficiency in a Fuzzy Environment

A three stage approach is proposed to measure technical efficiency in a fuzzy environment. This approach uses the traditional data envelopment analysis framework and then merges concepts developed in fuzzy parametric programming (Carlsson and Korhonen, 1986). In the first stage, vague input and output variables are expressed in terms of their risk-free and impossible bounds and a membership function. This membership function represents the degree to which a production scenario is plausible. In the second stage, conventional efficiency measurement models (Banker, Charnes and Cooper, 1984; Deprins, Simar and Tulkens, 1984) are re-formulated in terms of the risk-free and impossible bounds and the membership function for each of the fuzzy input and output variables. In the third stage, technical efficiency scores are computed for different values of the membership function so as to identify uniquely sensitive decision making units. The approach is illustrated in the context of a preprint and packaging manufacturing line which inserts commercial pamphlets into newspapers.