No abstract

Data envelopment analysis (DEA) is a non-parametric approach for measuring and evaluating the relative efficiencies of a set of entities with common crisp inputs and outputs. Whereas crisp input-output data are required in the traditional DEA evaluation process, the observed input-output data in real-world performance evaluation problems are quite often imprecise or vague. The impreciseness and vagueness related to the input-output data in DEA can be represented by fuzzy variables. The purpose of this paper is three-fold. First, the current study introduces a non-deterministic chance constrained DEA model, which solves the Charnes, Cooper and Rhodes (CCR) model by treating the input-output data as bifuzzy variables which are fuzzy variables with fuzzy parameters. Second, by assuming that decision making units operate in a bifuzzy environment, the study derives a deterministic model equivalent to the chance constrained model. Finally, two numerical examples are presented to demonstrate the applicability of the proposed framework.

Recently Leleu [A linear programming framework for free disposal hull (FDH) technologies and cost functions: Primal and dual models] presented a linear model for assessing the FDH-cost function with various returns to scale assumptions. He stated that economic inefficiency can be computed as the ratio of the observed cost to the minimum cost and, as usual, the allocative inefficiency is computed as the ratio between the economic and the technical inefficiencies. In this paper, we propose a modified model with various returns to scale assumptions that has fewer constraints and variables than Leleu's model and obtains the FDH-cost efficiency directly. Reducing nm constraints and nm variables, where n is the number of DMUs and m is the number of inputs, leads to the computational advantage of our model over that of Leleu.