Chance-constrained data envelopment analysis modeling with random-rough data

Data envelopment analysis (DEA) is a useful management tool for measuring the relative efficiency of decision making units (DMUs) which consumes multiple inputs to produce multiple out- puts. Although precise input and output data are fundamentally indispensable in classical DEA models, real-world problems often involve random and/or rough input and output data. We present a chance- constrained DEA model with random and rough (random-rough) input and output data and propose a deterministic equivalent model with quadratic constraints to solve the model. The main contributions of this paper are fourfold: (3.1) we propose a DEA model for problems characterized by random-rough variables; (3.2) we transform the proposed chance-constrained model with random-rough variables into a deterministic equivalent non-linear form that could be simplified as a deterministic model with quadratic constraints; (3.3) we perform sensitivity analysis to investigate the stability and robustness of the proposed model; and (3.4) we use a numerical example to demonstrate the feasibility and richness of the obtained solutions.