DEA models with random inputs and outputs

Data Envelopment Analysis (DEA) models are general tool for evaluation the relative efficiency of production units described by multiple inputs and outputs. The standard DEA models are based Oil deterministic inputs and outputs. The paper formulates basic DEA models Supposing that inputs and outputs are random variables with given continuous probabilistic distributions. Under this assumption the efficiency scores for evaluated production units are random variables. The aim of the paper is to try to describe the properties of the random efficiency scores by means of Monte Carlo experiments. The experiments are realised within the MS Excel environment together with LINGO optimisation solver and Crystal Ball add-in application for Monte Carlo analysis in spreadsheets. The computations were realised oil the real set of almost 200 bank branches of one of the Czech commercial banks. The paper shows that the simulation experiments can offer more information that standard linear programming approaches, e.g. by this way it is possible to define new concepts of super-efficiency in DEA. Their disadvantage is the time consumption for calculations connected with simulation compared to standard optimisation approaches. Nevertheless, the time consumption is compensated by possibilities to consider different probabilistic distributions for inputs and outputs and available detailed probabilistic characteristics of efficiency scores. The experiments show that this approach can be an appropriate instrument for analysing DEA problems with imprecise data and can produce interesting results in comparison with other approaches.