A New Dynamic Random Fuzzy DEA Model to Predict Performance of Decision Making Units

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiency of decision making units (DMUs) which ‮consume the same types of inputs and producing the same types of outputs. Believing that future planning and predicting the ‮efficiency are very important for DMUs, this paper first presents a new dynamic random fuzzy DEA model (DRF-DEA) with ‮common weights (using multi objective DEA approach) to predict the efficiency of DMUs under mean chance constraints and ‮expected values of the objective functions. In the initial proposed‏ ‏DRF-DEA model, the inputs and outputs are assumed to be ‮characterized by random triangular fuzzy variables with normal distribution, in which data are changing sequentially. Under this ‮assumption, the solution process is very complex. So we then convert the initial proposed DRF-DEA model to its equivalent multi-‮objective stochastic programming, in which the constraints contain the standard normal distribution functions, and the objective ‮functions are the expected values of functions of normal random variables. In order to improve in computational time, we then ‮convert the equivalent multi-objective stochastic model to one objective stochastic model with using fuzzy multiple objectives ‮programming approach. To solve it, we design a new hybrid algorithm by integrating Monte Carlo (MC) simulation and Genetic ‮Algorithm (GA). Since no benchmark is available in the literature, one practical example will be presented. The computational results ‮show that our hybrid algorithm outperforms the hybrid GA algorithm which was proposed by Qin and Liu (2010) in terms of ‮runtime and solution quality. ‮