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. Assuming 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.

کلیدواژه ها:

Stochastic Data envelopment analysis ، Dynamic programming ، random fuzzy variable ، Monte Carlo simulation ، Genetic algorithm