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

Subject Areas : Tectonostratigraphy

Ali Yaghoubi ¹ , Maghsoud Amiri ² , Azamdokht Safi Samghabadi ³

1 - Department of Industrial Engineering, Faculty of Engineering, Payam-e-Noor University, Tehran, Iran
2 - Department of Industrial Management, Allameh Tabatabaei University, Tehran, Iran
3 - Department of Industrial Engineering, Faculty of Engineering, Payam-e-Noor University, Tehran, Iran

Received: 2014-10-02 Accepted : 2015-06-26 Published : 2016-09-25

Keywords: Dynamic programming, Genetic Algorithm, Stochastic Data envelopment analysis, random fuzzy variable, Monte Carlo simulation,

Abstract :

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. ‎