Production Possibility Frontier and Stochastic Programming
نویسنده
چکیده
Data Envelopment Analysis (DEA) is the methodology for evaluating the relative productive efficiency of decision making units (DMUs) that produce multiple-outputs using multiple-inputs. DEA was proposed for the first time in 1957 by Farrell; nonetheless, the wide usage of this method begun with its generalization and the linear programming formulation which is due to Charnes et al. (1978) (for more information on the DEA history see, e.g. Cooper et al. (2004)). The main advantages of this approach is that DEA is completely non-parametric, i.e. no explicit form of production function is necessary. Therefore, there is a host of applications in such a distant areas beginning with banking industry, through public economics to agricultural economics. However, the DEA approach does not count for any uncertainty or noise in data, and this has been often cause for criticism. There were several attempts to improve this disadvantage. In 1993, Land et al. (1993) have taken the Banker et al. model (1984) and transform it in a such way that every single constraint must hold only with probability 1−α. This approach have used separated chance constraints, on the opposite, the concept of Huang and Li (2001) uses the joint probability of all constraints together, and this probability should exceed 1− α. In the following section we would introduce DEA more deeply, after that we show stochastic extensions, and we sum up previous attacks. Later we state two theorems and with its help we introduce two new criteria for efficiency in stochastic DEA.
منابع مشابه
Comparative Analysis of Stochastic Frontier Partially non-parametric and Stochastic Frontier Parametric Methods Case Study: Measuring Cost Efficiency in Wheat Production in Iran
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