Stochastic network DEA models for two-stage systems under the centralized control organization mechanism

A Novel Stochastic Two-Stage DEA Model for Evaluating Industrial Production and Waste Gas Treatment Systems

“…First, more complex network structures, such as a two-stage model with shared inputs and common outputs, should be extended to the sentiment of random numbers. Second, the present paper follows the practice in Zhou et al [44] and sets α ≤ 0.5 in efficiency calculation. However, the value of α will no longer be limited to smaller than 0.5 in some of the other research objects.…”

“…In model (1), and are random variables, and are intensity vectors corresponding to sub-stage 1 and sub-stage 2. Constraints and represent the weak Following the practice in Zhou et al [44] and Bi et al [47], the present paper ensures that the intermediate outputs used in sub-stage 2 are not greater than the output in sub-stage1. That is, n j=1 λ 1 j U tj ≥ n j=1 λ 2 j U tj .…”

“…In most cases, the risk is limited, especially for decision-makers of city and provincial governments. Therefore, this paper follows the practice of Zhou et al [44] and lets the value of α not exceed 0.5.…”

“…Secondly, although the above studies consider the undesirable output in data collection, they ignore the characteristics of undesirable output, such as weak disposability [42], which is widely used in environmental efficiency evaluation [43]. Based on a centralized control organization mechanism, Zhou et al [44] model random variables based on a simple two-stage structure, in which all the outputs of the first stage are used as the only inputs of the second stage. However, the structure of production process in real-life world is too complex to evaluate by using existing stochastic two-stage DEA model, such as Song et al [45], Chu et al [46] and Bi et al [47].…”

“…However, the structure of production process in real-life world is too complex to evaluate by using existing stochastic two-stage DEA model, such as Song et al [45], Chu et al [46] and Bi et al [47]. The stochastic two-stage DEA of Zhou et al [44] is also a radial model. The main contribution of this paper lies in two aspects.…”