A new two-stage Stackelberg fuzzy data envelopment analysis model

Data Envelopment Analysis (DEA) is a widely used mathematical programming approach for evaluating the relative efficiency of Decision Making Units (DMUs). Conventional DEA methods treat DMUs as “black boxes”, focusing entirely on their relative efficiencies. We propose an efficient two-stage fuzzy DEA model to calculate the efficiency scores for a DMU and its sub-DMUs. We use the Stackelberg (leader–follower) game theory approach to prioritize and sequentially decompose the efficiency score of the DMU into a set of efficiency scores for its sub-DMUs. The proposed models are linear and independent of the α-cut variables. The linear feature allows for a quick identification of the global optimum solution and the α-cut independency feature allows for a significant reduction in the computational efforts. Monte Carlo simulation is used to discriminately rank the efficiencies in the proposed method. We also present a case study to exhibit the efficacy of the procedures and to demonstrate the applicability of the proposed method to a two-stage performance evaluation problem in the banking industry.     

Developing distinctive two-stage data envelopment analysis models: An application in evaluating the sustainability of supply chain management

Sustainable supply chain management (SSCM) has received much attention from scholars and practitioners in the past years. It has become a method for simultaneous improvement of economic, social, and environmental performance. SSCM evaluation, therefore, is a significant duty for any types of organizations. Among evaluation methods, data envelopment analysis (DEA) seems to be an appropriate technique for assessment of the SSCM. One of the uses of DEA is to evaluate the efficiency of two-stage processes, where all the outputs from the first stage are intermediate measures that are considered as the inputs to the second stage. The resulting two-stage DEA models assess both the overall efficiency score of the whole process and each of the individual stages. Notwithstanding, there are major weaknesses in the previous extensions of two-stage DEA models. Firstly, a challenging issue is that suggestions for improvements are offered only for input and output measures, and intermediate measures are neglected. Although, some extensions for network structures take into account intermediate measures, they arbitrarily assign an input or output role for the measures, thus in optimal solution for inefficient DMUs, this measures are forced to respectively take a lower or upper amount. Secondly, the efficiency scores are calculated based on inputs and outputs. That is, while the models consider these measures by corresponding constraints, the intermediate measures are not included in the objective function, or incorrectly assign an input or output role. Thirdly, in some cases, the former developments specify points on the efficient frontier only for inefficient stages, while for a network which is entirely inefficient such points are also required. Moreover, the organization (which in DEA terminology is named decision making unit) is supposed to be divided into two autonomous departments. It means that the performance of one department is quite unrelated to another department, while from the organizational perspective this is called into the question. To overcome these shortcomings, in this paper, innovative models are proposed. The proposed ideas are used for evaluating the sustainability of supply chains in resin producing companies.     

A two-stage data envelopment analysis model for measuring performance in three-level supply chains

Data Envelopment Analysis (DEA) has been widely used to evaluate supply chain performances. In conventional DEA, supply chains are represented as black boxes where only the initial inputs and final outputs are considered to measure their efficiency. However, an integrated model measuring both the efficiency of the entire supply chain and that of all its components at all levels is essential for a comprehensive evaluation. This study presents a two-stage DEA method to evaluate the performance of a three-level supply chain including suppliers, manufacturers and distributors. The proposed model can be used both under the constant returns to scale and the variable returns to scale assumptions and can be easily implemented for comprehensive analysis of multi-level supply chains. We present a numerical example to demonstrate applicability of the proposed model and exhibit the efficacy and effectiveness of the proposed algorithms and procedures. In particular, the numerical results demonstrate that the entire supply chain is “comprehensively” efficient only if efficient supplier–manufacturer and manufacturer–distributor relationships are established.     

谐波齿轮传动中柔轮载荷分布规律分析研究

提出了关于谐波齿轮传动装置中,柔轮啮合区内载荷分布规律的实验与分析新方法。包括三部分：首先,在载荷状态下,通过安装在刚轮径向方向上三个可装、的活齿,测得大量的啮合数据;其次,通过数学统计方法获得啮合区内切向力Ft和径向力Fr的实验曲线;最后,应用函数逼近法获得载荷区内载荷分布方程。     

Sustainable cultivation location optimization of the Jatropha curcas L. under uncertainty: A unified fuzzy data envelopment analysis approach

Second-generation biodiesel production from non-edible high oil content feedstocks such as Jutropha curcas L. (JCL) has been found as a suitable alternative for the fossil diesel which is mostly consumed in transportation sector. Second-generation biodiesel eliminates the drawbacks of the first generation such as food-energy challenge and provides opportunity for rural development. Location optimization of JCL plays a vital role in the success and prosperity of JCL projects. In this study, sustainability and ecological indicators are defined to evaluate the performance and efficiency of the candidate locations for JCL cultivation under uncertainty. The values of defined indicators are highly tainted with uncertainty in real-life situation. To optimize the candidate locations for JCL cultivation under uncertainty, an efficient Unified Fuzzy Data Envelopment Analysis (UFDEA) model is developed. The proposed UFDEA model is verified and validated through investigating a real case study in Iran and the associated results are compared to those obtained by the crisp Unified Data Envelopment Analysis model under different levels of uncertainty. The obtained results show the applicability of the proposed UFDEA model in selecting suitable areas for JCL cultivation under uncertainty.