带有随机决策单元的广义数据包络分析方法  

Generalized Data Envelopment Analysis Method with Random Decision Making Units

作　　者：马生昀[1] 王钰鑫 马占新[2] 孙鹏哲[1] MA Sheng-yun;WANG Yu-xin;MA Zhan-xin;SUN Peng-zhe(School of Science,Inner Mongolia Agricultural University,Hohhot 010018,China;School of Economics and Management,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古农业大学理学院,内蒙古呼和浩特010018 [2]内蒙古大学经济管理学院,内蒙古呼和浩特010021

出　　处：《数学的实践与认识》2019年第24期76-82,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71661027)

摘　　要：广义DEA方法是一种相对效率评价方法,解决了决策单元相对于任意参考系(样本单元集)的效率比较问题.在实际中,有时评价标准是确定的,决策单元的生产具有不确定性,有必要在进行生产之前基于确定性样本单元对随机性决策单元进行相对效率评价.为了解决这个问题,研究样本单元为确定值,决策单元为随机变量的广义DEA模型,分别通过期望值和机会约束将随机模型转化为确定性规划,给出决策单元GEDEA有效和GCDEA有效的概念,GEDEA有效与多目标规划Pareto有效关系,以及利用移动因子对决策单元进行有效性排序方法.Generalized DEA method is a kind of relative efficiency evaluating met hod,which can solve the decision making unit's efficient comparison relative to any reference system(sample unit set).In practice,sometimes the evaluation criteria are deterministic and the productive process of decision making units has uncertainty,so it is necessary to evaluate the relative efficiency of the stochastic decision making unit based on the deterministic sample units before the beginning of productive process.For solving the problem,the generalized DEA model with random decision making units and deterministic sample units is researched in this paper.The stochastic programming is transformed into deterministic programming by expected value model and chance constrained programming,the definition of the GEDEA efficiency and GCDEA efficiency,the relationship between the GEDEA efficiency and Pareto efficiency of multiple objective programming and the efficiency sorting met hod of decision making units with mobile factor are given.

关 键 词：决策单元 样本单元 随机变量 期望值模型 机会约束规划 广义DEA方法 

分 类 号：O225[理学—运筹学与控制论]