| Data envelopment analysis(DEA)is a cross field of operations research,management science and mathematical economics.The traditional DEA method is to evaluate the relative efficiency of decision making units based on the effective frontier,it is an evaluation method based on self-evaluation system.The efficiency values of effective decision making units in the traditional DEA model are all equal,so traditional DEA model can not distinguish effective decision making units.However,the super efficiency DEA method can distinguish effective decision making units to some extent.On the other hand,in many problems in reality,the“reference set” chosen in the evaluation may be units or standards outside the decision making units.At this time,the traditional DEA method can not evaluate these decision making units.However,the generalized DEA method based on partial order set theory can solve the above problem.In this paper,the main work is to propose the projection concept of effective decision making unit in super efficiency DEA model,and research the corresponding properties of weight-restricted super efficiency DEA models at the same time.In the generalized output-oriented DEA model,the efficiency measurement methods of effective decision making units are given,when the model has no feasible solution and the efficiency value of some decision making units is overestimated.At the same time,in the generalized DEA model,a modified generalized DEA model allowing the inverse adjustment of indicators is proposed.Finally,a new method for evaluating the effectiveness of this type of unit is given for the decision making unit with different scale cross attributes.The main results obtained are:1.The concept of super efficiency projection of effective decision making unit is given in the input-oriented super efficiency DEA model.The super efficiency projection not only gives ineffective reasons of ineffective decision making units and the direction of improvement,the degree of improvement,but also gives the advantages of effective decision making units.The relationship between input-oriented traditional DEA model and input-oriented super efficiency DEA model as well as the shortage of input-oriented super efficiency DEA method are discussed and corresponding methods are given.For example,these problems are solved that how to measure the efficiency value of decision making units when input-oriented super efficiency DEA model has no feasible solution and give the reason why efficiency value of some decision making units is overestimated.2.The concept of super efficiency projection of effective decision making unit is given in the output-oriented super efficiency DEA model.The super efficiency projection not only gives ineffective reasons of ineffective decision making units and the direction of improvement,the degree of improvement,but also gives the advantages of effective decision making units.The relationship between output-oriented traditional DEA model and output-oriented super efficiency DEA model as well as the shortage of output-oriented super efficiency DEA method are discussed and corresponding methods are given.For example,these problems are solved that how to measure the efficiency value of decision making units when output-oriented super efficiency DEA model has no feasible solution and give the reason why efficiency value of some decision making units is overestimated.3.Considering the preferences of decision makers in super efficiency DEA model,input-oriented weight-restricted super efficiency DEA model is given,and the concept of super efficiency projection of decision making unit is proposed.Super efficiency projection can give more meaningful information to the effective decision making units.The relationship between optimal objective function value of the input-oriented weight-restricted super efficiency DEA model and the effectiveness of decision making unit is discussed.And then,the related properties of this model and its relationship with other super efficiency DEA models are studied.Finally,the relationship between the projection of input-oriented weight-restricted super efficiency DEA model and non-dominated solution of multi-objective programming is discussed.4.Output-oriented weight-restricted super efficiency DEA model is given,and the concept of super efficiency projection of decision making unit is proposed.Super efficiency projection can give more meaningful information to the effective decision making units.The relationship between optimal objective function value of the output-oriented weight-restricted super efficiency DEA model and the effectiveness of decision making unit is discussed.And then,the related properties of this model and its relationship with other super efficiency DEA models are studied.Finally,the relationship between the projection of output-oriented weight-restricted super efficiency DEA model and non-dominated solution of multi-objective programming is discussed.5.The following problems exist in the generalized output-oriented DEA model:(1)The efficiency value of some decision making units may be overestimated;(2)Similar to super efficiency DEA model,the efficiency value of some decision making units can not be characterized numerically.That is,the model has no feasible solution.For the above situation,the corresponding solutions are given.6.The DEA methods usually research the problems to minimize the inputs without reducing outputs(input-oriented DEA model)or to maximize the outputs without increasing inputs(output-oriented DEA model).In this paper,a generalized DEA model allowing inverse adjustment of indicators is proposed based on the input-oriented generalized DEA model and the output-oriented generalized DEA model.Meanwhile,the efficiency of original generalized DEA model and the generalized DEA model allowing inverse adjustment of indicators is discussed.However,for producers there is an upper bound of tolerance to adjusting output indicators or increasing input indicators.Adding the adjusting upper bound constraint conditions in the generalized DEA model allowing inverse adjustment of indicators,a modified generalized DEA model with adjusting upper bound constraint condition is obtained.7.Whether it is traditional DEA model or generalized DEA model based on partial ordering set theory,they are evaluate the same decision making units.However,sometimes the decision making units have the different scale returns cross attribute.At this time,the traditional DEA methods have encountered difficulties in solving such problems.In order to evaluate such decision making units,a new method for evaluating the effectiveness of this type of unit is given for the decision making unit with different scale returns cross attribute. |
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