Research On Data Envelopment Analysis Models For Groups

As the collectivization becomes the main way of business expansion and industrial distribution,groups exert more influence on development of the economy and society.The accurate evualation of groups' condition and secientific decision are important to the normal and steady operation of groups,as well as the sustainable and healthy development of economy and society.Data envelopment analysis(DEA),a data-driven decision-making tool,has made a series of remarkable achievements in decision analysis for individuals.A group is composed of multiple homogeneous individuals which are interrelated and mutually influenced.Then,the group must share several characteristics of its attached individuals,and methods applying to individuals may also be suitable for the group in some degree.Hence,this thesis analyzes the characteristics and needs of groups,then proposes several DEA models for evaluation and decision of groups,based on the existing models for individuals.Three issues are discussed in this thesis.The first issue is the performance evaluation of groups based on cross-evaluation.This study considiers two kinds of relationships between the performance of a group and its attached individuals,based on the analysis of reality.When a single individual has limited influence on the whole group,the group performance is the comprehensive reflection of the performance of all individuals.When each individual may exert the great impact on the whole group,the group performance is determined by the individual performing worst.According to the two mentioned kinds of relationships,this study defines the group efficiency based on the average criterion and the worst criterion,respectively.For each definition,the self-evaluation and cross-evaluation models are proposed to evaluate the group efficiency.The group efficiency based on the average criterion is defined as the average of all individual efficiencies.The group efficiency based on the worst criterion is equal to the minimum of all individual efficiencies.In addition,models ensure that all individuals belonging to the same group use a common set of weights for inputs and outputs,which reflects the unified management of all individuals in a group.The second issue is the performance evaluation of units in group based on double frontiers.According to the competitive attributes of units within the group,this study considers that the performance of the unit in a group should be the comprehensive reflection of its gap with the best performers and superiority over the worst performers.Fristly,the study gives the general directional distance functions to evaluate efficiencies based on the best and worst frontiers,respectively.Secondly,cross-evaluation models are developed based on directional distance functions.This study considers the cross-efficiency based on the best frontier as the efficiency loss,and the cross-efficiency based on the worst frontier as the efficiency gain.Then,the loss aversion principle of prospect theory is introduced to aggregate the two cross-efficnecies,and obtain a composite efficiency indicator.The application of the prospect theory reflects the competitive strategy that each unit catching up first in real groups.The third issue is the intra-group allocation of resources considering the group objective and individual preferences.Firstly,according to the idea of a related study,this research extends the concept of cross-evaluation to the resource allocation,and establishes an allocation model which comprehensively considers the individual preferences of all units in the group.Since the central unit of the group,as the final determinant and executor of resource allocation,is more likely to prioritize the group objective rather than the preferences of individuals,maximization of the group objective is added to the established model as a prerequisite,then,a new model which considers both the group objective and individual preferences is obtained.The model realizes the rational unity of effectiveness and fairness in resource allocation.Lastly,study extends the model for resource allocation in centralized procurement to the resource allocation in independent procurement,and analyzes the key factor which determines the selection of two procurement patterns.There are three main contributions of this thesis.First,this thesis gives specific definition of the group efficiency and proposes evaluation models,based on the analysis of the relationship between group and its attached individuals in reality.Second,envelopment models are successfully applied in cross-evaluation by chaging projective frontiers,based on the evaluation principle of directional distance functions.Third,extending the concept of cross to resource allocation,and really obtaining the fairness of allocation.