Efficiency Evaluation And Ranking For Decision Making Units Of DEA Based On SMAA

Data envelopment analysis(DEA)is a widely used non-parametric nonparametric mathematical programming method to measure the relative efficiency and ranking of decision making units(DMUs)which consume multiple inputs to produce multiple outputs.DEA has gradually become a very important analytical tool in management science,systems engineering,and economics.However,there are still some problems in the traditional DEA method.While traditional DEA models regard DMUs as "black boxes",researches in recent years have gradually shifted their attentions from a concern of overall efficiency to the internal structure of DMUs,named as network DEA research.Owing to the uncertain environment,the observed input and output values in real-world problems are often imprecise and vague.To address the network DEA with uncertain measures,this study introduces the stochastic multicriteria acceptability analysis(SMAA-2)method.In Chapter 3,taking a two-stage supply chain system as an example,a two-stage SMAA-DEA model is proposed to evaluate the efficiency and ranking of supply chains with stochastic measures.Two stochastic efficiency measures are defined for efficiency evaluation in the model:maximum eff-iciency and average efficiency.The maximum efficiency is the best efficiency score based the optimistic criterion.The average efficiency is the expected efficiency score based on the average criterion.In addition,the model provides rank acceptability and holistic acceptability index for the DMUs ranking.The proposed model is verified by a numerical analysis.Besides,while calculating DMUs' efficiencies in traditional DEA models each DMU chooses the weight that is most beneficial to itself,the DEA common weight models assesses all DMUs with a common set of input and output weights,in which the evaluation results are deemed more discriminative and objective.In Chapter 4,this study considers the satisfaction degree of a DMU to its ranking position and proposes new DEA common weight models based on maximizing the minimum satisfaction or maximizing the average satisfaction.The model first uses the SMAA to obtain the acceptability index of each DMU in each ranking position,and then explores the feasible weight space to find the weight which maximizes the minimum or average satisfaction as a set of common weight.After that,the efficiency scores of all DMUs and rankings are calculated using the derived DEA common weights.The two-stage SMAA-DEA model and the new DEA common weight model proposed in this study are based on the stochastic measures and satisfaction of DMUs,which expands the generality of the DEA method.Research results show that the proposed method framework can help decision makers in scientific management and has important application value in terms of operations and decision making.Contributions of this study are as follow:1)It extends two-stage DEA models to handle uncertain or imprecise inputs,intermediate measures and outputs.2)The two-stage SMAA-DEA model allows for variable process weights and does not need any prior preference information on processes.3)The new common weight model and algorithm based on DMU satisfaction are proposed.