| Data Envelopment Analysis(DEA)is a mathematical programming method with multiple inputs and multiple outputs,evaluating the relative efficiency of peer decision making units(DMUs)and identifying the best practices.An important area of development in recent years has been that devoted to applications wherein DMUs represent network processes.One of fundamental two-stage network DEA model is the simplest two-stage series DEA model,which has been widely studied both in theories and applications.This paper studies two theoretical issues in cooperative and Stackelberg game DEA model:(1)the efficiency decomposition of cooperative game model;(2)how to decide which stage is the leader when the leader stage is not clear for analyst in two-stage process.Then,we will apply the Stackelberg game DEA model proposed in this paper to reveal the company’s sustainability commitment.First,this paper studies the efficiency decomposition of cooperative game model.The purpose of efficiency decomposition is to decompose the overall efficiency fairly and reasonably,and achieve an unique stage efficiency.In this current study we redefine the“fairness”in efficiency decomposition,and develop a ranking-based model.For the purpose of comparison,we simplify the efficiency decomposition in traditional cooperative game model.We found an interesting result that the stage efficiencies are the totally same led by the method of efficiency decomposition in cooperative game model and Nash bargaining game model.In a particular case,our proposed model includes those two types of methods as a special case.Second,in the cases that the leader stage is not clear,we introduce an augmented Tchebycheff matric and ideal point model from bi-objective program,and propose a new model under the assumption of variable weights for the two stages.This new proposed model is a non-linear program.We proved that the optimal solution of the new model is leader-follower solution,only determined by the difference between the upper bound and lower bound of stage efficiency.If efficiency deviation of the first stage is greater than the second stage,then the first stage is the leader,vise versa.Intuitively,the stage which has the higher stage efficiency score should be the leader.However,our developed model demonstrates that is a misunderstanding.Last,based on the proposed model for the cases of unclear leader stage in two-stage process,we develop a new approach for the two-stage process included industrial design process and bio design process to reveal the companies’ sustainable commitment.On the purpose of illustrating the value of our new model,we use key engineering specifications,product attributes and vehicle emission data published by U.S Environmental Protection Agency in 2013 to evaluate and reveal the companies’product design strategy.Based upon a complete testing result,our model indicates that only 100 companies in total 940 companies take a positive product design strategy。Our model shows a shocked result,which is most companies still take reactive product design strategy even though they claimed a sustainable commitment in product design process. |
