Further Explore The Theory Of Dea Efficiency And Applications

The method of Data Envelopment Analysis(DEA) was put forward by Charnes A, Cooper W W and Rhodes earliest in 1978. It's a synthetical evaluation method which can be used to evaluate the relative efficiency of many Decision Making Units(DMU) which have a series of similar input and output objection. The two most classical DEA models are C²R model and C²GS² model. The former is used to evaluate the scale efficiency of DMUs, and the latter is used to evaluate the technical efficiency of DMUs. In this method to tell whether one DMU is DEA efficient or not is based on the frontier of real sample points, so it is called Data Envelopment Analysis. This method has strong economic background, therefore it can be broad used in many field and developed rapidly. Now it has become a very important analysis tool in many fields, such as manage science, systems engineering, decision-making analysis and evaluation technics.In this article we firstly introduced classical input oriented and output oriented C²R and C²GS² models and the input and output combinative model, then introduced these models to evaluate the relative efficiency of stocks. As long as. we know the daily closing price of some stocks needed to evaluating, we can calculate the expected profit rate and the risk to get the rate of each stock, as follows:in which: r_i(i = 1,2,…n) denotes the different observed value of profit rate; W₀ denotes the closing price on the first day of the period; W₁₁ denotes the closing price on the last day of the period; W₁₂ denotes the dividend of investing this stock in this period. σ denotes the risk to get the expected rate.To evaluate the relative efficiency of stocks, we regard the risk as input and the profit rate as output. Then we can use different DEA models to evaluate the relative efficiency of stocks.Finally we discussed the effect of the relative efficiency to primary DMUs when we increase one new DMU or get rid of one primary DMU, which is the foundation to put forward new conception of effective input.In the second chapter we discussed the case that if we increase the input or output of certain DMU, how to ascertain the corresponding output or input to get a new weaklyefficient DMU whose efficient value is 1. If the primary DMU isn't DEA efficient, we can use inverse DEA theory and multi-objective programming, alter the coefficient of the input or output to 1 to get the new DMU. If the primary DMU is weakly efficient, we can straight use the extended DEA model to get the new DMU.In the third chapter we put forward a new concept of efficient input, and give the correct method to ascertain the efficient input intervals of a known output. In last chapter we have known how to get a new weakly efficient DMU if the output of certain DMU were increased. Then we can use the model that contains non-Archimedes infinite small to get the projection of the DMU onto the efficient frontier, accordingly get a new relative efficient DMU. Then we discuss how to ascertain the efficient input intervals based on the new conception of efficient input. Because having gotten a new efficient DMU, we suppose the input of the new DMU as known proportional construction. Through the proof in this article we can respectively use the two below models to get the up-bound and low-bound ofefficient input intervals:max uTyn+l + avTx , - uT yy - a - 0(Er) - a > 0vTx0 = 17 >se^uf >eeT2(Gr)mm u yn^ + av' x r - u7 y j, - a =0 vTx; - uTy - a > 0 v'x0 = 1 v7 > se!,uT > ee\In which: (xo,yn+]) is the new efficient DMU relative to n+1 DMUs.Then: when the new output is yn+] , the corresponding efficient input interval is[Pxo,Qxo].In the forth chapter we discuss the problem to ascertain the efficient input intervals in two special cases. One case is that the component of output is interval data, that is:y. =[_y,,j>,] (/ = 1,2,---s). We can use the solution of last chapter to get the efficient inputintervals of yn+l = {yx,y1,—yt)T and yn+l = O\,y1, — y±)r. The up-bound of the efficient input interval of interval output is the up-bound of the efficient input interval of j>n+1, and the low-bound of the interval output is the low-bound of the efficient interval of yn+y. In the other case the input cannot be disposed of freely, for example some input denote the area of the factory that cannot be increased freely. Here we can split the input into two parts, one can be disposed of freely, the other cannot. The part that cannot be disposed of freely can be thought of having known, the emphases is on the first part. The correspondingmodels to ascertain the efficient input intervals of the first part are similar with the above.The fifth chapter is example analysis. We applied all the models introduced above to evaluate the relative efficiency of stocks. We choose 50 stocks at random, and find the closing price of every Monday from September 2004 to March 2005. We can calculate the expected profit rate and risk of each stock in this period without regard to dividend. Then we use different DEA models to analysis the relative efficiency of each stock. People should invest to these relative efficient stocks or some combination of these stocks. Then we introduced losing rate into another input to evaluate efficiency of each stocks. Finally we increase the output of certain stock, using the theory given in the second and third chapter to find a new efficient DMU and the relative efficient input intervals.