In the ever-changing today’s society, talent has increasingly become the key topic. As the cradle of talent training, colleges and universities also attract people’s focus of attention. Colleges and universities shoulder the responsibilities for conveying fresh blood for society and making basic research. The development of colleges is closely related to the development of country. So many charitable organizations dedicate to donations to improve educational performance.

Zhang and Guo [1] proposed a new model to measure the relative efficiency of the assessed DMU (Decision Making Unit) through analyzing its disadvantages based on DEA model and compare the DMUs’ efficiency rates and give their order. Li and Zuo [2] established the optimal investment bilevel programming models of prior development colleges as well as that of indiscriminate investment in all colleges and given the optimal investment scheme of both upper and lower level. Cai [3] introduced the higher education evaluation model of investment benefit based on DEA, collected a university’s data according to the time series and conducted empirical research investment benefit from 2001 to 2009. Ma [4] analyzed Inner Mongolian University’s scientific and technological input-output efficiency quantitatively applying generalized data envelopment analysis method. Gan [5] built input-output index of the Graduate School, screened index based on the factor analysis and DEA methods to analysis panel data. Juan [6] proposed a series of DEA models to accommodate settings where non- homogenous sub-units operate in parallel network structures with intermediate measures or links. Chang [7] developed a new type of DEA model referred to as intertemporal DEA model that can be used to fully measure a firm’s efficiency by explicitly considering its key inputs and outputs involving the past-present-future time span. Fuentes [8] analyzed the productivity growth of the SUMA tax offices located in Spain evolved between 2004 and 2006 by using Malmquist Index based on Data Envelopment Analysis (DEA) models. Merkert [9] applied two-stage Data Envelopment Analysis (DEA) models to estimate a single efficiency measure that combines the potentially conflicting indicators of perceived service quality and profitable for the airport context. Li [10] re- estimate the TFEE (Total-Factor Energy Efficiency) using an improved DEA model, which combines the super- efficiency and sequential DEA models to avoid “discriminating power problem” and “technical regress”, and then used it to calculated the TEI (target for energy intensity). Adel [11] proposed an alternative DEA model for centrally imposed resource or output reduction across the references set and determined the amount of input and output reduction needed for each DMU to increase the efficiency score of all the DMUs.

The Goodgrant Foundation is a charitable organization that wants to improve educational performance of undergraduates attending colleges and universities in the US. So the Foundation plans to contribute 50 million money for a suitable team of schools per year under the condition of avoiding repeated other large grant organizations’ investment.

To do this, two questions are solved for the Goodgrant Foundation: how to choose a suitable team of schools and how to allocate the investment. In order to solve the two questions, the DEA model is established to determine an optimal investment strategy, including the selection of schools and determination of investment amount. In this process, DEAP software and MATLAB software are used to solve the questions we face.

If the efficiency remains unchanged, but the inputs increase (), how much should the outputs of the increase ()? To formulate the question, the inverse DEA model is established to carry on the sensitivity analysis. The inverse DEA model is as follows:

Notes: crste is the Overall efficiency; vrste is the True technical efficiency; scale is the Scale efficiency; rts is the Scale Report, irs is increase, - is constant; drs is decrease.

Then we can select according to the specific circumstances.

To deal with the investment strategy problem for the Goodgrant Foundation, the DEA model is used to determine an optimal investment strategy in this paper. And two questions are solved about how to choose a suitable team of schools and how to allocate the investment. The CCR model is used to rank schools which use efficiency from DEAP 2.1 in order to solve the first question. Then, the resource allocation model is established to allocate investment. Finally, the optimal investment strategy is obtained for Goodgrant Foundation.

But in the analysis process, data processing may have tolerance, because the initial data have so many indexes and we have obtained part of indexes of every school. Because only the representative indexes are considered in this paper, some important indexes might be ignored; so some errors might appear in the result of data process- ing. And in model assumptions, the results will have a certain impact without considering some variables such as investment cycle. In the future, these factors in the improved model are investigated.

This work was supported by the National Natural Science Foundation of China (71540028, F012408), and Major Research Project of Beijing Wuzi University. Beijing Key Laboratory (NO: BZ0211), Beijing Intelligent Logistics System Collaborative Innovation Center.

Yulei Zhang,Shuai Zhang,Xinxin Zhang,Zhenping Li, (2016) The Optimal Investment Strategy Based on the DEA Model. Open Journal of Modelling and Simulation,04,46-54. doi: 10.4236/ojmsi.2016.42006

clear;

formatshortg

X = load('c:\x.txt');

Y = load('c:\y.txt');

n = size(X',1); m = size(X,1); s = size(Y,1);

A = [-X' Y'];

b = zeros (n, 1);

LB = zeros(m + s, 1); UB = [];

for i = 1:n;

f = [zeros (1, m) -Y(:,i)'];

Aeq = [X(:,i)' zeros(1,s)]; beq = 1;

w(:,i) = LINPROG(f, A, b, Aeq, beq, LB, UB);

E(i, i) = Y(:,i)'*w(m + 1:m + s,i);

end

Omega = w(1:m,:)

mu = w(m + 1:m + s,:)