Input-output benefit evaluation of major projects based on DEA

: The data envelopment analysis DEA method is used to calculate the input-output ratio of some major projects in terms of annual funds, equipment, fixed assets, personnel, etc., and evaluate the comprehensive benefits and economies of scale of some projects. The analysis results show that there is redundancy in the input of most projects, so the input value can be further optimized. The optimal value and saving value of different input types are calculated for specific projects. This model provides technical support for future major project planning of military construction


INTRODUCTION
Entering the new stage of the new century, the situation and tasks faced by the PLA have undergone profound changes. The increase in our national defense expenditure is in harmony with the level of economic development, and our country is accelerating the military reform, so it is necessary to support many national defense projects to further advance the strategy of strengthening the army in science and technology and strengthening the army with talents. With large scale, long construction period and high investment, major projects in the construction of the Chinese People's Liberation Army (PLA) occupy an important proportion in the investment of military expenditure, personnel and equipment, etc. Therefore, the calculation of the input-output ratio of major projects is helpful for the PLA to formulate reasonable project investment policies, and is of great significance for controlling the macro-control of project investment and strengthening the management of the PLA. It is a complex systematic project to improve the evaluation ability of the input-output of major projects. Efficient, reasonable and accurate calculation model is the key to improve the inputoutput of PLA [1][2][3][4] .
The input-output ratio model of major projects takes the implementation process and results of major projects as the evaluation object, and realizes the input-output ratio analysis of the comprehensive benefits of major projects by analyzing the factors that affect and reflect the funds, equipment, quantity and expected benefits of major projects. This model mainly carries out quantitative evaluation and display of the input-output ratio of major projects according to the investment and input of annual funds, equipment, fixed assets and personnel of major projects, and provides comprehensive benefit assessment [5][6][7] . It is of great significance to provide technical support for major project planning to better serve military construction in the coming period.
Data enveloping analysis is an efficiency evaluation method proposed by the famous American operations research scientist A. Charnes and W-W. Cooper based on the concept of 'relative efficiency evaluation' [8] . This method extends the concept of single input and single output to quantitative evaluation of effectiveness of multiinput and multi-output Decision making Unit (DMU), and has the characteristics of objectivity, simple calculation and small error. Since the establishment of CZR model, the first DEA model, in 1978, DEA method has made rapid development in both theoretical research and practical application, and has become a common and important analysis tool and research means in the fields of operations research, management, systems science and mathematical economics [9][10][11][12] .
Set ℎ � � �′� � �′� � as the efficiency evaluation index of the �ℎ decision making unit � to evaluate the efficiency of � . The weight coefficient , can always be selected. Under the condition that the efficiency evaluation index of each � does not exceed 1, ℎ � is maximized, and the following optimization model--C 2 R model is obtained: By Charess-Cooper transformation, the fractional programming form of C 2 R model is equivalent to linear programming form： Its dual programming model is： (6) SE-DEA model: Introduce a new relaxation variable, linear programming model with non-Archimedean infinitesimal and relaxation variable super efficiency Data Enveloping Where is a non-Archimedean infinite small quantity, a number greater than zero but less than any positive number, the general value is 10 -6 , � � � �,�,���, � is the optimal solution; � , � are the input-output relaxation vectors respectively.
Effectiveness analysis of the model： Set the optimal solution for � , �� , �� , � ，then： (1) If � � � , and �� � � or �� � � , then the decision unit � is DEA efficient, that is, the decision unit is both technology efficient and scale efficient, indicating that the input reaches the best combination and the output reaches the maximum.
(2) If � � �, and �� � �, �� � �, the decision unit � is DEA weak and efficient, indicating that the decision is not simultaneously technology efficiency or scale efficiency, and the input of part of the unit is excessive or the output of the department is insufficient.
Scale economy determination of the mode (1) When � � indicates that the � reaches the maximum output scale point when the scale gain of the � remains unchanged; (2) When � � , it means that when the scale gain of � is increasing, and the smaller the value of the larger the scale increasing trend, indicating that � will have a higher proportional increase in the output quantity by appropriately increasing the input quantity on the basis of the input � ; (3) When � � , it means that when the diminishing returns to scale of � , and the larger the value of the larger the diminishing trend, indicating that � on the basis of inputs � increase the amount of inputs is unlikely to bring a higher proportion of output, at this time there is no need to increase the inputs of the decision unit. The model flow chart is shown in Figure 1.

EXAMPLE ANALYSIS
The input-output values of an army in terms of number of personnel, funding, and equipment for certain major projects are shown in Table 1:

DEA validity analysis
As calculated by the model, � , � The results are shown in    The ordering of � calculated by SE-DEA is shown in Table 3: (1) From the SE-DEA calculation of � , it is concluded that among the 10 major projects, Project 1 has the best overall effectiveness, followed by Project 9, Project 1, Project 4, and the last in the list are Project 10, Project 3, Project 5, and the others are in the middle; (2) Based on the values of � and the slack variables , it is concluded that under the current input and each unit level conditions, all projects are weakly DEA efficient and are on the production frontier of technically efficient and scale efficient, and the various resources invested are relatively fully utilized and the output achieved is maximized.  Table 4 and Table 5:

Scale benefit analysis
(1) Increasing scale benefits, Project 2, Project 4, Project 7, Project 8, Project 9, k smaller, with larger marginal outputs within certain limits, indicating that by increasing inputs appropriately, outputs will increase in a larger proportion; (2) The decreasing scale benefit type, which are Project 1, Project 3, Project 5, Project 6, and Project 10, indicate that increasing the input will not result in a higher proportion of output and there is no need to increase the input.

Projection analysis of non-effectiv DMU
Using the formula � � � � � � � � �� , � � � � � � �� , the non-valid � decision unit is turned into a valid � and The results are shown in Table 6: According to the above calculation and analysis, the optimization of the number of personnel input, the optimization of financial input, the optimization of equipment input and the optimization of fixed assets input are shown in Figure 2, Figure 3, Figure 4 and Figure 5 respectively.   It can be seen that, except for Project 2 and Project 6, all other projects have different degrees of resource wastage in terms of the number of personnel, funding, equipment and fixed assets.

CONCLUSION
In this paper, by establishing a data envelopment analysis DEA model, we calculated and analyzed the input-output ratios of certain large projects of the army in terms of the number of personnel, equipment, funds, and fixed assets, and made an objective evaluation of the input-output ratio of each project, and gave reasonable suggestions for the input optimization of projects that could be optimized.