AN APPLICATION OF GREY SYSTEM THEORY AND DEA IN STRATEGIC ALLIANCE IN VIETNAMESE AGRICULTURAL INDUSTRY

Collaboration is at the heart of every business success [1]. Indeed, every aspect of a business is dependent on a partnership one way or another. However, successful partnerships require a lot of factors and efforts from both sides in order to assure the necessary cooperation needed to harness the respective potency of each partner ([2]; [3]; [4]). Therefore, this study aims to develop tools which are Grey Theory and DEA models generate the effectiveness of enterprises in Vietnamese agricultural industry then offer an effective way to figure out the most suitable strategic partners. The most influenced enterprises are selected to collect realistic data from financial reports of Vietnam issued stock market in four consecutive financial years. The targeted decision making unit (DMU) has some potential partner for collaboration in the future, but they are also advised to stay away with some DMUs, which may make them even weaker after doing alliance. Although this research is specifically applied to the fertilizer industry, the proposed method could also be applied to other manufacturing industries. Int. J. Anal. Appl. 16 (6) (2018) 922


I. INTRODUCTION
The fertilizer industry development relies on low labor costs, efficiency, large system of foreign exchange, an easy import and export procedures for exporters and the open policies for foreign investors ( [5]; [6]).Currently, the fertilizer industry is facing more challenges such as how to maintain their competitiveness in today's fierce market, to diversify products, and divert from processing into other forms which can bring more advantages for the industry ( [7]; [8]).In specific, there are three major problems: equipment and modern technology selection, maintaining a stable and capable workforce and floating capital.The problems cannot be overcome when firms are doing individually [9].We would recommend finding the alliance partners for companies to solve those existing problems by combining Data Envelopment Analysis (DEA) and Grey Theory.Since errors in information are unavoidable, consequently, Grey theory and DEA Model are hired to forecast the business in the future and productively evaluatethe performance in firm's efficiency ranking [10].
The purpose of this research is to provide an assessment model based on Grey theory GM (1,1) and Data Envelopment Analysis (DEA) and suggest an appropriated establishment of partnership after many thoughtful considerations.

Grey Forecasting Model and Data Envelopment Analysis
In Grey System Theory, GM (n, m) denotes a Grey model, where n is the order of the difference equation and m is the number of variables ( [11]; [12]).Although various existing types of Grey models can be applied for forecasting, most of researchers, lecturers have paid focused on GM (1, 1) models in their prediction method due to its computational efficiency ( [13]; [14]).It should be noted that in real time applications, with the complex data sets, the reduction in the computing time is even more important than the rest of parameters ( [15]; [16]; [17]; [18]).
GM (1,1) is applied with the purpose of a forecasting for a series of time.And it can only been applied in non-negative data sequences, in this analysis, future values of the original data points can be predicted by Grey model because they are positive.
During recent years, some models have been presented to solve negative data in DEA models.However, they do not discriminate between efficient DMUs and only evaluate them as being efficient.In this part, we propose a model by which we discriminate between such DMUs it is "Slacks -based measure of efficiency" (SMB) introduced by Tone [19].Then, we extend the "Slack -based measure of supper -efficiency" (Super -SBM) for DEA model with positive and negative inputs and outputs.In this model with n DMUs with the input and output matrices indicate the input excess and output shortfall respectively.SBM model in fractional form is as follows [19]:

   
Let an optimal solution for SBM be This condition is equivalent to * 0 S − = and 0 S + = , no input excesses and no output shortfalls in any optimal solution.SBM is non-radial and deals with input/output slacks directly.The SBM returns and efficiency measure between 0 and 1.
The top onehave the full effective status indicated by unity.According to super-SBM model by Tone [20], assuming that the DMU 00 ( , ) xy is SBM-efficient, 1 p  = , super-SBM model is as follows: Where B is a large positive number, (in DEA-Solver B=100).

Development of research
In this study, Grey Theory and DEA model are combined in a group of methodical evaluation models.The development of research in this paper is implemented by the data information of Vietnamese Fertilizer Industry and also selected all related documentations as references.Then after subject confirming and proceeding industrial analysis, the development of this study is presented in Figure 1 as below:

Data Collection
To apply the research on Grey Forecasting model and DEA literature review, three main participations are selected as fixed assets, cost of goods sold, operating costs which are essential to the sources of fertilizer industry.And we select the net sales, operating profit, net profits as our output factors owing to the essential index to analyze the company's financial effectiveness.
We show the realistic data of 2016 which are gained from the financial statement that they are selected at Vietnam issued stock market website with the Vietnam currency unit.The companies are listed in Table 1.

Sources: Financial statements of companies
The Grey Model (1, 1) is utilized to predict the input and output factors values for each decision making unit in 2016 and 2017.In the Table 2, we take the total deposits of DMU1 as an example to explain how to calculation.Other variables are calculated in the same way.
In this research, we use 5 periods of data (2012-2016) to forecast the input and output variables value in 2017 and 2018.Here, we select the fixed assets of company A as example to calculate in detail the procedure as following (Table 3 and Table 4).Source: Calculating by author

Alliance Setting-up Stages
DEA expects that the input and output factors must be metis tonicity ( [22]; [23]).Prior to the procedure of DEA analysis, we have to ensure the connection between input and output factors and tonicity ( [24]; [25]; [26]; [27]; [28]).Therefore, in this paper, we employ Pearson correlation analysis to see if our data fits the assumption of DEA.Correlation coefficient between input and output variables are high than 0.6, which exhibits a highly positive correlation and well complies with the prerequisite condition of the DEA model.
Here, we run the software of Super-SBM-I-V by choosing the realistic data of 2016 to rank the companies' effectiveness before alliances.The empirical results are obtained in the below Finally, we use the software of DEA-Solver for calculation of Super-SBM-I-V model for 21 DMUs.Table 7 shows the score and ranking results of virtual alliance in 2018.First, the companies, which acquires brighter outcome after strategic alliance and also put their partnership more effectively, are the first prioritized candidate.Both corporationF and D helped the E to develop the result into a higher level after strategic alliance, which can be observed in Table 8.

Source: Calculating by author
The importance of strategic alliance has been consistently emphasized as the key factors of business survival in the era of globalization.It helps companies to reduce risk and easily penetrate into the market.However, it is a big challenge to have a successful strategic alliance.
Application of a strategic alliance can give rise to less than competitiveness or cause large enterprises to become even larger and small enterprises even smaller.

IV. Recommendations and Conclusions
At this moment, more and more competition dramatically arises in fertilizer industry.
According to the Viet Nam Fertilizer Association, the domestic fertilizer industry has experienced a growth in output, but lacking of competitive ability.The industry still continues to widely apply the usage of old-fashioned production technology while the world's fertilizer Many related subjects of strategic alliance have been already done research by many scholars and experts.However, this study provides firms with a method tolimit the possibilities of risks, creates the mode of penetration.But how strategic alliance opens up for firms to be roaring successful is the enormous challenge.

This research concentrates on the connection between key collusion and firms' execution of
Vietnamese Fertilizer by using GM (1, 1) model and DEA model.This study reaches some conclusions through a series of literature reviews and empirical results.
1.The GM(1, 1) model helps the enterprises to predict what will happen in the future regarding particular elements: fixed assets, cost of goods sold, operating costs, net profits, operating profit ,which are important to the firm's efficiency in doing business based on the realistic data and information in the past time.However, there are alwaysexistent errors in predicting processes, thus the MAPE is utilized to ensure whatever collection of inputs or outputs is almost precise or not.In this examination, the range of MAPE values from 2% to 20%, whichguarantee that GM (1, 1) delivers high accurateness.
2. This study shows that the DEA model is based on the resource-based theory.The Super-SBM model was used to assess the11 firms separately and calculate the operational performance of 21simulated decision making units for strategic alliances.Thanks to this methodology, we can simply divide 11 candidates into three groups.
In this study, company E, among famous fertilizer companies in Vietnam, is an objective company for strategic alliance with the others 10 firms.We observe the two companies which are the best candidates because profits are generated for both sides: target company E and 2 candidate companies due to the effective alliance.This factled to the outstanding efforts from both: collaborative innovation agreement and renewal products.The second priority is a group of companies with five companies and Target Company should carefully consider when implementing alliance because they can get the risk after strategic alliances.The third group includes companies: E, H & B, which are unnecessarily to be cared because there is no advantage for two alliances.

APENDIX INPUT AND OUTPUT FACTORS OF TARGET DMUs IN 2012
Companies DEA models, determine how to deal with negative outputs in model efficiency evaluation is fairly important[21].But the properly role of negative data is effectiveness measurement, therefore DEA-Solver pro 4.1 Manuel had new change as below Let us suppose 0.

FIGURE 1 :
FIGURE 1: STUDY DEVELOPMENT industry uses many modern technologies to reduce production costs.In long term, local fertilizer factories will lose their market shares or even have to dissolve if they do not embrace new creation advancement in technology.Although the industry counts around600 companiesbut most of them are small-medium sized.Products made in Vietnam are low-tomedium quality.Supplementary to this, like any existing market, one of the essential challenges is operating the management of the supply chain, in-depth understanding the import requirements and ensuring that the product can be delivered to the customer and/or consumer.Input/ output factors fluctuate in different periods, which makes "business future" in uncertain success.Therefore, in this research, we propose a new methodology which combines the GM (1, 1) model and DEA model to find the right alliance partners for Target Company under several inputs and outputs.

Table 5
indicated that the forecasting value of DMUs are good because most of MAPE of DMU less than 10% and the MAPE average of all thirty commercial banks is 10.48% (less than 20%) which confirm GM (1, 1) model suitable in this case study.Therefore, this means the results in table 5 have a good reliability.

table . TABLE 6 :
EFFICIENCY, RANKING BEFORE STRATEGIC ALLIANCESHere, company Eis chosen as target Company for alliance considering to the outcome of data ranking of 2016 before strategic alliance by reason of couple of reasons.Firstly, company E acquired the point less than 1 all of the period from 2012 -2016, implying that they did not have good business performance.Subsequently, they should boldly develop their effectiveness by alliance model.Secondly, company E is in major position in the fertilizer industry.To implement our empirical research, we combine E with the rest of DMUs to reach 21 virtual alliances.

TABLE 7 :
PERFORMANCE RANKING OF VIRTUAL ALLIANCE solid and liquid Yogen fertilizer, Phosphorous fertilizer, sulfuric acid, and agricultural organic minerals among others.The Southern Fertilizer JSC looks for strategic alliances.As indicated by the positioning of virtual cooperation, the examinations of observational outcomes split into three gatherings and translate as underneath: (SFG) takes a hand in manufacturing, sale of fertilizer and other chemical products.The Company's main products include Nitrogen-Phosphorous-Potassium (NPK) fertilizer, organic NPK fertilizer,

TABLE 8 :
THE Source: Calculating by authorSecond, the DMU which increases performance after strategic alliance while other DMU gets worst is the second priority.Total five companies in this group are shown in Table9.

TABLE 9 :
THE