1. INTRODUCTION
In the world as well as in Vietnam, plastic industry is still young compared to other longterm industries such as mechanics, electricity  electronics, chemicals, or textiles; but there has been strong development in recent years (Pham et al., 2019;Nguyen, 2019a;Nguyen and Nguyen, 2019;Nguyen and Tran, 2015). Plastic industry, in the period of 20102015, is one of the industries experiencing the highest growth in Vietnam with an annual increase of 16%18% (only lower than the telecommunications and textile industries), having products with growth rate reaching 100% per year. With rapid growth, the plastics industry is considered a dynamic industry in Vietnam’s economy.
In Vietnam, the average plastic consumption per person has increased rapidly in recent years. In the period of 20122014, the figure was at 38 kg / person / year and increased to 49kg / person / year in 2015 and it is estimated at 5354kg / person / year in 2016, equivalent to an average increase of 16.5% / year in the last 2 years (calculating the average plastic consumption per person based on import and export volume of plastic and plastic materials 20122015, estimated domestic production materials).
Vietnam’s per person plastic consumption index is quite similar to regional countries such as Thailand and China (equivalent to the world average) (Nguyen and Tran, 2016;Nguyen and Tran, 2018a). In the two years 20152016, benefiting from falling raw material prices and increasing domestic demand (from construction and consumer industries), Vietnamese plastic enterprises have boosted production, which has caused total production Imported plastic materials to increase by 23% / year on average in the last 2 years, from 2.9 million tons in 2014 to 4.4 million tons in 2016.
Most plastic products in Vietnam are in the lowend segment, so small and mediumsized companies (accounting for more than 90% of the total of 2,000 plastic companies) often pay less attention to the current technology and modern machinery investment (Cusolito, 2016;Nguyen and Tran, 2018b;Nguyen et al., 2015). Competition from plastic companies with foreign involvement, companies exporting plastic products to Vietnam, impacts from international trade agreements.
Increasing integration into the international market also makes Vietnamese plastic companies face more competitive pressure. Competitors from Korea, Japan and Thailand with higher brand recognition and product quality, while Chinese companies have the advantage of low cost, especially after Central Bank of China adjusted the Yuan depreciation. Barriers to entry into the industry are on average, so the pressure on competition is relatively high. Currently, large corporations in Vietnam such as Hoa Sen and Vinaconex, Licogi also have largescale investment projects, producing plastic pipes (Nguyen, 2019b;Vyas et al., 1995;Wang et al., 2015).
The competition of foreign companies with great financial potential, modern technology, diversified product designs, good quality and reasonable prices. Typically, Srithai Superware PLC  a leading plastic company in Thailand has stepped up investment in plastic products factories in Vietnam (the company currently has 3 factories in the south and is investing in constructing a new factory in the North) with a total investment of US $ 20 million. One of the weaknesses of Vietnam plastic industry is that the technology is not modern (Nguyen and Tran, 2019). Heavy competitors such as Thailand and Malaysia are constantly improving technology and embracing the trend of world consumption (environmentally friendly bioplastic products and so on cf. Nguyen, 2019b). Without early investment in technology improvements, domestic plastic enterprises may soon be overtaken by the businesses in the region and see them dominating the Vietnam plastic market.
From the above mentioned difficulties and barriers, this study tries to investigate Viet Nam plastic companies’ performance, especially the existing companies listed in the stock market with a specific concentrate on the influential use of their capital in business activities. Although having promising growth the operation cost of this industry as well as the debt controlling are not effective towards small local enterprises. Therefore, the purpose of this research is to access the evaluation of performance of priority enterprises in Vietnamese plastic industry based on Grey theory GM (1, 1) and the Data Envelopment Analysis model (DEA). Furthermore, forecasting the potential opportunities in strategic alliance between those giants by thoroughly collecting a target company whether to find favorable partners is an added reason. In parallel, the paper will recommend the forecasting information for business improvement in the future, which is applicable for enterprises in managerial roles.
Moreover, this study would offer inclusive insights into business improvement by analytical results which assist the managers in management decision and policy making to avoid the risk of bankruptcy and maintain the sustainable performance. It would serve as a basis for further researches on how to improve firm’s efficiency in other potential industry in Viet Nam through applying DEA model.
2. METHODOLOGY
Figure 1 illustrates the stepbystep process to conduct the study. The preparation step includes the collection of input and output data of a set of DMUs. This step should be conducted carefully to help reflect the nature of the problem objectively while securing the model assumptions (Färe et al., 1997;Chen and Huang, 2013;Charnes et al., 1978;Caves et al., 1982;Foos et al., 2006). At stage 2, we examine companies’ productivity of over the past five years using the rankings of super SBM IV model. Heading to prediction stage, we apply GM (1,1) to forecast future factor values of DMUs from the data series collected at stage 1; we then apply MAPE to test forecasting accuracy. At this stage, if forecasting errors are high, a review of input and outputs factors is needed to eliminate outliers. All of the input and out factors are forecasted for the future values, which then are reevaluated by using the Super SBM model (DEA) for further analysis. We have to test the errors of the values. At the third stage, Pearson correlation test is performed as the setting stage for DEA. Factors are also reviewed if they fail to give desired results. DEA is performed with DEASolver 5.0 software by Saitech Company on the forecasted data of original DMUs and virtual alliances. Results of section 2 and 4 will propose direction for efficiency improvement as well as which alliances can be formed between the target DMU and other DMUs.
2.1 Collect the Data of Plastic Companies (DMUs)
The researcher investigated plastic companies which basically point at foundation to discover all potential candidates to be DMUs list. As the DEA demonstrate is all around characterized as a benchmarking strategy and DMUs set ought to be a reliable gathering having the comparable considerable extent in related activities. In this manner, the researcher chooses 13 organizations dependent on common characteristics: over 70% complete income spent on plastic work. In the stock market list, 13 manufacturers published their financial statement in the period 2014 to 2018 and provided the completely data for 5 consecutive years. Besides, with affected capital in Vietnam market, 13 companies play essential parts within the development industry which can get to be agents for entirety plastic industry. When applying the DEA model, the overall number of factors ought to be a half of the number of those DMUs (Golany and Roll, 1989). In this research, the Target Company is DPC Company to put together with the rest of other DMUs to exalt the efficiency by putting in an application for the strategic alliance
2.2 Choose Input/ Output Variables
Data Envelopment Analysis (DEA) has been regarded as a tool to support practical and valuable. But, in order to conduct DEA based research, the ability to change, test and select variable production sets is essential due to the sensitive characteristics of the method. Therefore, to have expected results, this model must be chosen a wider set of variables. The reason that leads to insensitivity in advantage analysis is to have too many numerous weakened factors which will influence the alternatives between DMUs. This research identified 9 steps to ensure important factors in selecting input and output sectors by monitoring the relevant literature discussion and using the Pearson correlation coefficient to measure efficiency of several DMUs by forming relatively effective points. The essential criteria for collecting input / output factors: those items must correlate with units, have nonnegative data series required by the Grey forecasting model, data must be collected from audited financial statements and each variable can be listed for analysis
2.3 Grey Prediction
Based on Grey model GM (1,1), Grey Prediction predicted the data values on 2019 to 2023, which correlate with the writing review said within the chapter 2. In spite of the fact that GM show is perfect demonstrate due to the confinement of time arrangement, the determining result continuously exist error. Hence, to check the estimating exactness, the author employments the Mean Absolute Percent Error (MAPE) to evaluate the accuracy which would be altered within the following area.
2.4 Forecasting Accuracy
Be one of the valuable strategic worked out to compute determining accurateness in a fittedtime arrangement in measurements or tendency, this is necessary to utilize MAPE to guarantee the connected models have precision or not (Nguyen and Tran, 2018b). Hence, the MAPE is drawn to meet the prediction accuracy applying the following model. In case the determining mistake is over the satisfactory run, the new couple of factors has to collected
which n is the number of forecasting steps
MAPE extend result are allocated in the following criteria.
2.5 Choose the DEA Model
DEA model execute continuously the data when the high relationship of those variables are welldetermined. The software of DEASolver is utilized to compute the nonnegative arrangements independently with super SBMOV. Then by ranking DMU’s performance, the efficiency is achieved in the super SBM model. At that point the proficiency is accomplished by positioning DMU’s execution within the super SBM show which is considered as a suitable adaptation of DEA (Tone, 2001). This model outlines the productivity apportioned for each unit compared with other DMUs (Nguyen and Tran, 2016).
2.6 Pearson Correlation Coefficient Test
The isotonic relations within the examined variables are suggested in DEA model. Consequently, testing the data relations is a must in DEA and correlation between multiple variables is estimated in this work. The accuracy for selecting input/output variables depends on the correlation degree. If the correlation degree increases, the accuracy will increase accordingly. In some circumstances, negative output variables might happen, and then a reselection of these variables needs to be made in step 2 to satisfy condition (Nguyen, 2019b;Selsky and Parker, 2010;Ireland et al., 2002). In this work, to choose variables, Pearson Correlation Test is used in efficiency testing before each of decisionmaking units is ranked. The Pearson correlation coefficient is regarded as a widely used measure, which shares the highest pair wise degree of association between two variables with reference to the statistical distribution (Di Lena and Margara, 2010).
2.7 Analysis before Alliance
By applying the super SBMOV, the execution assessment of each choice making unit is then reached in order ranking. The examination result must determine from the practical information from 2014 to 2018 based on the checked financial report. In expansion, this step can be recognized as the planning for the vital collusion which helps the author in examining the effectiveness of the selected target company in the first step. If the target one cannot fulfill the investigate condition, the analyst straightforwardly makes choice on which DMU is the foremost fitting one in comparison with other competitors.
2.8 Virtual Alliance Analysis
After being clearly defined, the researcher merged the target company with other DMUs to make modern set of virtual alliances by adding the practical or estimating values of all factors together. A set of 26 virtual organizations together of those companies are combined to create together, at that point using the superSBMOV model to figure out and rank 26 candidates in odder list. When the integration and collocation is achieved, the result will be illustrated in measurement within the next chapter
Eventually, the suggestions are given based on the investigation result. All the candidates will be exceedingly rated in strategic alliance (score>1) if they have the most elevated score. However, for the remaining virtual alliances cannot appreciate efficiency (even descending rankings), this mean that the target company as well as other companies cannot get any competence development from specified strategy. Moreover, the analyst cannot recommend key union between those big companies.
2.9 Alliance Selection
With positive outcome of the virtual alliance ranking, the productivity of both enterprises involved in this strategy would be highly improved. In contrast, the cooperation with the target company will not be formed if the virtual alliances cannot enhance or even lessen the ranking since the strategy brings no benefit to the target company. The researcher should define the feasible partnership through standing on the side of the candidate company.
3. EMPIRICAL RESEARCH RESULTS
3.1 Establish Input/Output Variables
Before applying DEA model, it is essential for the researcher to clearly indicate the input and output components (Nguyen and Tran, 2018a). The choice of input and yield factors is exceedingly connected to working execution of each company. Thus, utilizing fitting components would prevent the ultimate result from deceiving. Other than that, the use of nonnegative data sets affects the Grey prediction model. The analyst must collect the information from their financial related examined reports and guarantee that there’s no lost information for at least 4 years. To meet the requirements, as below is the input and output which are welldefined and meet the requirements mentioned and play a vital part in commerce execution both in existing and future circumstances.
Therefore, the research selects the set of inputs: total asset, total liability, total operating expenses which corresponds to the set of outputs: total revenue and total equity (Kamaruddin et al., 2017;Kuppusamy and Anantharaman, 2019;Tran, 2016, 2017a). The variables mentioned present for the high correlation and total 13 companies in 2017 for the next step in the research (Table 1).
3.2 DMU Selection Analysis
The study found 13 businesses as below analyzed conducted at largest plastic market in Vietnam and can provide complete data for five consecutive terms (2014 2018) in Table 2 and Table 3. By using DEA model and GREY in helping the target company perform consideration decisions in the search for rights partners (Nguyen et al., 2015). SuperSBM model is evaluated as an essential approach for any business to get accurate information about business performance, to rank business performance points and to know where it is on the current market (Nguyen and Tran, 2018b).
3.3 Use the Grey Prediction Model in Reality
There are various predictive techniques used in publications, including GM(1,1) when an increasing application is proved to be recognized and popular with regard to economic, operational and other industries (Bagherinia and Olapour, 2016;Tran, 2017b). Furthermore, forecasting the future from past performance can help companies evaluate business efficiency and compete against their competitors. The researchers find that GM models are able to deal with time series limitations due to the particular nature of this research, the threshold for conducting data from 2014 to 2018. In practice, this model could predict the performance of companies in the next two years, which can be shown simply on the basis of realistic data from the past. Table 4 below shows how the Grey forecasting model is actually working.
In selecting the total assets of the BMP Company, the calculation process is presented in the following steps, and other factors are similar. At first, GM (1,1) is used to predict the variation in the original sequence:

Set the initial sequence:
X^{(0)} = (210.26; 423.06; 593.7; 423.17; 356.46)

Perform the accumulated generating operation (AGO):
X^{(1)} = (210.26; 633.32; 1227.02; 1650.19; 2006.65)
$\begin{array}{l}{x}^{(1)}(1)={x}^{(0)}(1)=210.26\\ {x}^{(1)}(2)={x}^{(0)}(1)+{x}^{(0)}(2)=633.32\\ {x}^{(1)}(3)={x}^{(0)}(1)+{x}^{(0)}(2)+{x}^{(0)}(3)=1227.02\\ {x}^{(1)}(4)={x}^{(0)}(1)+{x}^{(0)}(2)+{x}^{(0)}(3)+{x}^{(0)}(4)=1650.19\\ {x}^{(1)}(5)={x}^{(0)}(1)+{x}^{(0)}(2)+{x}^{(0)}(3)+{x}^{(0)}(4)+{x}^{(0)}(5)\\ =2006.65\end{array}$

Create the different equation of GM (1, 1)
To find X^{(1)} series, and the following mean obtained by the mean equation is:

Solve equations to find a and b, to achieve the primitive series values, the differential equation Grey is replaced:
Transform the linear equations into a matrix:
Then use the least square method to locate a and b:
To produce the whitening equation of the differential equation, use the two coefficients one and b:
Search for the equation prediction model:
Replace k in the equation with a different value:
Deduce the predicted value of the original series according to the generation process accumulated and obtain:
The same applies to the previous procedure, which was shown in Table 4, respectively, step by step, for all DMUs in 2018 and 2019:
3.4 Use Mean Absolute Per Cent Error in the Accuracy of Forecasting
The computational result of all DMUs is nearly less than 10% and a company code exceeds 10% of the error (NHP), the average overall result of 13 enterprises reaches 5.57%. This means an “excellent” result is achieved with the forecast value. The prediction value can be concluded with the dramatic conviction that the GM (1,1) model is an exact prediction method (Table 5). The researchers continue the investigation by selecting the DEA model after confirming the accuracy of MAPE variables.
Moreover, some papers have proved that GM(1,1) reaches a good level of forecasting (cf. Nguyen and Tran, 2017a;Nguyen and Tran, 2015; ChiaNan and Ty, 2013; Trinh and Tran, 2017). We also try to make some comparisons for better insights of GM(1,1) applicable to this topic. We use the Moving Average (MA) of three to make forecasting. The Moving Average demonstrates good trend when its forecasts with lower level of error. The same series of numbers used in GM(1,1) which are 10,636; 11,795; 11,763; and 12,026. The detailed results of both methods are shown in the results. One or more drawbacks of MA is that it requires a large sequence of data, so when we conduct the MA of three, we do not have the results for the two first series (which can be done completely by GM(1,1)). With this sample calculation, we also see the high performance from MA of three when the error at low level (i.e. 1.39% and 3.20%, compared with 0.41% and 0.83% of the Grey forecasting model), see Table 6.
The same process is repeated for the whole data we used for this study. Gradually developing and calculating the data with those models, we get the new forecasted data for the next procedure of evaluation the industry. We have to use the highlyevaluated data with higher accuracy in forecasting. Thus, we make a table (Table 7) to summarize all the Mean Absolute Percentage Errors (MAPE) to see the differences. This gives us an overall of all the MAPEs for the DMUs for this study. The indexes in the table clearly show that the GM(1,1) and Moving Average models gain high accuracy. Based on that, we would see that both GM(1,1) and Moving Average are good models to be considered. Notably, the MAPE of the virtual alliances at only 3.2% and 18.28% from GM(1,1); and these numbers are higher from MA of three, which means that GM(1,1) is more accurate. Moreover, based on their MAPE values, it can be concluded that the calculated values based on these two models follow closely to the actual values; while GM(1,1) is strongly suggested since its relevant indexes in the tables are better, Moving Average demonstrates the trend at higher percentage of accuracy (the average of all MAPEs from GM(1,1) is at 10.3%; at this category, it takes to 19.29% when it’s done by MA). Highly precise forecasting result will help the policymakers and the further analysis more accurate and reliable. The results of MAPE are displayed as follows:
Bellowing numbers present MAPE of forecasted data of year 20112016 (year 20122016 for DMU1). Average MAPE = 10.33% indicates “Good” accuracy. Grey method is therefore a reliable predicting tool and forecasted data of year 2017 will be brought to further stage for alliance performance analysis.
3.5 DEA Method Selection
There are currently several fruitful experimental models that can be connected to evaluate the common efficiencies of any enterprise by building the DEA model. It is responsible for changing over a set of inputs into outputs. Hence, the completed DEA progress connected in this research can fulfill the reason in assessing the plastic companies while the ordinary DEA strategies cannot be used. Partially, performing traditional DEA methods in an attempt are to lead to a similar position of lack of objectivity as they do not alter the key requirement for each DMU as well as selected input and output items. They allocate the focused model for input/output selection directly. In addition, nonradial processes can manage more statistics even if they have large amounts input or output deficiencies to achieve more practical implications. When participating in the DEA, it is considered a problem to define which DMUs have the best effective performance by comparing a limited amount of DMUs with the total criteria. In this research, advanced techniques should be applied to examine and arrange order performance during examination in order to determine the best performance of 13 companies. The DEA model is the most suitable for handling just a small number of decisionmaking units and measuring the efficiency of productivity by scoring for all the reasons discussed. The super SBM model is therefore a useful tool for dealing with the small group of companies selected. The research strongly suggests that the super SBM model built in the processing of results is persuasive
3.6 Pearson Correlation Coefficient Test between Variables
When conducting the DEA model, it requires the isotonic relationship among collected variables and the linear correlation of those factors should be guaranteed by its position linked to the envelopment frontier before implementing the model. Thanks to the Pearson correlation coefficient test, the degree of connection between variables is evaluated. The high adjacent relation is recorded when the high degree of correlation is considered. The criteria of the mentioned test are illustrated as below (Table 8):
After manipulating the experimental research, the results from 2014 to 2018 simultaneously yield the high correlation to the precondition of the DEA model. It is clearly that the degree of correlation ranges from 0.5 to 1.0 which indicates it is closer to an expected isotonic relationship. Hence, the positive consequences also prove the initial factors establishment is practical. Remarkably, there is no need to reject any factors in this paper.
3.7 Ranking Result before Strategic Alliance
Through the period surveyed, the experimental outcomes of BMP is recorded as the highest as opposed to TPP and DNP, which means BMP company has the best performance with the impressive score at 3.5448 in 2018. In this paper, the author selects the TPC as the target company incorporating with other alliances. This company presents the good result when ranking 9^{th} in 2018. Although the average results gradually fluctuate in the previous year, it does not affect the applied strategy in the next section. It is potential for TPC goes through the strategic alliance to have the general better performance.
3.8 Analysis of Virtual Alliances
TPC (Tan Dai Hung Plastic Joint Stock Company was ranked as one of 500 largest enterprises in Vietnam and awarded the title of “Prestigious Export Enterprise” by the Ministry of Industry and Trade for many years. This target company gets the computed result of 0.831608 which is interpreted quite good opposed to competitors. However, the company should enhance its production efficiency and attain more merits because the ranking order of TPC just at 9^{th} out of 13 enterprises. It is critical for TPC to enter into the alliance group to take advantages from its partners. The study firstly creates virtual alliance to conduct the experimental research by combining the variables value of the target company respectively with the rest companies. This preparation produces a set of 25 virtual alliances which intently calculated by the software of DEASolver Pro 5.0 constructed by Saitech company.
Ranking promotion of following companies in the Table 10 illustrates the significant change of HCD, VKC, NTP, RDP and SPP from combined values with TPC Company. Ranking score indicates clearly difference when those enterprises conduct the strategic alliances. To be more precise, this paper recommends an added equation to calculate the difference after alliance: Difference = Ranking of target TPC – Ranking of virtual alliance. The researcher divides the ultimate results into two groups. The first one presents all the positive virtual alliances which means this group demonstrates better results and take more advantages from proposed strategy. The second group obviously includes the negative couple of alliances which may worsen the mutual result of each other. As a consequence, this paper cannot offer insights into the partnership establishment in the next section.
There are 8 companies yield the considerable result after alliances and have necessary features to complement with partner’s expectation: HCD, VKC, NTP, RDP and SPP.
Although there are three virtual alliances (AAA+TPC, BMP+TPC, HCD+TPC) have the acceptable opportunities with overall score is higher than 1, the other partners mentioned also raise to a higher scale after cooperating with TPC company. Hence, 8 over 12 candidates will be a substantial result which convinces that entering the strategic alliances is a better choice for planning business management. Regarding the second group, only 04 enterprises contain DPC, NHP, TPP and DNP which worsen the efficiency performance of TPC. Though the difference is not important, it could not better off the performance for the target company in the future.
4. IMPLICATIONS AND CONCLUSION
This research contribution is to assist the target company to seek for appropriate partnership entering the strategic alliance planning by conducting GM (1,1) and DEA model in forecasting the performance in the following next years. The researcher also proposed the added idea to integrate the combination of Grey theory, super SBMOV model which employs the target enterprise to determine alliance advantages if it has potential partners. Furthermore, the mentioned method provides a precise evaluation for Vietnam construction industry through detailed description by analyzing the efficiency and ranking position in order. Based on this, the company can develop the improvement planning for it as well as take the business merits from partners.
Although, they are rivals in the same industry competing in the similar market to gain that much profit to maintain the business, alliance strategy is needed when it can enhance the mutual performance and bring the bene fits for enterprise. The problem of any company is to balance the financial situation. Therefore, it is properly speaking they can be their partners as long as maintaining the improvement in the longterm.
Therefore, we can summarize that strategic alliances not always can help firms increase their efficiency and performance. Blindly proceeding strategic alliances may cause the company lose their overall competitiveness. The crucial thing in implementing strategic alliance is that enterprise should consider different aspects to get benefits. Once strategic alliance is considered and treated carefully and properly, firm’s operation efficiency is surely raised.
Concluding the results of data analysis, the main contributions of this study are listed as follows:

This is a new studying method in both academic research and practical applications by combining Grey theory and Super  SBM model. The proposed method of this research not only forecasts some important business factors for Vietnamese plastic industry but also provides an accurate and appropriate evaluation of the industry at current situation. That could be useful information helping Vietnamese plastic enterprises’ top managers to have effective decision making for business strategy (including alliance strategy) in the future. The result after strategic alliance provides a meaningful reference to help many other industries’ manager in finding the future candidates of strategic alliance.

Basing on the results of this study, the researcher concludes clearly alliances model and methodology we bring up in this research can also apply in the other industries to evaluate the strategic alliances partners’ selection, enhance the overall competitiveness and avoid the wrong strategic alliances.
Hopefully, the study might be of some benefits for EMS companies to improve their operation efficiency.
It is undeniable that this research still has limitation corresponding to the limited number of observed companies for an empirical study. Although the research already indicates conditions to select the input/output variables to avoid the subjective results, it is only about the financial factors which cannot completely present for whole construction industry. The performance evaluation of any enterprise is also evaluated by various nonfinancial factors such as human resources allocation, effective equipment and so on. Further research should consider developing more aspects based on the results of this paper and address to ensure that strategic alliances could be managed well and content it with partners’ demands. Specially, when researching into the multinational companies with different working environments requires a broaden based study and methods to discuss more.
The authors declare that there is no conflict of interests regarding the publication of this paper.