International Journal of Analysis and Applications Volume 16, Number 6 (2018), 921-948 URL: https://doi.org/10.28924/2291-8639 DOI: 10.28924/2291-8639-16-2018-921 Received 2018-07-29; accepted 2018-09-09; published 2018-11-02. 2010 Mathematics Subject Classification. 91B26. Key words and phrases. strategic alliance; grey forecasting model (GM); data envelopment analyses (DEA); Vietnam fertilizer industry. ©2018 Authors retain the copyrights of their papers, and all open access articles are distributed under the terms of the Creative Commons Attribution License. 921 AN APPLICATION OF GREY SYSTEM THEORY AND DEA IN STRATEGIC ALLIANCE IN VIETNAMESE AGRICULTURAL INDUSTRY THANH-TUYEN TRAN* Scientific Research Office, Lac Hong University, No. 10 Huynh Van Nghe, Bien Hoa City, Dong Nai Province, Vietnam *Corresponding author: copcoi2@gmail.com ABSTRACT. 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. https://doi.org/10.28924/2291-8639 https://doi.org/10.28924/2291-8639-16-2018-921 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. II. RESEACH METHODOLOGY 2.1 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]). Int. J. Anal. Appl. 16 (6) (2018) 923 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 ( ) m nijX x R  =  and ( ) s nijY Y R  =  , respectively.  is a non-negative vector in nR . The vectors m S R −  and sS R+  indicate the input excess and output shortfall respectively. SBM model in fractional form is as follows [19]: 01 01 1 1- / mmin = 1 1 / m i ii s i ii s x s y s  − = − = +   s.t 0 ,x X s − = + 0 ,y Y s + = − - +0, s 0, s 0.    Let an optimal solution for SBM be * * * *( , , , )p s s − + . A DMU 0 0 ( , )x y is SBM-efficient, if * 1p = . This condition is equivalent to * 0S − = and 0S + = , 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 0 0 ( , )x y is SBM-efficient, 1p  = , super-SBM model is as follows: Int. J. Anal. Appl. 16 (6) (2018) 924 01 01 1 / mmin = 1 / m i ii s r rr x x y y s  = =   s.t 1, 0 , n j j j x x =    1, 0 , n j j j y x =    0 0 and y ,y x y  0 y , 0.y y   Comparable to other 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. ro y  it is defined and rry y + + − by   1,..., max 0 , rj rjr j n y y y + = =    1,..., min 0 . rj rjr j n y y y + = =  (1) 1 rr y y + + − = = , the term is replaced by ( ) 0 / r rr r rr y y y s y y + + + − − + + − − ( ) ( ) 2 0 / r r rr y s B y y + −+ + − , Where B is a large positive number, (in DEA-Solver B=100). 2.2 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: Int. J. Anal. Appl. 16 (6) (2018) 925 FIGURE 1: STUDY DEVELOPMENT Int. J. Anal. Appl. 16 (6) (2018) 926 III. APPLICABLE CASE RESULT AND ANALYSIS 3.1 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. TABLE 1: COMPANIES LIST Number order Code Companies 1 A Petrovietnam Fertilizer and Chemicals Corporation 2 B Petrovietnam Ca Mau Fertilizer JSC 3 C BinhDien Fertilizer JSC 4 D Lam Thao Fertilizers and Chemicals JSC 5 E The Southern Fertilizers JSC 6 F Quang Binh Import and Export JSC 7 G NinhBinh Phosphate Fertilizer JSC 8 H Central PetroVietnam Fertilizer And Chemicals JSC 9 I South-East PetroVietnam Fertilizer & Chemicals JSC 10 K Van Dien Fused Magnesium Phosphate Fertilizer JSC 11 N South-West PetroVietnam Fertilizer and Chemicals JSC 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. Int. J. Anal. Appl. 16 (6) (2018) 927 TABLE 2: INPUT AND OUTPUT FACTORS OF COMPANIES IN FERTILIZER INDUSTRY IN 2016 Company Input (Units: Volume million, $thousand) Input (Units: Volume million, $thousand) Fix assets Cost of Goods sold Operating Cost Net sales Net profits Operating profit A 1,910,477 5,528,946 1,248,517 7,924,787 1,164,775 1,385,216 B 8,754,407 3,595,508 963,306 4,910,171 624,340 632,709 C 742,125 5,038,820 489,927 5,942,917 350,100 421,064 D 193,750 3,233,437 562,608 3,964,661 138,150 171,686 E 150,386 2,105,100 149,510 2,338,362 90,589 102,510 F 272,675 4,300,199 224,435 4,495,270 13,561 16,690 G 9,559 447,691 75,801 546,139 19,334 23,145 H 45,939 1,910,249 60,932 1,997,252 25,168 31,289 I 35,167 2,071,763 69,801 2,165,958 23,353 26,457 K 16,853 689,058 176,225 907,609 44,432 54,398 N 31,797 2,153,810 56,339 2,237,995 28,117 35,149 S o u r c e s : F i n a n c i a l s t a t e m e n t s o f c o m p a n i e s 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). Int. J. Anal. Appl. 16 (6) (2018) 928 TABLE 3: INPUTS AND OUTPUTS DATA OF ALL DMUS IN 2017 Company Fixed Assets Cost of goods sold Operating costs Net sales Net profits Operating profit A 1,685,963.9 0 5,458,073.0 4 1,328,062.5 6 7,787,165.4 2 898,571.13 1,119,514.3 5 B 8,276,456.7 4 3,173,383.2 0 1,125,406.6 9 4,671,239.0 4 711,194.13 736,011.19 C 895,353.32 4,770,331.4 5 529,771.77 5,687,218.0 4 366,951.03 437,892.40 D 202,773.07 3,262,600.7 2 592,196.17 3,969,420.5 3 156,268.90 194,096.28 E 107,026.31 1,991,256.2 2 129,892.69 2,187,819.0 1 77,099.39 84,327.45 F 343,824.05 5,616,309.6 7 318,580.84 5,883,841.4 6 42,496.76 52,313.94 G 7,996.72 381,027.75 65,632.55 461,389.60 12,934.22 16,429.11 H 41,678.48 1,902,502.9 5 64,176.59 1,983,763.9 2 22,869.33 27,362.72 I 38,872.59 1,858,105.7 1 70,642.69 1,948,927.1 1 21,974.00 24,062.58 K 3,458.66 684,922.27 188,073.55 906,731.96 43,991.94 50,259.14 N 37,166.07 2,043,969.4 9 58,719.15 2,127,340.1 8 29,031.92 33,935.78 Source: Calculating by author Int. J. Anal. Appl. 16 (6) (2018) 929 TABLE 4: INPUTS AND OUTPUTS DATA OF ALL DMU S IN 2018 Company Fixed Assets Cost of goods sold Operating costs Net sales Net profits Operating profit A 1,545,418.0 9 5,075,411.34 1,352,662.8 3 7,232,792.69 740,254.75 926,069.79 B 7,625,272.6 4 2,821,149.52 1,208,493.7 2 4,320,868.44 727,436.45 769,271.25 C 1,083,730.4 0 4,517,465.95 590,576.54 5,483,607.79 401,330.76 475,474.11 D 207,478.12 3,135,209.31 602,198.50 3,747,812.28 117,641.82 144,764.92 E 70,160.26 1,937,956.48 118,505.13 2,113,179.50 70,160.84 74,911.50 F 430,583.44 7,382,882.89 536,768.63 7,716,047.30 41,852.48 51,236.70 G 6,545.77 343,641.55 56,991.30 410,420.12 9,649.57 12,546.64 H 37,782.09 1,782,638.32 69,989.40 1,860,623.01 19,980.84 23,313.15 I 36,493.75 1,622,388.64 69,521.73 1,706,539.05 20,017.98 20,720.02 K 1,636.32 673,631.40 202,180.74 894,452.32 37,039.20 41,643.87 N 39,446.23 1,892,235.76 63,977.69 1,975,691.83 28,427.04 32,268.06 Source: Calculating by author 3.2 Evaluating Process 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. Int. J. Anal. Appl. 16 (6) (2018) 930 TABLE 5: AVERAGE MAPE ERROR OF DMUS Company Fixed Assets Cost of goods sold Operating costs Net sales Net profits Operating profit Average MAPE of DMUs A 4.36 4.87 3.71 4.02 17.88 12.17 7.84 C 2.48 1.05 8.41 2.32 14.30 15.14 7.28 D 8.88 0.70 6.63 0.66 4.61 4.90 4.40 E 4.73 4.45 3.75 5.11 21.41 21.47 10.15 F 24.93 4.73 5.39 4.17 4.66 5.59 7.28 G 53.28 1.26 14.29 1.80 101.01 104.12 45.96 H 4.10 4.59 3.34 4.69 14.97 14.69 7.73 I 0.15 4.58 4.70 4.29 8.43 8.49 4.40 K 12.75 2.79 4.48 2.80 2.38 4.06 4.88 N 37.71 0.98 2.35 1.44 11.15 5.94 9.93 Source: Calculating by author 3.3 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 table. Int. J. Anal. Appl. 16 (6) (2018) 931 TABLE 6: EFFICIENCY, RANKING BEFORE STRATEGIC ALLIANCES Rank DMU Score 1 G 1.875656 2 K 1.703822 3 F 1.377278 4 N 1.321511 5 D 1.268671 6 C 1.213142 7 A 1 8 I 0.94212 9 E 0.937486 10 H 0.86823 11 B 0.612298 Source: Calculating by author Here, 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. 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. Int. J. Anal. Appl. 16 (6) (2018) 932 TABLE 7: PERFORMANCE RANKING OF VIRTUAL ALLIANCE Rank DMU Score Group 1 K 4.44656 2 G 1.887691 3 E + F 1.675027 1 4 N 1.189458 5 E + D 1.178774 1 6 B 1.127153 7 E + K 1.11175 2 8 A 1.098635 9 E + N 1.090146 2 10 E 1.076125 11 E + C 1.053355 2 12 C 1.012596 13 D 1.006937 14 E + A 1 2 15 E + G 0.991406 2 16 E + I 0.976105 3 17 E + H 0.967737 3 18 I 0.932377 19 H 0.918227 20 F 0.902863 21 E + B 0.681111 3 Source: Calculating by author In this examination, enterprise E is established as the objective enterprise which was positioned as the ten in comparison to the other 11 DMUs in 2016.The Southern Fertilizer JSC (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 Int. J. Anal. Appl. 16 (6) (2018) 933 NPK fertilizer, 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: 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. TABLE 8: THE FIRST PRIORITY IN ALLIANCE STRATEGY Rank DMU Score Group 3 E+F 1.675027 1 5 E+D 1.178774 1 Source: Calculating by author Second, 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 Table 9. TABLE 9: THE SECOND PRIORITY IN ALLIANCE STRATEGY Rank DMU Score Group 7 E + K 1.11175 2 9 E + N 1.090146 2 11 E + C 1.053355 2 14 E + A 1 2 15 E + G 0.991406 2 Source: Calculating by author Thirdly, the DMUs which become worse and worse after strategic alliances are not suggested in this study. It is unnecessary to put in any effort for partnership because no advantages between both candidates and target candidates. Table 10 presented 3 companies in the group as below Int. J. Anal. Appl. 16 (6) (2018) 934 TABLE 10: THE THIRD PRIORITY IN ALLIANCE STRATEGY Rank DMU Score Group 16 E + I 0.976105 3 17 E + H 0.967737 3 21 E + B 0.681111 3 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 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-to- medium 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. 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, Int. J. Anal. Appl. 16 (6) (2018) 935 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. 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Appl. 16 (6) (2018) 938 APENDIX INPUT AND OUTPUT FACTORS OF TARGET DMUs IN 2012 Companies Fix Assets Cost of goods sold Operating cost Net sales Net profits Operating profit A 2,371,392 8,997,366 1,318,093 13,321,852 3,067,647 3,574,740 B 12,436,315 2,967,940 410,051 4,076,182 736,671 730,296 C 425,142 6,869,767 366,813 7,422,968 158,867 197,199 D 219,612 3,495,007 502,080 4,494,851 394,091 509,684 E 563,219 2,544,853 202,360 2,840,282 98,79 119,108 F 31,870 2,302,833 92,291 2,391,848 2,038 2,382 G 19,403 551,271 142,841 770,310 63,697 79,316 H 65,240 2,347,980 43,250 2,440,980 43,649 53,177 I 30,373 3,546,253 64,083 3,649,449 40,376 50,015 K 42,682 659,152 153,577 875,652 68,800 90,547 N 26,853 3,087,222 43,145 3,178,573 53,324 66,068 Int. J. Anal. Appl. 16 (6) (2018) 939 INPUT AND OUTPUT FACTORS OF TARGET DMUs IN 2013 Companies Fix Assets Cost of goods sold Operating cost Net sales Net profits Operating profit A 2,368,444 7,011,191 1,194,639 10,363,418 2,179,191 2,586,225 B 11,209,745 5,065,121 830,907 6,263,118 531,710 495,135 C 466,150 5,895,935 379,110 6,585,110 261,684 318,832 D 173,294 3,668,449 531,103 4,768,477 446,820 580,370 E 537,410 2,343,321 185,888 2,638,857 115,398 140,514 F 57,542 1,861,569 57,992 1,939,946 21,348 25,760 G 17,316 579,585 112,844 735,370 40,451 46,074 H 61,656 2,447,841 48,183 2,542,168 36,380 48,519 I 44,993 3,218,254 76,630 3,336,440 31,409 42,486 K 76,255 731,509 145,336 959,652 80,543 105,472 N 23,564 2,811,818 44,765 2,890,025 30,394 40,606 Int. J. Anal. Appl. 16 (6) (2018) 940 INPUT AND OUTPUT FACTORS OF TARGET DMUs IN 2014 Companies Fix Assets Cost of goods sold Operating cost Net sales Net profits Operating profit A 2,295,454 7,121,096 1,276,866 9,548,850 1,134,458 1,557,395 B 11,004,157 4,586,281 840,164 6,044,143 820,887 798,534 C 426,608 5,696,732 336,303 6,377,225 288,549 356,146 D 207,529 3,856,523 587,436 4,985,068 438,723 553,003 E 519,572 1,962,180 180,825 2,237,982 100,898 115,315 F 299,256 2,503,864 72,899 2,655,043 64,419 84,372 G 15,787 533,179 106,828 682,933 36,468 44,322 H 56,177 2,252,616 46,832 2,348,012 40,198 51,855 I 52,297 2,712,487 69,519 2,821,395 29,570 39,741 K 19,131 713,894 144,563 929,122 85,211 87,618 N 38,205 2,470,498 42,643 2,548,198 31,887 40,914 Int. J. Anal. Appl. 16 (6) (2018) 941 INPUT AND OUTPUT FACTORS OF TARGET DMUs IN 2015 Companies Fix Assets Cost of goods sold Operating cost Net sales Net profits Operating profit A 1,853,676 6,612,424 1,355,133 9,764,947 1,522,461 1,855,678 B 9,848,606 3,950,628 1,145,494 5,582,239 712,460 712,527 C 652,335 5,278,378 425,014 6,037,884 280,234 337,002 D 191,584 3,673,450 590,926 4,651,235 306,285 391,334 E 159,206 2,118,099 141,198 2,337,950 86,046 99,837 F 171,237 3,319,407 113,278 3,516,965 77,278 93,609 G 11,508 427,693 83,221 532,533 17,638 21,653 H 50,728 2,369,227 51,944 2,452,136 27,958 34,392 I 50,050 2,562,297 78,202 2,673,131 27,286 33,264 K 17,974 722,029 164,166 956,801 65,183 81,636 N 34,790 2,519,510 46,905 2,600,069 32,042 37,566 Int. J. Anal. Appl. 16 (6) (2018) 942 INPUT AND OUTPUT FACTORS OF TARGET DMUs IN 2016 Companies Fix Assets Cost of goods sold Operating cost Net sales Net profits Operating profit A 1,910,477 5,528,946 1,248,517 7,924,787 1,164,775 1,385,216 B 8,754,407 3,595,508 963,306 4,910,171 624,340 632,709 C 742,125 5,038,820 489,927 5,942,917 350,100 421,064 D 193,750 3,233,437 562,608 3,964,661 138,150 171,686 E 150,386 2,105,100 149,510 2,338,362 90,589 102,510 F 272,675 4,300,199 224,435 4,495,270 13,561 16,690 G 9,559 447,691 75,801 546,139 19,334 23,145 H 45,939 1,910,249 60,932 1,997,252 25,168 31,289 I 35,167 2,071,763 69,801 2,165,958 23,353 26,457 K 16,853 689,058 176,225 907,609 44,432 54,398 N 31,797 2,153,810 56,339 2,237,995 28,117 35,149 Int. J. Anal. Appl. 16 (6) (2018) 943 FORECASTING RESULTS FOR DMUs FROM 2013 TO 2016 DMU s Fixed Assets Cost of goods sold Operating costs Net sales Net profits Operating profit Year s A 2,388,126.86 7,299,812.9 9 1,234,054.8 1 10,463,402.5 1 1,950,911.0 8 2,390,966.2 6 2013 2,189,047.14 6,788,028.1 8 1,256,913.7 3 9,718,506.95 1,607,186.3 0 1,977,823.3 6 2014 2,006,563.15 6,312,124.2 5 1,280,196.0 8 9,026,640.92 1,324,021.2 8 1,636,068.7 7 2015 1,839,291.45 5,869,585.6 1 1,303,909.6 9 8,384,029.22 1,090,746.2 1 1,353,367.0 8 2016 B 11,486,844.5 3 5,080,520.1 3 846,388.72 6,380,816.98 649,771.36 616,742.81 2013 10,583,070.0 2 4,516,601.3 7 908,876.29 5,902,217.90 664,610.90 644,613.17 2014 9,750,403.67 4,015,275.4 9 975,977.22 5,459,516.59 679,789.36 673,742.99 2015 8,983,250.76 3,569,594.9 1 1,048,032.1 0 5,050,020.50 695,314.46 704,189.16 2016 C 417,145.17 5,931,482.1 3 343,035.68 6,580,120.63 256,466.57 315,013.78 2013 504,910.07 5,617,066.4 1 382,407.74 6,344,543.24 280,494.99 342,049.55 2014 611,140.18 5,319,317.2 3 426,298.75 6,117,399.84 306,774.63 371,405.63 2015 739,720.48 5,037,351.1 2 475,227.36 5,898,388.48 335,516.41 403,281.17 2016 D 184,995.92 3,826,074.9 9 553,820.83 4,994,870.56 486,537.02 627,238.47 2013 Int. J. Anal. Appl. 16 (6) (2018) 944 189,288.48 3,676,682.1 8 563,175.00 4,716,012.59 366,273.13 467,820.04 2014 193,680.64 3,533,122.5 6 572,687.15 4,452,722.96 275,736.48 348,919.26 2015 198,174.71 3,395,168.3 6 582,359.97 4,204,132.48 207,578.99 260,238.22 2016 E 579,545.95 2,219,522.9 9 187,488.58 2,513,688.16 112,428.28 135,410.05 2013 379,916.84 2,160,113.2 6 171,051.66 2,427,931.32 102,310.31 120,290.25 2014 249,051.53 2,102,293.7 4 156,055.74 2,345,100.16 93,102.91 106,858.71 2015 163,263.79 2,046,021.8 7 142,374.50 2,265,094.85 84,724.13 94,926.93 2016 F 139,782.22 1,880,837.6 4 39,532.09 1,989,414.54 45,174.60 56,854.20 2013 175,054.39 2,472,442.7 4 66,606.59 2,608,910.65 44,489.72 55,683.47 2014 219,227.03 3,250,133.3 3 112,223.73 3,421,315.50 43,815.23 54,536.84 2015 274,546.03 4,272,441.3 6 189,082.87 4,486,700.12 43,150.96 53,413.83 2016 G 17,812.17 575,917.57 115,441.56 736,926.97 41,751.20 48,301.58 2013 14,580.27 519,408.91 100,242.40 655,519.01 31,148.48 36,887.10 2014 11,934.78 468,444.85 87,044.38 583,104.14 23,238.31 28,170.06 2015 9,769.29 422,481.34 75,584.03 518,688.91 17,336.94 21,513.00 2016 H 61,718.53 2,468,162.4 5 45,368.49 2,563,400.06 39,247.53 51,926.86 2013 55,948.66 2,312,659.2 49,477.75 2,404,278.59 34,290.40 44,241.91 2014 Int. J. Anal. Appl. 16 (6) (2018) 945 1 50,718.19 2,166,953.2 4 53,959.20 2,255,034.49 29,959.38 37,694.30 2015 45,976.70 2,030,427.2 8 58,846.56 2,115,054.62 26,175.39 32,115.70 2016 I 50,042.98 3,196,925.4 3 75,310.21 3,315,225.38 31,905.42 43,767.33 2013 46,980.56 2,791,367.2 9 74,115.19 2,902,910.81 29,065.35 37,687.57 2014 44,105.56 2,437,257.7 6 72,939.13 2,541,875.81 26,478.10 32,452.35 2015 41,406.49 2,128,070.1 5 71,781.73 2,225,742.73 24,121.15 27,944.36 2016 K 69,034.53 732,010.20 140,824.91 957,559.67 87,542.56 106,627.95 2013 32,660.79 719,943.09 151,388.03 944,591.68 73,706.82 88,350.10 2014 15,452.08 708,074.91 162,743.48 931,799.31 62,057.77 73,205.39 2015 7,310.51 696,402.38 174,950.69 919,180.19 52,249.80 60,656.74 2016 N 29,289.43 2,782,729.9 6 41,666.27 2,859,617.14 31,582.90 41,514.28 2013 31,086.36 2,576,154.4 7 45,397.65 2,655,768.12 30,924.88 39,474.13 2014 32,993.53 2,384,914.0 7 49,463.20 2,466,450.57 30,280.56 37,534.24 2015 35,017.71 2,207,870.3 8 53,892.83 2,290,628.60 29,649.67 35,689.69 2016 Int. J. Anal. Appl. 16 (6) (2018) 946 MAPE CALCULATING FOR DMUs FROM 2013 TO 2016 DMUs Fixed Assets Cost of goods sold Operating costs Net sales Net profits Operating profit Year A 0.831046126 4.116590049 3.299390862 0.9647832 10.475444 7.549951686 2013 4.635547643 4.677198847 1.562597015 1.7767265 41.669969 26.99561505 2014 8.247781831 4.541447342 5.529857586 7.5607792 13.034141 11.83444692 2015 3.726061535 6.161022481 4.436678796 5.7950103 6.3556301 2.29920229 2016 B 2.471952086 0.304022899 1.863231306 1.8792393 22.204088 24.56053657 2013 3.82661733 1.519305739 8.178437474 2.3481426 19.037468 19.27542536 2014 0.997119035 1.636385084 14.7985746 2.1984442 4.5856106 5.443163906 2015 2.61404069 0.720707464 8.795346636 2.8481595 11.367918 11.29747875 2016 C 10.51267363 0.60290911 9.515527255 0.0757674 1.9937899 1.197563902 2013 18.35457038 1.398443681 13.70928726 0.5124762 2.7912122 3.95805446 2014 6.314979658 0.775602403 0.302283726 1.3169487 9.4708804 10.20873198 2015 0.324004609 0.029151344 3.000373581 0.7492704 4.1655485 4.223307378 2016 D 6.75264103 4.296802082 4.277481516 4.747712 8.8888184 8.075619689 2013 8.789383771 4.663289108 4.129982405 5.3972264 16.513808 15.40370719 2014 1.094371267 3.82004489 3.086485535 4.2679427 9.9738885 10.83849993 2015 2.283723542 5.001840549 3.51078815 6.0401502 50.256233 51.57800809 2016 E 7.840559703 5.283015274 0.861046281 4.7432974 2.5734587 3.632341309 2013 26.87888539 10.08741602 5.404861424 8.4875268 1.3997435 4.314484942 2014 56.43350477 0.746200265 10.52263082 0.3058301 8.201324 7.033176797 2015 8.56315681 2.806428744 4.772587155 3.1332679 6.4741546 7.397391298 2016 F 142.9220754 1.035075386 31.83182459 2.5499955 111.61045 120.707288 2013 41.50346437 1.25491082 8.631675732 1.7375368 30.936956 34.00243411 2014 28.02549984 2.086929224 0.93069136 2.7196603 43.301808 41.73974439 2015 0.686175888 0.645496541 15.75161309 0.1906421 218.19896 220.0349318 2016 G 2.865376084 0.632767883 2.30190748 0.2117258 3.2142614 4.834787255 2013 7.643815581 2.58263864 6.164671664 4.0141558 14.586828 16.7747376 2014 Int. J. Anal. Appl. 16 (6) (2018) 947 3.708543236 9.52829413 4.594251804 9.4963393 31.751415 30.09770429 2015 2.199958954 5.631039699 0.286241911 5.0262094 10.329263 7.051216505 2016 H 0.101422786 0.830178572 5.841293482 0.8351949 7.8821559 7.023767879 2013 0.40646951 2.665488071 5.64944064 2.3963502 14.696244 14.6814982 2014 0.019338597 8.537542344 3.87956054 8.0379518 7.1585402 9.601931657 2015 0.08207085 6.291236393 3.422569495 5.8982354 4.0026662 2.64214953 2016 I 11.22391796 0.662737159 1.72228776 0.6358459 1.5804908 3.015896799 2013 10.16585478 2.908042972 6.611411841 2.8892025 1.7066201 5.167039374 2014 11.87701298 4.879966566 6.729845073 4.9101668 2.9608697 2.440034955 2015 17.7424437 2.717837439 2.837677776 2.7601978 3.2892842 5.621788834 2016 K 9.468852659 0.068515274 3.103902509 0.2180303 8.6904612 1.095976026 2013 70.72182241 0.847337559 4.721148677 1.6649781 13.500811 0.835561257 2014 14.03090946 1.932621349 0.866510581 2.6130502 4.7945484 10.32707351 2015 56.62193163 1.065858078 0.723112981 1.2749086 17.594975 11.50545964 2016 N 24.29736247 1.034492368 6.922215208 1.0521661 3.9116337 2.236813993 2013 18.63274851 4.27672745 6.459803005 4.2214194 3.0172939 3.519253898 2014 5.163756206 5.342147014 5.453997959 5.1390339 5.4972881 0.084534393 2015 10.12896285 2.50998816 4.341881054 2.3518195 5.451032 1.538273265 2016 Int. J. Anal. Appl. 16 (6) (2018) 948 MAPE RESULTS FOR DMUs FROM 2013 TO 2016 DMUs Fixed Assets Cost of goods sold Operating costs Net sales Net profits Operating profit Average MAPE of DMUs A 4.36010928 4.87406468 3.70713106 4.02432479 17.88379591 12.16980399 7.83653829 B 2.47743229 1.04510530 8.40889750 2.31849642 14.29877108 15.14415115 7.28214229 C 8.87655707 0.70152663 6.63186796 0.66361569 4.60535774 4.89691443 4.39597325 D 4.73002990 4.44549416 3.75118440 5.11325783 21.40818698 21.47395873 10.15368533 E 24.92902667 4.73076508 5.39028142 4.16748058 4.66217019 5.59434859 7.28214229 G 4.10442346 4.59368509 3.33676821 4.68710757 14.97044169 14.68961141 7.73033957 H 0.15232544 4.58111134 4.69821604 4.29193307 8.43490155 8.48733682 4.39597325 I 12.75230736 2.79214603 4.47530561 2.79885326 2.38431622 4.06118999 4.87735308 K 37.71087904 0.97858307 2.35366869 1.44274180 11.14519889 5.94101761 9.92868152 N 14.55570751 3.29083875 5.79447431 3.19110971 4.46931193 1.84471889 5.52436018