# Applying Data Envelopment Analysis and Grey Model for the Productivity Evaluation of Vietnamese Agroforestry Industry

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Research Procedure

## 4. Methodology

#### 4.1. Grey Forecasting Model

^{(1)}(k) is the mean value of two adjacent data, i.e.,:

#### 4.2. Malmquist Productivity Index

_{s}to outputs y

_{s}in the period s (note that DEA efficiency is considered a distance measure in the literature as it reflects the efficiency of converting inputs to outputs).

## 5. Empirical Results

_{1}’s historical data (2011–2014) used by the GM (1,1).

_{1}in Table 3 to illustrate the generation of the forecasting data of DMU

_{1}step-by-step.

- (1)
- Create the primitive series$${X}^{\left(0\right)}=\left(2,430,078,\text{}2,821,172,\text{}3,328,252,\text{}3,312,062\right)$$
- (2)
- Generate the accumulated series ${X}^{(1)}$$${X}^{\left(1\right)}=\left(2,430,078,\text{}5,251,250,\text{}8,579,502,\text{}11,891,564\right)$$Where$${X}^{(1)}(1)={X}^{(0)}(1)=2,430,078\phantom{\rule{0ex}{0ex}}{X}^{(1)}(2)={X}^{(0)}(1)+{X}^{\left(0\right)}(2)=5,251,250\phantom{\rule{0ex}{0ex}}{X}^{(1)}(3)={X}^{(0)}(1)+{X}^{\left(0\right)}(2)+{X}^{(0)}(3)=8,579,502\phantom{\rule{0ex}{0ex}}{X}^{(1)}(4)={X}^{(0)}(1)+{X}^{\left(0\right)}(2)+{X}^{(0)}(3)+{X}^{(0)}(4)=11,891,564$$
- (3)
- Create mean series dataset ${Z}^{(1)}$To find the mean series dataset ${Z}^{(1)}$, Equation (6) is used and we derive the following data.$${X}^{(1)}(1)={X}^{(0)}(1)=2,430,078\phantom{\rule{0ex}{0ex}}{Z}^{(1)}(2)=\frac{1}{2}(2,430,078+5,251,250)=3,840,664\phantom{\rule{0ex}{0ex}}{Z}^{(1)}(3)=\frac{1}{2}(5,251,250+8,579,502)=6,915,376\phantom{\rule{0ex}{0ex}}{Z}^{(1)}(4)=\frac{1}{2}(8,579,502+11,891,564)=10,235,533$$Then, ${Z}^{(1)}=({Z}^{(1)}(2),{Z}^{(1)}(3),{Z}^{(1)}(4))=\left(3,840,660,\text{}6,915,376,\text{}10,235,533\right).$
- (4)
- Find the values for coefficients a and bLet $B=\left[\begin{array}{c}-3,840,664\\ -6,915,376\\ -10,235,533\end{array}\begin{array}{c}1\\ 1\\ 1\end{array}\right]$, $\hat{\theta}=\left[\begin{array}{c}a\\ b\end{array}\right]$, ${y}_{N}=\left[\begin{array}{c}2,821,172\\ 3,328,252\\ 3,312,062\end{array}\right]$.Then, using the Equation (8), we can derived the values of a and b as below.$$\left[\begin{array}{c}a\\ b\end{array}\right]=\hat{\theta}={({B}^{T}B)}^{-1}{B}^{T}{y}_{N}=\left[\begin{array}{c}-0.0756791\\ 2,624,287.78\end{array}\right]$$
- (5)
- Generate the accumulated data seriesSubstitute the two coefficients a and b, as well as the k values (k = 0, …, 7), into the Equation (9); then we can derive the accumulated data series in the third column in Table 4.
- (6)
- Generate the series values of predictionSubstitute the two coefficients a and b, as well as the k values (k = 0, …, 7) into the Equation (11); then we can the derive the fifth column in Table 4.

_{3}, DMU

_{4}, and DMU

_{8}. DMU

_{3}had experienced a dramatic efficiency rise during the time period 2011–2015, and DMU

_{4}experienced a dramatic efficiency drop during the time period 2015–2016, while the DMU

_{8}had experienced a dramatic drop during the time period 2014–2015. Except for DMU

_{2}and DMU

_{6}, which had experienced slight efficiency changes, the other DMUs all had experienced some degree of efficiency fluctuations. In terms of “efficiency change”, DMU

_{9}, DMU

_{4}, and DMU

_{6}are the top three best companies, while the top three worst companies are DMU

_{3}, DMU

_{7}, and DMU

_{1}. DMU

_{2}is found with a stable efficiency, but it also had not improved its efficiency in the current and near future. From Figure 2, we can determine and predict the efficiency changes, or the “catch-up” effects, of each DMU.

_{5}, other DMUs had experienced an upward technological change, though most of them had experienced an efficiency drop during 2013–2014. This implies most of these DMUs had continued to improve their technological capabilities. DMU

_{5}always keeps a lower “technological changes” score, indicating that it has not actively improved its technology. Thus, DMU

_{5}requires further investigation into the causes that lead to its tardiness on technology development. In terms of “technological change”, DMU

_{10}, DMU

_{4}, and DMU

_{9}are the top three best companies, while the top three worst companies are DMU

_{5}, DMU

_{1}, and DMU

_{8}.

_{6}and DMU

_{9}had a long-term upward trend during 2011–2016, though DMU

_{6}had experienced a drop during 2013–2014. In terms of MPI, DMU

_{9}, DMU

_{4}, and DMU

_{10}are the top three best companies, while the top three worst companies are DMU

_{5}, DMU

_{1}, and DMU

_{7}. DMU

_{8}appears unstable due to having the largest fluctuation; thus, it requires intense care for its development. In summary, to sustain the development of the agroforestry industry, the Vietnamese government needs to especially focus on DMU

_{5}, DMU

_{1}, DMU

_{7}, and DMU

_{8}.

## 6. Conclusions

_{5}, DMU

_{1}, DMU

_{7}, and DMU

_{8}.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

DEA | data envelopment analysis |

GM | grey model |

MPI | Malmquist productivity index |

DMU | decision making unit |

CCR | Charnes, Cooper and Rhodes |

BCC | Banker, Charnes and Cooper |

MAPE | mean absolute percent error |

CRS | constant returns to scale |

VRS | variable returns to scale |

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Number Order | DMU | Company Name | Stock Market Code |
---|---|---|---|

1 | DMU_{1} | Dong Phu Rubber Joint Stock Company | HOSE: DPR |

2 | DMU_{2} | HAGL Joint Stock Company | HOSE: HAG |

3 | DMU_{3} | Hoa Binh Rubber Joint Stock Company | HOSE: HRC |

4 | DMU_{4} | National Seed Joint Stock Company | HOSE: NSC |

5 | DMU_{5} | Phuoc Hoa Rubber Joint Stock Company | HOSE: PHR |

6 | DMU_{6} | Southern Seed Corporation | HOSE: SSC |

7 | DMU_{7} | Thong Nhat Rubber Joint Stock Company | HOSE: TNC |

8 | DMU_{8} | Tay Ninh Rubber Joint Stock Company | HOSE: TRC |

9 | DMU_{9} | Quang Nam Rubber Investment JSC | HOSE: VHG |

10 | DMU_{10} | Vinacafe Son Thanh Joint Stock Company | OTC: AUM |

DMU_{s} | Inputs ( Millions of VND) | Outputs (Millions of VND) | |||
---|---|---|---|---|---|

(I) Total Asset | (I) Liabilities | (I) Equity | (O) Net Revenue | (O) Gross Profit | |

DMU_{1} | 3,312,062 | 658,039 | 2,195,471 | 938,682 | 285,480 |

DMU_{2} | 36,368,864 | 20,978,624 | 14,237,728 | 3,054,331 | 1,226,993 |

DMU_{3} | 686,336 | 181,918 | 504,418 | 161,394 | 7059 |

DMU_{4} | 953,008 | 202,337 | 744,946 | 719,136 | 287,323 |

DMU_{5} | 3,428,830 | 1,129,528 | 2,253,082 | 1,604,981 | 275,288 |

DMU_{6} | 537,355 | 162,978 | 373,160 | 608,625 | 190,717 |

DMU_{7} | 332,605 | 30,901 | 301,704 | 63,873 | −355 |

DMU_{8} | 1,587,255 | 140,308 | 1,446,947 | 500,638 | 121,259 |

DMU_{9} | 1,071,970 | 126,832 | 900,392 | 394,873 | 46,077 |

DMU_{10} | 13,283 | 2675 | 10,608 | 21,611 | 158 |

DMU_{1} | Inputs (Millions of VND) | Outputs (Millions of VND) | |||
---|---|---|---|---|---|

(I) Total Asset | (I) Liabilities | (I) Equity | (O) Net Revenue | (O) Gross Profit | |

2011 | 2,430,078 | 491,056 | 1,910,113 | 1,837,202 | 866,224 |

2012 | 2,821,172 | 556,960 | 2,179,990 | 1,376,951 | 553,307 |

2013 | 3,328,252 | 606,600 | 2,298,599 | 1,100,122 | 424,953 |

2014 | 3,312,062 | 658,039 | 2,195,471 | 938,682 | 285,480 |

k | X(k) | Value | X(k) | Value |
---|---|---|---|---|

k = 0 | X(1) | 2,430,078 | X(1) | 2,430,078 |

k = 1 | X(2) | 5,347,264.63 | X(2) | 2,917,186.63 |

k = 2 | X(3) | 8,493,789.83 | X(3) | 3,146,525.2 |

k = 3 | X(4) | 11,887,683.4 | X(4) | 3,393,893.54 |

k = 4 | X(5) | 15,548,392.5 | X(5) | 3,660,709.08 |

k = 5 | X(6) | 19,496,893.1 | X(6) | 3,948,500.68 |

k = 6 | X(7) | 23,755,810.6 | X(7) | 4,258,917.41 |

k = 7 | X(8) | 28,349,548.5 | X(8) | 4,593,737.97 |

Year | DMU_{s} | Inputs (Currency Unit: Millions of VND) | Outputs (Currency Unit: Millions of VND) | |||
---|---|---|---|---|---|---|

(I) Total Asset | (I) Liabilities | (I) Equity | (O) Net Revenue | (O) Gross Profit | ||

2015 | DMU_{1} | 3,660,709.08 | 715,051.35 | 2,239,955.23 | 759,042.36 | 216,764.72 |

DMU_{2} | 38,126,475.9 | 19,810,053.2 | 17,301,061.4 | 2,169,114.51 | 1,234,682.16 | |

DMU_{3} | 710,528.52 | 192,011.93 | 518,491.25 | 140,856.83 | 2963.25 | |

DMU_{4} | 1,427,295.43 | 256,101.60 | 1,160,150.10 | 816,038.05 | 343,084.35 | |

DMU_{5} | 3,646,880.39 | 1,210,168.95 | 2,382,125.12 | 1,369,690.16 | 209,289.74 | |

DMU_{6} | 601,752.38 | 169,376.87 | 436,089.19 | 715,599.93 | 213,766.23 | |

DMU_{7} | 308,391.58 | 21,024.41 | 288,886.80 | 49,637.40 | 1344.39 | |

DMU_{8} | 1,765,695.56 | 259,012.54 | 1,529,264.81 | 370,704.24 | 80,840.40 | |

DMU_{9} | 1,534,558.85 | 108,114.20 | 1,366,325.23 | 584,979.71 | 43,400.28 | |

DMU_{10} | 13,221.75 | 2551.08 | 10,749.15 | 24,795.80 | 177.04 | |

2016 | DMU_{1} | 3,948,500.68 | 777,109.40 | 2,247,634.11 | 624,477.72 | 158,370.95 |

DMU_{2} | 41,364,890.23 | 20,100,095.76 | 20,670,001.67 | 1,748,357.56 | 1,248,329.47 | |

DMU_{3} | 725,873.82 | 196,885.59 | 528,955.14 | 91,601.17 | 1261.76 | |

DMU_{4} | 2,418,284.18 | 349,367.53 | 2,116,736.15 | 939,274.77 | 412,839.94 | |

DMU_{5} | 3,829,240.64 | 1,250,205.83 | 2,512,384.37 | 1,167,365.28 | 142,525.83 | |

DMU_{6} | 678,367.07 | 173,410.58 | 517,540.57 | 813,804.44 | 242,919.54 | |

DMU_{7} | 288,308.59 | 15,960.23 | 276,386.25 | 31,491.09 | 398.52 | |

DMU_{8} | 1,816,554.47 | 248,283.06 | 1,606,736.41 | 275,684.53 | 52,543.82 | |

DMU_{9} | 2,386,716.78 | 101,837.68 | 2,318,982.81 | 971,069.14 | 138,457.14 | |

DMU_{10} | 12,975.19 | 2287.63 | 10,853.25 | 29,651.57 | 109.37 |

DMU_{s} | MAPE | DMU_{s} | MAPE |
---|---|---|---|

DMU_{1} | 1.626% | DMU_{6} | 7.792% |

DMU_{2} | 5.663% | DMU_{7} | 2.069% |

DMU_{3} | 2.256% | DMU_{8} | 1.124% |

DMU_{4} | 4.001% | DMU_{9} | 14.513% |

DMU_{5} | 5.021% | DMU_{10} | 7.046% |

Average MAPE: 5.111% |

2011 | Total Asset | Liabilities | Equity | Net Revenue | Gross Profit |

Total asset | 1 | 0.997951 | 0.993387 | 0.755161 | 0.781175 |

Liabilities | 0.997951 | 1 | 0.98401 | 0.719137 | 0.744403 |

Equity | 0.993387 | 0.98401 | 1 | 0.81337 | 0.840045 |

Net Revenue | 0.755161 | 0.719137 | 0.81337 | 1 | 0.99058 |

Gross profit | 0.781175 | 0.744403 | 0.840045 | 0.99058 | 1 |

2012 | Total Asset | Liabilities | Equity | Net Revenue | Gross Profit |

Total asset | 1 | 0.997593 | 0.987721 | 0.916987 | 0.865799 |

Liabilities | 0.997593 | 1 | 0.97452 | 0.892273 | 0.832981 |

Equity | 0.987721 | 0.97452 | 1 | 0.957569 | 0.924983 |

Net Revenue | 0.916987 | 0.892273 | 0.957569 | 1 | 0.983508 |

Gross profit | 0.865799 | 0.832981 | 0.924983 | 0.983508 | 1 |

2013 | Total Asset | Liabilities | Equity | Net Revenue | Gross Profit |

Total asset | 1 | 0.997283 | 0.997084 | 0.847284 | 0.927948 |

Liabilities | 0.997283 | 1 | 0.988945 | 0.821053 | 0.90642 |

Equity | 0.997084 | 0.988945 | 1 | 0.874179 | 0.946157 |

Net Revenue | 0.847284 | 0.821053 | 0.874179 | 1 | 0.967438 |

Gross profit | 0.927948 | 0.90642 | 0.946157 | 0.967438 | 1 |

2014 | Total Asset | Liabilities | Equity | Net Revenue | Gross Profit |

Total asset | 1 | 0.998139 | 0.99682 | 0.901523 | 0.964055 |

Liabilities | 0.998139 | 1 | 0.990301 | 0.88317 | 0.955216 |

Equity | 0.99682 | 0.990301 | 1 | 0.923212 | 0.970017 |

Net Revenue | 0.901523 | 0.88317 | 0.923212 | 1 | 0.956117 |

Gross profit | 0.964055 | 0.955216 | 0.970017 | 0.956117 | 1 |

2015 | Total Asset | Liabilities | Equity | Net Revenue | Gross Profit |

Total asset | 1 | 0.998182 | 0.998555 | 0.829165 | 0.960343 |

Liabilities | 0.998182 | 1 | 0.993988 | 0.810135 | 0.955803 |

Equity | 0.998555 | 0.993988 | 1 | 0.846913 | 0.961551 |

Net Revenue | 0.829165 | 0.810135 | 0.846913 | 1 | 0.895381 |

Gross profit | 0.960343 | 0.955803 | 0.961551 | 0.895381 | 1 |

2016 | Total Asset | Liabilities | Equity | Net Revenue | Gross Profit |

Total asset | 1 | 0.997754 | 0.998123 | 0.722542 | 0.95035 |

Liabilities | 0.997754 | 1 | 0.992805 | 0.693972 | 0.94331 |

Equity | 0.998123 | 0.992805 | 1 | 0.749176 | 0.955682 |

Net Revenue | 0.722542 | 0.693972 | 0.749176 | 1 | 0.818206 |

Gross profit | 0.95035 | 0.94331 | 0.955682 | 0.818206 | 1 |

Catch-up | ||||||

DMUs | 2011–2012 | 2012–2013 | 2013–2014 | 2014–2015 | 2015–2016 | Average |

DMU_{1} | 0.829064 | 1.017534 | 0.481122 | 0.480225 | 0.588611 | 0.679311 |

DMU_{2} | 1 | 1 | 1 | 1 | 1 | 1 |

DMU_{3} | 0.507493 | 0.750196 | 0.49117 | 0.769674 | 0.560938 | 0.615894 |

DMU_{4} | 1.50032 | 1.511764 | 1.219231 | 1.639257 | 0.924659 | 1.359046 |

DMU_{5} | 0.734399 | 1.295857 | 0.878322 | 1.130413 | 0.69098 | 0.945994 |

DMU_{6} | 0.654229 | 1.36234 | 1.36408 | 1.353088 | 1.36118 | 1.218983 |

DMU_{7} | 0.464872 | 0.938184 | 0.522882 | 0.827553 | 0.431461 | 0.63699 |

DMU_{8} | 1.311197 | 0.251778 | 1.519396 | 0.453193 | 0.694019 | 0.845917 |

DMU_{9} | 0.642412 | 1.125074 | 1.68504 | 2.313033 | 2.063988 | 1.565909 |

DMU_{10} | 1.146358 | 0.860033 | 1.023463 | 0.897824 | 0.935341 | 0.972604 |

Frontier | ||||||

DMUs | 2011–2012 | 2012–2013 | 2013–2014 | 2014–2015 | 2015–2016 | Average |

DMU_{1} | 0.294275 | 0.492147 | 0.572874 | 1.042527 | 1.166415 | 0.713647 |

DMU_{2} | 1 | 1.046866 | 0.925847 | 1 | 1 | 0.994543 |

DMU_{3} | 1.069373 | 1.016991 | 0.825623 | 1.08088 | 1.072451 | 1.013064 |

DMU_{4} | 0.883812 | 0.963577 | 0.776533 | 1.286913 | 1.603398 | 1.102847 |

DMU_{5} | 0.402361 | 0.358968 | 0.521382 | 0.392711 | 0.455877 | 0.42626 |

DMU_{6} | 1.107621 | 1.001566 | 0.74005 | 1.023985 | 1.10437 | 0.995519 |

DMU_{7} | 1.037761 | 1.067316 | 0.643354 | 1.156675 | 1.334136 | 1.047848 |

DMU_{8} | 0.730453 | 0.954731 | 0.791898 | 1.093495 | 1.05964 | 0.926043 |

DMU_{9} | 1.115798 | 1.024782 | 0.796385 | 1.072349 | 1.343707 | 1.070604 |

DMU_{10} | 1.063773 | 1.049261 | 1.178219 | 1.181882 | 1.223364 | 1.1393 |

MPI | ||||||

DMUs | 2011–2012 | 2012–2013 | 2013–2014 | 2014–2015 | 2015–2016 | Average |

DMU_{1} | 0.243973 | 0.500777 | 0.275622 | 0.500648 | 0.686564 | 0.441517 |

DMU_{2} | 1 | 1.046866 | 0.925847 | 1 | 1 | 0.994543 |

DMU_{3} | 0.542699 | 0.762943 | 0.405521 | 0.831925 | 0.601579 | 0.628934 |

DMU_{4} | 1.326001 | 1.456701 | 0.946773 | 2.109581 | 1.482596 | 1.464331 |

DMU_{5} | 0.295494 | 0.465171 | 0.457941 | 0.443925 | 0.315002 | 0.395506 |

DMU_{6} | 0.724637 | 1.364473 | 1.009488 | 1.385542 | 1.503246 | 1.197477 |

DMU_{7} | 0.482426 | 1.001338 | 0.336398 | 0.957209 | 0.575628 | 0.6706 |

DMU_{8} | 0.957768 | 0.24038 | 1.203207 | 0.495564 | 0.73541 | 0.726466 |

DMU_{9} | 0.716802 | 1.152955 | 1.34194 | 2.480379 | 2.773395 | 1.693094 |

DMU_{10} | 1.219464 | 0.902399 | 1.205864 | 1.061122 | 1.144262 | 1.106622 |

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Wang, C.-N.; Lin, H.-S.; Hsu, H.-P.; Le, V.-T.; Lin, T.-F.
Applying Data Envelopment Analysis and Grey Model for the Productivity Evaluation of Vietnamese Agroforestry Industry. *Sustainability* **2016**, *8*, 1139.
https://doi.org/10.3390/su8111139

**AMA Style**

Wang C-N, Lin H-S, Hsu H-P, Le V-T, Lin T-F.
Applying Data Envelopment Analysis and Grey Model for the Productivity Evaluation of Vietnamese Agroforestry Industry. *Sustainability*. 2016; 8(11):1139.
https://doi.org/10.3390/su8111139

**Chicago/Turabian Style**

Wang, Chia-Nan, Han-Sung Lin, Hsien-Pin Hsu, Van-Tinh Le, and Tsung-Fu Lin.
2016. "Applying Data Envelopment Analysis and Grey Model for the Productivity Evaluation of Vietnamese Agroforestry Industry" *Sustainability* 8, no. 11: 1139.
https://doi.org/10.3390/su8111139