# A New DEA Model for Evaluation of Supply Chains: A Case of Selection and Evaluation of Environmental Efficiency of Suppliers

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## Abstract

**:**

## 1. Introduction

## 2. Previous Research

#### Methodology of Literature Review

## 3. Results of the Literature Review and Classification

#### 3.1. Efficiency and Performance Evaluation of SC with the DEA Method

#### 3.2. Application of DEA in the Evaluation of SC Parts

#### 3.3. Application of DEA in SC Network Design

#### 3.4. Evaluation of Information Sharing in SC with DEA

#### 3.5. Application of DEA in Sustainable SCM

#### 3.6. Non-Categorized Works

## 4. The Proposal of a Non-Radial DEA Model in SC

#### A Brief Description of the Non-Radial DEA Model

## 5. Illustration of Application of the Non-Radial Model M—Numerical Example

_{2}) emission as undesirable output. However, for the application of model M, energy consumption was used as an undesirable input.

#### Validation of Non-Radial DEA Model M

## 6. Discussion

_{n}and weight W

_{n}in terms of desirable inputs, an unreal picture regarding the efficiency can be presented. With model M, the consideration of environmental evaluation and selection of supplier and other components of SC regarding sustainability is more precise, providing better relative efficiency. Further, through the selection of the set of preference weights, the degree of desirability of the adjustment of the input and output levels can be achieved. Therefore, the selection of the weight, for example, for undesirable output, will affect the reduction of that output. Consequently, based on their preferences and the goal of evaluation, decision makers should select weights carefully because the selection of weights can influence the results of model M. In this paper, all weights were selected to be 1/3.

_{2}, as well as Number of employees in comparison with other suppliers.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Table 1.**Dataset taken from Mahdiloo et al. [5] for application of model M.

Suppliers | Number of Employees (N1) | Energy Consumption (kWh/year) (L1) | Sales (1000 Korean Won) (M1) | ROA (M2) | Environmental R&D Investment (100,000 Korean Won) (M3) | CO_{2} (kg) (J1) |
---|---|---|---|---|---|---|

1 | 1112 | 1267 | 119,477 | 0.04046 | 67 | 43,562 |

2 | 118 | 968 | 125,762 | 0.04499 | 65 | 45,000 |

3 | 458 | 1001 | 58,770 | 0.02221 | 57 | 42,400 |

4 | 416 | 1393 | 62,989 | 0.02920 | 62 | 43,734 |

5 | 413 | 1586 | 67,088 | 0.03269 | 50 | 44,890 |

6 | 430 | 1802 | 72,318 | 0.03116 | 36 | 42,913 |

7 | 426 | 1998 | 74,626 | 0.02184 | 47 | 39,438 |

8 | 452 | 1824 | 74,476 | 0.0348 | 44 | 40,078 |

9 | 503 | 1479 | 79,710 | 0.03976 | 47 | 39,500 |

10 | 498 | 1623 | 79,384 | 0.03723 | 89 | 45,023 |

11 | 192 | 1322 | 73,124 | 0.01269 | 256 | 41,324 |

12 | 171 | 831 | 62,529 | 0.00385 | 423 | 45,000 |

13 | 163 | 913 | 65,424 | 0.02776 | 508 | 42,400 |

14 | 161 | 893 | 71,027 | 0.04847 | 536 | 43,734 |

15 | 161 | 903 | 74,093 | 0.0514 | 570 | 44,890 |

16 | 162 | 778 | 72,830 | 0.04356 | 472 | 42,913 |

17 | 159 | 710 | 71,940 | 0.03932 | 426 | 39,438 |

18 | 157 | 695 | 82,203 | 0.02599 | 386 | 40,078 |

19 | 151 | 637 | 55,681 | 0.00001 | 376 | 39,500 |

20 | 151 | 781 | 64,839 | 0.02742 | 369 | 38,570 |

**Table 2.**Results of the efficiency from models 2, 4, and 5 presented in Mahdiloo et al. [5] and model M.

Suppliers | Technical Efficiency (Model 2) | Environmental Efficiency (Model 4) | Eco-Efficiency (Model 5) | Model M |
---|---|---|---|---|

1 | 0.73 | 0.99 | 0.99 | 0.60 |

2 | 1.00 | 1.00 | 1.00 | 1.00 |

3 | 0.47 | 0.52 | 0.52 | 0.37 |

4 | 0.40 | 0.63 | 0.63 | 0.41 |

5 | 0.39 | 0.68 | 0.68 | 0.44 |

6 | 0.34 | 0.69 | 0.69 | 0.42 |

7 | 0.29 | 0.68 | 0.68 | 0.38 |

8 | 0.37 | 0.82 | 0.82 | 0.47 |

9 | 0.50 | 0.93 | 0.93 | 0.56 |

10 | 0.44 | 0.78 | 0.78 | 0.48 |

11 | 0.55 | 0.80 | 0.80 | 0.62 |

12 | 0.83 | 0.79 | 0.83 | 0.80 |

13 | 0.88 | 0.94 | 0.94 | 0.90 |

14 | 0.96 | 0.98 | 0.98 | 0.96 |

15 | 1.00 | 1.00 | 1.00 | 1.00 |

16 | 1.00 | 0.95 | 1.00 | 0.97 |

17 | 1.00 | 0.99 | 1.00 | 0.98 |

18 | 1.00 | 1.00 | 1.00 | 1.00 |

19 | 0.96 | 0.80 | 0.96 | 0.85 |

20 | 0.84 | 0.89 | 0.89 | 0.89 |

Suppliers | Case 1 (C1) | Case 2 (C2) | Case 3 (C3) | Remarks ^{1} | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

2% | 5% | 10% | 2% | 5% | 10% | 2% | 5% | 10% | 2% | 5% | 10% | |

1 | 0.63 | 0.67 | 0.74 | 0.63 | 0.66 | 0.73 | 0.63 | 0.67 | 0.75 | C1=C2=C3 | C1>C2<C3 | C3>C1<C2 |

2 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | C1=C2=C3 | C1=C2=C3 | C1=C2=C3 |

3 | 0.39 | 0.41 | 0.45 | 0.39 | 0.40 | 0.44 | 0.39 | 0.41 | 0.46 | C1=C2=C3 | C1>C2<C3 | C3>C1>C2 |

4 | 0.43 | 0.45 | 0.47 | 0.43 | 0.44 | 0.46 | 0.43 | 0.45 | 0.48 | C1=C2=C3 | C1>C2<C3 | C3>C1>C2 |

5 | 0.45 | 0.47 | 0.49 | 0.45 | 0.46 | 0.48 | 0.45 | 0.47 | 0.50 | C1=C2=C3 | C1>C2<C3 | C3>C1>C2 |

6 | 0.43 | 0.45 | 0.48 | 0.43 | 0.45 | 0.47 | 0.43 | 0.45 | 0.49 | C1=C2=C3 | C1=C2=C3 | C3>C1>C2 |

7 | 0.40 | 0.42 | 0.46 | 0.39 | 0.41 | 0.45 | 0.40 | 0.43 | 0.48 | C1>C2<C3 | C3>C1>C2 | C3>C1>C2 |

8 | 0.49 | 0.51 | 0.53 | 0.49 | 0.50 | 0.53 | 0.49 | 0.51 | 0.54 | C1=C2=C3 | C1>C2<C3 | C1<C3>C2 |

9 | 0.58 | 0.60 | 0.63 | 0.58 | 0.60 | 0.62 | 0.58 | 0.60 | 0.63 | C1=C2=C3 | C1=C2=C3 | C1>C2<C3 |

10 | 0.50 | 0.52 | 0.55 | 0.50 | 0.51 | 0.54 | 0.50 | 0.52 | 0.55 | C1=C2=C3 | C1>C2<C3 | C1>C2<C3 |

11 | 0.65 | 0.67 | 0.69 | 0.64 | 0.66 | 0.68 | 0.66 | 0.67 | 0.71 | C3>C1>C2 | C1>C2<C3 | C3>C1>C2 |

12 | 0.83 | 0.83 | 0.83 | 0.82 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | C1>C2<C3 | C1=C2=C3 | C1=C2=C3 |

13 | 0.94 | 0.95 | 0.95 | 0.93 | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 | C3>C1<C2 | C1=C2=C3 | C1=C2=C3 |

14 | 1.00 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | C1>C2<C3 | C1=C2=C3 | C1=C2=C3 |

15 | 1.00 | 0.95 | 0.86 | 1.00 | 0.98 | 0.92 | 1.00 | 0.92 | 0.81 | C1=C2=C3 | C2>C1>C3 | C2>C1>C3 |

16 | 1.00 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | C1=C2=C3 | C1=C2=C3 | C1=C2=C3 |

17 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | C1=C2=C3 | C1=C2=C3 | C1=C2=C3 |

18 | 1.00 | 0.97 | 0.89 | 1.00 | 0.99 | 0.94 | 1.00 | 0.94 | 0.84 | C1=C2=C3 | C2>C1>C3 | C2>C1>C3 |

19 | 0.88 | 0.88 | 0.88 | 0.87 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 | C1>C2<C3 | C1=C2=C3 | C1=C2=C3 |

20 | 0.88 | 0.88 | 0.89 | 0.87 | 0.88 | 0.89 | 0.88 | 0.88 | 0.89 | C1>C2<C3 | C1=C2=C3 | C1=C2=C3 |

^{1}Remarks: Show the relationships between the results of the efficiency calculated for each supplier and for each data perturbation through Cases 1, 2, and 3.

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**MDPI and ACS Style**

Krmac, E.; Djordjević, B.
A New DEA Model for Evaluation of Supply Chains: A Case of Selection and Evaluation of Environmental Efficiency of Suppliers. *Symmetry* **2019**, *11*, 565.
https://doi.org/10.3390/sym11040565

**AMA Style**

Krmac E, Djordjević B.
A New DEA Model for Evaluation of Supply Chains: A Case of Selection and Evaluation of Environmental Efficiency of Suppliers. *Symmetry*. 2019; 11(4):565.
https://doi.org/10.3390/sym11040565

**Chicago/Turabian Style**

Krmac, Evelin, and Boban Djordjević.
2019. "A New DEA Model for Evaluation of Supply Chains: A Case of Selection and Evaluation of Environmental Efficiency of Suppliers" *Symmetry* 11, no. 4: 565.
https://doi.org/10.3390/sym11040565