# An Interactive Decision-Making Method for Third-Party Logistics Provider Selection under Hybrid Multi-Criteria

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Selection Criteria for 3PL Providers

#### 2.2. Related Definitions

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

- (1)
- $d({H}_{1},{H}_{2})\ge 0$;
- (2)
- $d({H}_{1},{H}_{2})=0$if and only if${H}_{1}={H}_{2}$;
- (3)
- $d({H}_{1},{H}_{2})=d({H}_{2},{H}_{1})$.

**Definition**

**4.**

**Definition**

**5.**

**Definition**

**6.**

- (1)
- $d({I}_{1},{I}_{2})\ge 0$;
- (2)
- $d({I}_{1},{I}_{2})=0$if and only if${I}_{1}={I}_{2}$;
- (3)
- $d({I}_{1},{I}_{2})=d({I}_{2},{I}_{1})$.

**Definition**

**7.**

## 3. Interactive HMCDM Method

#### 3.1. Description of a HMCDM Problem

#### 3.2. Setting the Ideal Solution of Hybrid Multi-Criteria

#### 3.3. Interactive Decision-Making Process

- (1)
- $\{{w}_{{j}_{1}}\ge {w}_{{j}_{2}}\}({j}_{1}\ne {j}_{2})$;
- (2)
- $\{{w}_{{j}_{1}}-{w}_{{j}_{2}}\ge \alpha \}({j}_{1}\ne {j}_{2};\alpha >0)$;
- (3)
- $\{{w}_{{j}_{1}}-{w}_{{j}_{2}}\ge {w}_{{j}_{3}}-{w}_{{j}_{4}}\}({j}_{1}\ne {j}_{2}\ne {j}_{3}\ne {j}_{4})$;
- (4)
- $\{{w}_{{j}_{1}}\ge \alpha {w}_{{j}_{2}}\}({j}_{1}\ne {j}_{2};0\le \alpha \le 1)$;
- (5)
- $\{\alpha \le {w}_{j}\le \alpha +\beta \}(0\le \alpha \le \alpha +\beta \le 1)$

## 4. Case Study

## 5. Sensitivity Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Variable | Criterion | Definition | Authors |
---|---|---|---|

Y_{1} | Total assets | All assets owned by a logistics enterprise | Wang et al. [14], Prakash and Barua [16], Huang et al. [18], Guarnieri et al. [63], Aguezzoul and Aicha [64] |

Y_{2} | Transport cost | Costs related to logistics activities | Stefan et al. [9], Yu et al. [12], Patricija and Suban [13], Sremac et al. [15], Guarnieri et al. [63], Zarbakhshnia et al. [65] |

Y_{3} | On time rate | Logistics delivery on time rate | Stefan et al. [9], Patricija and Suban [13], Sremac et al. [15], Guarnieri et al. [63], Zarbakhshnia et al. [65], Li et al. [66] |

Y_{4} | Customer satisfaction | Matching degree of customer expectation and customer experience | Patricija and Suban et al. [13], Guarnieri et al. [63], Aguezzoul and Aicha [64], Zarbakhshnia et al. [65], Li et al. [66] Senthil et al. [67], Zouggari and Benyoucef [68] |

Y_{5} | Personalized service | Diversification degree of logistics products and services | Prakash and Barua [20], Guarnieri et al. [63], Aguezzoul and Aicha [64], Zarbakhshnia et al. [65], Li et al. [66], Senthil et al. [67], Zouggari and Benyoucef [68] |

Y_{6} | User compatibility | Degree of information sharing with user | Shan [29], Feng et al. [69] |

Y_{7} | Transport equipment | Number of transportation equipment | Shan [29], Feng et al. [69] |

Y_{8} | Employee structure | Proportion of employees with bachelor degree or above in the total number of employees | Sremac et al. [15], Huang et al. [18], Guarnieri et al. [63], Zarbakhshnia [65], Li et al. [66], Senthil [67] |

Y_{9} | Technology level | Technical development ability to monitor and implement logistics activities | Stefan et al. [9], Sremac et al. [15], Prakash and Barua et al. [20], Guarnieri et al. [63], Aguezzoul and Aicha [64], Arpachshad et al. [65] |

Alternative | Criteria | ||||
---|---|---|---|---|---|

Y_{1} | Y_{2} | Y_{3} | Y_{4} | Y_{5} | |

X_{1} | 0.57 | 0.45 | (0.8, 0.2) | (0.7, 0.75, 0.8, 0.9) | (0.5, 0.7, 0.9, 0.9) |

X_{2} | 0.48 | 0.47 | (0.6, 0.4) | (0.6, 0.7, 0.7, 0.7) | (0.3, 0.5, 0.5, 0.5) |

X_{3} | 0.66 | 0.46 | (0.6, 0.4) | (0.7, 0.75, 0.8, 0.8) | (0.5, 0.7, 0.9, 0.9) |

X_{4} | 0.08 | 0.33 | (0.8, 0.2) | (0.6, 0.7, 0.8, 0.8) | (0.5, 0.7, 0.9, 0.9) |

X_{5} | 0.01 | 0.51 | (0.6, 0.4) | (0.1, 0.2, 0.2, 0.2) | (0.5, 0.7, 0.9, 0.9) |

Parameter | Satisfaction | Ranking Order | ||||
---|---|---|---|---|---|---|

${\mathit{S}}_{1}({\mathit{w}}^{0})$ | ${\mathit{S}}_{2}({\mathit{w}}^{0})$ | ${\mathit{S}}_{3}({\mathit{w}}^{0})$ | ${\mathit{S}}_{4}({\mathit{w}}^{0})$ | ${\mathit{S}}_{5}({\mathit{w}}^{0})$ | ||

$\theta =0.3$ | 0.8032 | 0.712 | 0.7848 | 0.7028 | 0.6026 | ${X}_{1}>{X}_{3}>{X}_{2}>{X}_{4}>{X}_{5}$ |

$\theta =0.4$ | 0.7292 | 0.626 | 0.7067 | 0.6127 | 0.4933 | ${X}_{1}>{X}_{3}>{X}_{2}>{X}_{4}>{X}_{5}$ |

$\theta =0.5$ | 0.6422 | 0.5334 | 0.6163 | 0.5133 | 0.3936 | ${X}_{1}>{X}_{3}>{X}_{2}>{X}_{4}>{X}_{5}$ |

$\theta =0.6$ | 0.5448 | 0.4365 | 0.5171 | 0.4128 | 0.3021 | ${X}_{1}>{X}_{3}>{X}_{2}>{X}_{4}>{X}_{5}$ |

$\theta =0.7$ | 0.4284 | 0.3331 | 0.4011 | 0.3028 | 0.2178 | ${X}_{1}>{X}_{3}>{X}_{2}>{X}_{4}>{X}_{5}$ |

Limit | Satisfaction | Ranking Order | ||||
---|---|---|---|---|---|---|

${\zeta}_{i}{}^{1}$ | ${S}_{1}({w}^{1})$ | ${S}_{2}({w}^{1})$ | ${S}_{3}({w}^{1})$ | ${S}_{4}({w}^{1})$ | ${S}_{5}({w}^{1})$ | ${X}_{1}>{X}_{3}>{X}_{2}>{X}_{4}>{X}_{5}$ |

0.4348 | 0.3351 | 0.4077 | 0.3113 | 0.2177 | ||

${\zeta}_{i}{}^{2}$ | ${S}_{1}({w}^{2})$ | ${S}_{2}({w}^{2})$ | ${S}_{3}({w}^{2})$ | ${S}_{4}({w}^{2})$ | ${S}_{5}({w}^{2})$ | ${X}_{1}>{X}_{3}>{X}_{2}>{X}_{4}>{X}_{5}$ |

0.4360 | 0.3413 | 0.4081 | 0.3106 | 0.2055 |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Zhou, P.; Li, L.; Zhu, F.
An Interactive Decision-Making Method for Third-Party Logistics Provider Selection under Hybrid Multi-Criteria. *Symmetry* **2020**, *12*, 729.
https://doi.org/10.3390/sym12050729

**AMA Style**

Liu Y, Zhou P, Li L, Zhu F.
An Interactive Decision-Making Method for Third-Party Logistics Provider Selection under Hybrid Multi-Criteria. *Symmetry*. 2020; 12(5):729.
https://doi.org/10.3390/sym12050729

**Chicago/Turabian Style**

Liu, Yumin, Peng Zhou, Liyuan Li, and Feng Zhu.
2020. "An Interactive Decision-Making Method for Third-Party Logistics Provider Selection under Hybrid Multi-Criteria" *Symmetry* 12, no. 5: 729.
https://doi.org/10.3390/sym12050729