# A Forecast Model of the Number of Containers for Containership Voyage

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## Abstract

**:**

## 1. Introduction

## 2. Gray Relation Analysis

## 3. Mixed Kernel Function SVM Prediction Model

#### 3.1. Support Vector Machine for Regression

#### 3.2. Construction of Mixed Kernel Function

#### 3.3. Parameter Optimization

## 4. Example Analysis

#### 4.1. Data Samples

- (1)
- ${X}_{1}$, local GDP of the region in which the port of call is located, which can be calculated on the basis of the formula actual amount/100 million yuan;
- (2)
- ${X}_{2}$, changes in port industrial structures, which can calculated according to the percentage occupied by the tertiary industry;
- (3)
- ${X}_{3}$, completeness of the collection and distribution system, which can calculated according to the actual annual throughput of containers per million twenty-foot equivalent units (TEU) at the port of call;
- (4)
- ${X}_{4}$, company’s capacity, which can be calculated according to the actual number of containers/10,000 TEU;
- (5)
- ${X}_{5}$, inland turnaround time of containers, which can be calculated according to the actual number of days;
- (6)
- ${X}_{6}$, seasonal changes in cargo volume, which can be calculated as a percentage;
- (7)
- ${X}_{7}$, quantity of containers handled by the company, which can be calculated according to the actual number of containers/10,000 TEU;
- (8)
- ${X}_{8}$, transport capacity for a single ship, which can be calculated according to the actual number of containers/TEU; and
- (9)
- ${X}_{9}$, full-container-loading rate of the ship, which can be calculated as a percentage.

#### 4.2. Determining the Weight of Influencing Factors

#### 4.3. Prediction of Number of Allocated Containers for One Voyage Using Mixed Kernel SVM

#### 4.4. Simulation Results and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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No. | ${\mathit{X}}_{1}$ | ${\mathit{X}}_{2}$ | ${\mathit{X}}_{3}$ | ${\mathit{X}}_{4}$ | ${\mathit{X}}_{5}$ | ${\mathit{X}}_{6}$ | ${\mathit{X}}_{7}$ | ${\mathit{X}}_{8}$ | ${\mathit{X}}_{9}$ | ${\mathit{X}}_{0}$ |
---|---|---|---|---|---|---|---|---|---|---|

1 | 2395 | 75 | 2461 | 10.3 | 11 | 20 | 21 | 5200 | 77 | 1100 |

2 | 27,689 | 66 | 776 | 85 | 38 | 10 | 170 | 1700 | 85 | 279 |

3 | 29,960 | 77 | 2521 | 102.3 | 10 | 15 | 230 | 4700 | 69 | 1739 |

4 | 29,841 | 82 | 4123 | 162 | 49 | 13 | 201 | 3410 | 64 | 177 |

5 | 13,562 | 63 | 2357 | 68.9 | 39 | 20 | 150 | 1200 | 73 | 110 |

6 | 17,369 | 59 | 2037 | 60.3 | 22 | 26 | 120 | 800 | 62 | 205 |

7 | 14,650 | 71 | 1521 | 59 | 13 | 29 | 147 | 2800 | 73 | 347 |

8 | 30,550 | 58 | 798 | 47.7 | 26 | 15 | 128 | 3600 | 88 | 561 |

9 | 25,103 | 54 | 567 | 110.3 | 13 | 10 | 235 | 2000 | 65 | 850 |

10 | 14,650 | 65 | 668 | 85.6 | 25 | 12 | 164 | 2590 | 86 | 496 |

11 | 14,023 | 49 | 732 | 77.7 | 16 | 30 | 139 | 2810 | 59 | 594 |

12 | 19,776 | 67 | 651 | 56 | 30 | 21 | 98 | 1400 | 71 | 350 |

Factors | Relevance | Factors | Relevance | Factors | Relevance |
---|---|---|---|---|---|

${X}_{1}$ | 0.1669 | ${X}_{4}$ | 0.1773 | ${X}_{7}$ | 0.1770 |

${X}_{2}$ | 0.6672 | ${X}_{5}$ | 0.3998 | ${X}_{8}$ | 0.8345 |

${X}_{3}$ | 0.7084 | ${X}_{6}$ | 0.6206 | ${X}_{9}$ | 0.6232 |

Factors | Weight | Factors | Weight | Factors | Weight |
---|---|---|---|---|---|

${X}_{1}$ | 0.038 | ${X}_{4}$ | 0.041 | ${X}_{7}$ | 0.040 |

${X}_{2}$ | 0.153 | ${X}_{5}$ | 0.091 | ${X}_{8}$ | 0.191 |

${X}_{3}$ | 0.162 | ${X}_{6}$ | 0.142 | ${X}_{9}$ | 0.142 |

No. | ${\mathit{X}}_{1}$ | ${\mathit{X}}_{2}$ | ${\mathit{X}}_{3}$ | ${\mathit{X}}_{4}$ | ${\mathit{X}}_{5}$ | ${\mathit{X}}_{6}$ | ${\mathit{X}}_{7}$ | ${\mathit{X}}_{8}$ | ${\mathit{X}}_{9}$ | ${\mathit{X}}_{0}$ |
---|---|---|---|---|---|---|---|---|---|---|

1 | 4365 | 76 | 1596 | 24 | 13 | 18 | 43 | 5400 | 72 | 1250 |

2 | 23,560 | 69 | 882 | 87 | 29 | 12 | 185 | 1900 | 83 | 900 |

3 | 9841 | 81 | 2143 | 112 | 12 | 17 | 251 | 4580 | 70 | 750 |

4 | 25,590 | 74 | 4265 | 159 | 50 | 14 | 211 | 3390 | 66 | 500 |

5 | 18,763 | 62 | 1983 | 73 | 41 | 21 | 163 | 1080 | 74 | 310 |

No. | Actual | SVM-Mixed | GRA-SVM-Mixed | GRA-SVM-Mixed-D | |||
---|---|---|---|---|---|---|---|

Predictive | Relative Error | Predictive | Relative Error | Predictive | Relative Error | ||

1 | 1250 | 1406 | 12.48 | 1263 | 1.04 | 1264 | 1.12 |

2 | 900 | 870 | −3.33 | 899 | −0.11 | 781 | −13.22 |

3 | 750 | 807 | 7.60 | 769 | 2.53 | 757 | 0.93 |

4 | 500 | 526 | 5.20 | 479 | −4.20 | 484 | −3.20 |

5 | 310 | 328 | 5.81 | 314 | 1.29 | 325 | 4.84 |

MSE | 5897 | 197.6 | 2977.4 | ||||

${e}_{\mathrm{MAPE}}$ | 6.88 | 1.83 | 4.66 | ||||

$R$ | 0.9908 | 0.9993 | 0.9877 |

No. | Relative Error | ||
---|---|---|---|

BP | SVM | GRA-SVM-Mixed | |

1 | −8.88 | 3.12 | 1.04 |

2 | 2.22 | 4.56 | −0.11 |

3 | −13.6 | −2.80 | 2.53 |

4 | −3.6 | 9.80 | −4.20 |

5 | 4.84 | −0.97 | 1.29 |

MES | 4734.8 | 1210.6 | 197.6 |

$R$ | 0.9883 | 0.9969 | 0.9993 |

t/s | 57.63 | 45.61 | 27.53 |

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**MDPI and ACS Style**

Wang, Y.; Shi, G.; Sun, X.
A Forecast Model of the Number of Containers for Containership Voyage. *Algorithms* **2018**, *11*, 193.
https://doi.org/10.3390/a11120193

**AMA Style**

Wang Y, Shi G, Sun X.
A Forecast Model of the Number of Containers for Containership Voyage. *Algorithms*. 2018; 11(12):193.
https://doi.org/10.3390/a11120193

**Chicago/Turabian Style**

Wang, Yuchuang, Guoyou Shi, and Xiaotong Sun.
2018. "A Forecast Model of the Number of Containers for Containership Voyage" *Algorithms* 11, no. 12: 193.
https://doi.org/10.3390/a11120193