# Entropy as an Objective Function of Optimization Multimodal Transportations

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## Abstract

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## 1. Introduction

## 2. Statement of the Problem of Optimization of Multimodal Transportation for Deterministic, Stochastic and Uncertain Risks

## 3. Mathematical Formulation of the Problem

- Natural risks (weather or biological factors that cause damage to cargo; natural disasters);
- Technological risks (damage to cargo caused by overloading and transportation; depletion of equipment; computer and information dangers; fires, accidents);
- Political risks (military and political instability; economic sanctions, closure of borders);
- Legal and Tariff Risks (amendments to laws and legislation that regulate the carriage of goods; changes in tariffs);
- Commercial risks (customers refusing to collect or pay for the transportation of the goods; changes in the cost of transportation after the contract is signed; non-fulfillment of contract terms);
- Financial risks (change in the exchange rate; lending threats; inflation threats);
- Social risks (intentional damage or destruction of the goods: territorial conflicts; air strikes or potential threats of it occurring).

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Total cargo turnover for all seaports of the country, the ports of Mariupol and Pivdennyi.

**Figure 3.**Transit cargo transportation for the ports of Mariupol and Izmail for the period 2012–2016.

**Figure 4.**Transit cargo transportation for the ports of Mariupol and Izmail for the period 2017–2021.

**Figure 5.**The total impact of normal risks on the cost of transportation for all ports and the port of Mariupol for the period 2012–2020, %.

**Table 1.**The degree of correlation of the coefficients of linear approximation of the total cargo turnover through the port of Mariupol for the time interval and levels of integrated risk.

Parameter | The Absolute Value of the Coefficient in the Approximation Equation | The Magnitude of the Integrated Risk | |
---|---|---|---|

Years | 2013–2015 | 3257.7 | 0.63 |

2016–2019 | 1038.0 | 0.27 | |

2019–2020 | 499.66 | 0.149 | |

Correlation coefficient | - | 0.998257 |

**Table 2.**Relative error of the forecast of the basic model and entropy method according to the data of 2020.

Port | Forecast Using the Base Model, Thousand Tons | Forecast Using the Entropy Method, Thousand Tons | Actual Results, Thousand Tons | Relative Error of the Base Model, % | The Relative Error of the Entropy Method, % |
---|---|---|---|---|---|

Mariupol | 6988.7 | 6952.2 | 7025.43 | −0.523 | −1.042 |

Izmail | 412.5 | 404.3 | 428.49 | −3.732 | −5.645 |

Pivdennyi | 47,512.2 | 47,145.4 | 47,629.48 | −0.246 | −1.016 |

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**MDPI and ACS Style**

Bazaluk, O.; Kotenko, S.; Nitsenko, V.
Entropy as an Objective Function of Optimization Multimodal Transportations. *Entropy* **2021**, *23*, 946.
https://doi.org/10.3390/e23080946

**AMA Style**

Bazaluk O, Kotenko S, Nitsenko V.
Entropy as an Objective Function of Optimization Multimodal Transportations. *Entropy*. 2021; 23(8):946.
https://doi.org/10.3390/e23080946

**Chicago/Turabian Style**

Bazaluk, Oleg, Sergiy Kotenko, and Vitalii Nitsenko.
2021. "Entropy as an Objective Function of Optimization Multimodal Transportations" *Entropy* 23, no. 8: 946.
https://doi.org/10.3390/e23080946