### Abstract

We address the problem of minimizing the aggregated fuel consumption by the vessels in an inland waterway (a river) with a single lock. The fuel consumption of a vessel depends on its velocity and the slower it moves, the less fuel it consumes. Given entry times of the vessels into the waterway and the deadlines before which they need to leave the waterway, we decide on optimal velocities of the vessels that minimize their private fuel consumption. Presence of the lock and possible congestions on the waterway make the problem computationally challenging. First, we prove that in general Nash equilibria might not exist, i.e., if there is no supervision on the vessels velocities, there might not exist a strategy profile from which no vessel can unilaterally deviate to decrease its private fuel consumption. Next, we introduce simple supervision methods to guarantee existence of Nash equilibria. Unfortunately, though a Nash equilibrium can be computed, the aggregated fuel consumption of such a stable solution is high compared to the consumption in a social optimum, where the total fuel consumption is minimized. Therefore, we propose a mechanism involving payments between vessels, guaranteeing Nash equilibria while minimizing the fuel consumption. This mechanism is studied for both the offline setting, where all information is known beforehand, and online setting, where we only know the entry time and deadline of a vessel when it enters the waterway.

Original language | English |
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Title of host publication | Mathematical Optimization Theory and Operations Research |

Subtitle of host publication | MOTOR 2019: International Conference on Mathematical Optimization Theory and Operations Research |

Editors | Michael Khachay, Yury Kochetov, Panos M. Pardalos |

Place of Publication | Cham |

Publisher | Springer |

Pages | 202-217 |

Number of pages | 16 |

Volume | 11548 |

ISBN (Electronic) | 978-3-030-22629-9 |

ISBN (Print) | 978-3-030-22628-2 |

DOIs | |

Publication status | Published - 12 Jun 2019 |

Event | Mathematical Optimization Theory and Operations Research: 18th International Conference - Ekaterinburg, Russian Federation Duration: 8 Jul 2019 → 12 Jul 2019 Conference number: 18 http://motor2019.uran.ru/index.html |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 11548 |

### Conference

Conference | Mathematical Optimization Theory and Operations Research |
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Abbreviated title | MOTOR 2019 |

Country | Russian Federation |

City | Ekaterinburg |

Period | 8/07/19 → 12/07/19 |

Internet address |

### JEL classifications

- c71 - Cooperative Games
- c00 - Mathematical and Quantitative Methods: General

### Keywords

- Lock scheduling
- Congestions
- Social Welfare
- Mechanism design
- Online scheduling

## Cite this

Defryn, C., Golak, J., Grigoriev, A., & Timmermans, V. (2019). Inland Waterway Efficiency Through Skipper Collaboration and Joint Speed Optimization. In M. Khachay, Y. Kochetov, & P. M. Pardalos (Eds.),

*Mathematical Optimization Theory and Operations Research: MOTOR 2019: International Conference on Mathematical Optimization Theory and Operations Research*(Vol. 11548, pp. 202-217). Springer. Lecture Notes in Computer Science, Vol.. 11548 https://doi.org/10.1007/978-3-030-22629-9_15