Inland Waterway Efficiency Through Skipper Collaboration and Joint Speed Optimization

Christof Defryn, Julian Golak, Alexander Grigoriev*, Veerle Timmermans

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

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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 languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research
Subtitle of host publicationMOTOR 2019: International Conference on Mathematical Optimization Theory and Operations Research
EditorsMichael Khachay, Yury Kochetov, Panos M. Pardalos
Place of PublicationCham
Number of pages16
ISBN (Electronic)978-3-030-22629-9
ISBN (Print)978-3-030-22628-2
Publication statusPublished - 12 Jun 2019
EventMathematical Optimization Theory and Operations Research: 18th International Conference - Ekaterinburg, Russian Federation
Duration: 8 Jul 201912 Jul 2019
Conference number: 18

Publication series

SeriesLecture Notes in Computer Science


ConferenceMathematical Optimization Theory and Operations Research
Abbreviated titleMOTOR 2019
Country/TerritoryRussian Federation
Internet address

JEL classifications

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


  • Congestions
  • Lock scheduling
  • Mechanism design
  • Online scheduling
  • Social Welfare
  • Social welfare

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