Inland Waterway Efficiency Through Skipper Collaboration and Joint Speed Optimization

  • Christof Defryn
  • Julian Golak
  • Alexander GrigorievEmail author
  • Veerle Timmermans
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)


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.


Lock scheduling Congestions Social welfare Mechanism design Online scheduling 


  1. 1.
    Bialystockia, N., Konovessis, K.: On the estimation of vessel’s fuel consumption and speed curve: a statistical approach. J. Ocean Eng. Sci. 1(2), 157–166 (2016)CrossRefGoogle Scholar
  2. 2.
    Eurostat: Navigable inland waterways, by horizontal dimensions of vessels and pushed convoys (2016). Accessed 1 Apr 2019
  3. 3.
    Inland Navigation in Europe, Market Observation. Central commission for the navigation of the Rhine, annual report (2017). Accessed 1 Apr 2019
  4. 4.
    Günther, E., Lübbecke, M.E., Möhring, R.H.: Vessel traffic optimization for the Kiel canal. TRISTAN VII Book of Extended Abstracts 104 (2010)Google Scholar
  5. 5.
    Nauss, R.M.: Optimal sequencing in the presence of setup times for tow/barge traffic through a river lock. Eur. J. Oper. Res. 187(3), 1268–1281 (2008)CrossRefGoogle Scholar
  6. 6.
    Passchyn, W., Briskorn, D., and Spieksma, F.C.R.: No-wait scheduling for locks. Technical Report KBI\(\_\)1605, KU Leuven, Research group Operations Research and Business Statistics, Leuven, Belgium (2016)Google Scholar
  7. 7.
    Passchyn, W., Briskorn, D., Spieksma, F.C.R.: Mathematical programming models for lock scheduling with an emission objective. Eur. J. Oper. Res. 248(3), 802–814 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Passchyn, W., Coene, S., Briskorn, D., Hurink, J.L., Spieksma, F.C.R., Vanden Berghe, G.: The lockmaster’s problem. Eur. J. Oper. Res. 251(2), 432–441 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Petersen, E.R., Taylor, A.J.: An optimal scheduling system for the Welland Canal. Transp. Sci. 22(3), 173–185 (1988)CrossRefGoogle Scholar
  10. 10.
    Prandtstetter, M., Ritzinger, U., Schmidt, P., Ruthmair, M.: A variable neighborhood search approach for the interdependent lock scheduling problem. In: Ochoa, G., Chicano, F. (eds.) EvoCOP 2015. LNCS, vol. 9026, pp. 36–47. Springer, Cham (2015). Scholar
  11. 11.
    Psaraftis, H.N., Kontovas, C.A.: Speed models for energy-efficient maritime transportation: a taxonomy and survey. Transp. Res. Part C: Emerg. Technol. 26, 331–351 (2013)CrossRefGoogle Scholar
  12. 12.
    Smith, L.D., Nauss, R.M., Mattfeld, D.C., Li, J., Ehmke, J.F., Reindl, M.: Scheduling operations at system choke points with sequence-dependent delays and processing times. Transp. Res. Part E: Logistics Transp. Rev. 47(5), 669–680 (2011)CrossRefGoogle Scholar
  13. 13.
    Smith, L.D., Sweeney, D.C., Campbell, J.F.: Simulation of alternative approaches to relieving congestion at locks in a river transportion system. J. Oper. Res. Soc. 60(4), 519–533 (2009)CrossRefGoogle Scholar
  14. 14.
    Ching-Jung, T., Schonfeld, P.: Effects of speed control on tow travel costs. J. Waterw. Port Coastal Ocean Eng. 125(4), 203–206 (1999)CrossRefGoogle Scholar
  15. 15.
    Ching-Jung, T., Schonfeld, P.: Control alternatives at a waterway lock. J. Waterw. Port Coastal Ocean Eng. 127(2), 89–96 (2001)CrossRefGoogle Scholar
  16. 16.
    Verstichel, J., De Causmaecker, P., Spieksma, F.C.R., Vanden Berghe, G.: Exact and heuristic methods for placing vessels in locks. Eur. J. Oper. Res. 235(2), 387–398 (2014)CrossRefGoogle Scholar
  17. 17.
    Verstichel, J., De Causmaecker, P., Spieksma, F.C.R., Vanden Berghe, G.: The generalized lock scheduling problem: an exact approach. Transp. Res. Part E: Logistics Transp. Rev. 65, 16–34 (2014)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Maastricht University School of Business and EconomicsMaastrichtThe Netherlands
  2. 2.RWTH Aachen, Department of Management ScienceAachenGermany

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