Inland Waterway Efficiency Through Skipper Collaboration and Joint Speed Optimization
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.
KeywordsLock scheduling Congestions Social welfare Mechanism design Online scheduling
- 2.Eurostat: Navigable inland waterways, by horizontal dimensions of vessels and pushed convoys (2016). http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=iww_if_hordim&lang=en. Accessed 1 Apr 2019
- 3.Inland Navigation in Europe, Market Observation. Central commission for the navigation of the Rhine, annual report (2017). https://www.inland-navigation-market.org/wp-content/uploads/2017/09/CCNR_annual_report_EN_Q2_2017_BD_-1.pdf. Accessed 1 Apr 2019
- 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
- 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
- 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). https://doi.org/10.1007/978-3-319-16468-7_4CrossRefGoogle Scholar