A learning-based co-planning method with truck and container routing for improved barge departure times

Rie B. Larsen*, Rudy R. Negenborn, Bilge Atasoy

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Cooperation between container transport service providers can increase efficiency in the logistics sector significantly. However, cooperation between competitors requires co-planning methods that not only give the cooperating partners an advantage towards external competition but also protect the partners from losing information, clients and autonomy to one another. Furthermore, modern freight transport requires real-time methods that react to new information and situations. We propose a real-time, co-planning method called departure learning based on model predictive control where a barge operator considers the joint cost of themselves and a truck operator when deciding barge departures. At regular time-intervals, the barge operator uses previous information to propose a number of departure schedules for which the truck operator discloses their corresponding expected operational costs. Co-planning thus only requires limited exchange of aggregate data. The impact of using departure learning on the transport system’s performance and the method’s learning quality are thoroughly investigated numerically on an illustrative, simulated, realistic hinterland network. With as little as six schedules being exchanged per timestep, departure learning outperforms decentralized benchmark methods significantly in terms of operational costs. It is found that using knowledge about the performance of related schedules is important for the exploration of opportunities, but if this is relied upon too much, the realized solution becomes more costly. It is also found that departure learning is a reliable and realistic co-planning method that especially performs well when peaks in the demand make departure times highly correlated to the cost of operating the transport system, such as in hinterland areas of ports which receive large container ships.

Original languageEnglish
Number of pages31
JournalAnnals of Operations Research
Publication statusPublished - 2023


Funding Information:
This research is supported by the project “Complexity Methods for Predictive Synchromodality” (project 439.16.120) of the Netherlands Organisation for Scientific Research (NWO) and by the project “Novel inland waterway transport concepts for moving freight effectively” of European Union Horizon 2020 Programme under grant agreement n 858508.


  • Barge scheduling
  • Co-planning
  • Cooperative planning
  • Model predictive control
  • Online learning
  • Synchromodal transport
  • Vehicle utilization


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