Optimal duty rostering for toll enforcement inspectors

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We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, we developed a personalized crew rostering model, to schedule the crews of the tours. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The main focus of this paper extends our previous publications on how different requirements for the rostering can be modeled in detail. The second focus is on a bi-criteria analysis of the planning problem to find the balance between the control quality and the roster acceptance. Finally, computational results on real-world instances show the practicability of our method and how different input parameters influence the problem complexity.

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Fig. 1
Fig. 2


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    Staying on toll roads allows a continuous control.


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We thank Doris Ludwig-Schreiber and Christian Hoffmann from the German Federal office for Goods Transport (BAG) for initiating the project on optimal toll enforcement with the Zuse Institute Berlin. Furthermore, we thank the technical project managers Eduardo Pinto and Thomas Dankert for organising the project, and in addition, for giving a lot of technical support according to the installation and operation of our tool at the BAG. Our sincere thanks go also to Daniel Schneider, Ralf Haas and Uta Sperling from the planning department of the BAG, who provided us with many test instances, gave us excellent feedback, and helped us to understand the manifold requirements from real operations. Furthermore, we thank Hans-Stefan Madlung and his colleagues from IVU Traffic Technologies AG for the joint development of a small and flexible interface to exchange the data between TC-OPT and the commercial planning tool “IVU.Plan”. In addition, we want to thank two anonymous referees for improving this paper by their valuable comments.

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Correspondence to Elmar Swarat.

Additional information

This work was funded by the Federal Office for Goods Transport (BAG).

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Borndörfer, R., Sagnol, G., Schlechte, T. et al. Optimal duty rostering for toll enforcement inspectors. Ann Oper Res 252, 383–406 (2017) doi:10.1007/s10479-016-2152-1

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  • Vehicle routing
  • Crew rostering
  • Integer Programming
  • Bi-criteria optimization

Mathematics Subject Classification

  • 90B20
  • 90C06