A Case Study on Optimizing Toll Enforcements on Motorways

Authors Ralf Borndörfer, Guillaume Sagnol, Elmar Swarat

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Ralf Borndörfer
Guillaume Sagnol
Elmar Swarat

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Ralf Borndörfer, Guillaume Sagnol, and Elmar Swarat. A Case Study on Optimizing Toll Enforcements on Motorways. In 3rd Student Conference on Operational Research. Open Access Series in Informatics (OASIcs), Volume 22, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to feasible rosters for one month. We present computational results in a case-study on a German subnetwork which documents the practicability of our approach.
  • Vehicle Routing Problem
  • Duty Rostering
  • Integer Programming
  • Operations Research


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