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The line planning routing game

Author

Listed:
  • Gattermann, P.
  • Schiewe, A.
  • Schmidt, M.E.

Abstract

In this paper, we propose a novel algorithmic approach to solve line planning problems. To this end, we model the line planning problem as a game where the passengers are players which aim at minimizing individual objective functions composed of travel time, transfer penalties, and a share of the overall cost of the solution. To find equilibria of this routing game, we use a best-response algorithm. We investigate, under which conditions on the line planning model a passenger’s best-response can be calculated efficiently and which properties are needed to guarantee convergence of the best-response algorithm. Furthermore, we determine the price of anarchy which bounds the objective value of an equilibrium with respect to a system- optimal solution of the line planning problem. For problems where best-responses cannot be found efficiently, we propose heuristic methods. We demonstrate our findings on some small computational examples.

Suggested Citation

  • Gattermann, P. & Schiewe, A. & Schmidt, M.E., 2014. "The line planning routing game," ERIM Report Series Research in Management ERS-2014-017-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:77431
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    References listed on IDEAS

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    Keywords

    transportation; game theory; routing; line planning; routing game;
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