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Scheduling trams in the morning

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Abstract.

In this note, we prove ??-completeness of the following problem: Given a set of trams of different types, which are stacked on sidings in their depot and an order in which trams of specified types are supposed to leave. Is there an assignment of trams to departure times without any shunting movements? In the particular case where the number of sidings is fixed, the problem is solvable in polynomial time. We derive a dynamic program and improve its performance by a state elimination scheme. We implemented three variants of the dynamic program and applied them to random data as well as to real-world data.

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Authors and Affiliations

  1. Zentrum für Paralleles Rechnen, Universität zu Köln, Albertus-Magnus-Platz, D-50923 Köln, Germany, , , , , , DE

    Ulrich Blasum & Winfried Hochstättler

  2. Abteilung für Mathematische Optimierung, TU Braunschweig, Pockelsstraße 14, D-38106 Braunschweig, Germany, , , , , , DE

    Michael R. Bussieck, Hans-Helmut Scheel & Thomas Winter

  3. Siemens AG, ZT SE 4, D-81730 München, Germany, , , , , , DE

    Christoph Moll

Authors
  1. Ulrich Blasum
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  2. Michael R. Bussieck
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  3. Winfried Hochstättler
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  4. Christoph Moll
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  5. Hans-Helmut Scheel
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  6. Thomas Winter
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Additional information

Manuscript received: March 1997/final version received: June 1998

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Blasum, U., Bussieck, M., Hochstättler, W. et al. Scheduling trams in the morning. Mathematical Methods of OR 49, 137–148 (1999). https://doi.org/10.1007/PL00020912

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  • DOI: https://doi.org/10.1007/PL00020912

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