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Graph representation of the fixed route dial-a-ride problem

Author

Listed:
  • Tal Grinshpoun

    (Ariel University)

  • Elad Shufan

    (SCE – Shamoon College of Engineering)

  • Hagai Ilani

    (SCE – Shamoon College of Engineering)

  • Vadim Levit

    (Ben-Gurion University of the Negev)

  • Haya Brama

    (Ariel University)

Abstract

The fixed route dial-a-ride problem (FRDARP) is a variant of the famous dial-a-ride problem, in which all the requests are chosen between terminals that are located along a fixed route. A reduction to the shortest path problem enables finding an optimal solution for FRDARP in polynomial time. However, the basic graph construction ends up with a huge graph, which makes the reduction impractical due to its memory consumption. To this end, we propose several pruning heuristics that enable us to considerably reduce the size of the graph through its dynamic construction. Additionally, we utilize the special features of the problem to apply parallelization to the graph traversal process. Our experiments show that each of the proposed heuristics on its own improves the practical solvability of FRDARP. Moreover, using them together is considerably more efficient than any single heuristic. Finally, the experiments confirm the efficiency of our suggested parallelization policy.

Suggested Citation

  • Tal Grinshpoun & Elad Shufan & Hagai Ilani & Vadim Levit & Haya Brama, 2023. "Graph representation of the fixed route dial-a-ride problem," Journal of Scheduling, Springer, vol. 26(5), pages 479-495, October.
    • Handle: RePEc:spr:jsched:v:26:y:2023:i:5:d:10.1007_s10951-022-00757-3
    DOI: 10.1007/s10951-022-00757-3
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    References listed on IDEAS

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    1. Yvan Dumas & François Soumis & Jacques Desrosiers, 1990. "Technical Note—Optimizing the Schedule for a Fixed Vehicle Path with Convex Inconvenience Costs," Transportation Science, INFORMS, vol. 24(2), pages 145-152, May.
    2. Jean-François Cordeau & Gilbert Laporte, 2007. "The dial-a-ride problem: models and algorithms," Annals of Operations Research, Springer, vol. 153(1), pages 29-46, September.
    3. Yves Molenbruch & Kris Braekers & An Caris, 2017. "Typology and literature review for dial-a-ride problems," Annals of Operations Research, Springer, vol. 259(1), pages 295-325, December.
    4. Gerardo Berbeglia & Jean-François Cordeau & Gilbert Laporte, 2012. "A Hybrid Tabu Search and Constraint Programming Algorithm for the Dynamic Dial-a-Ride Problem," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 343-355, August.
    5. Willem E. de Paepe & Jan Karel Lenstra & Jiri Sgall & René A. Sitters & Leen Stougie, 2004. "Computer-Aided Complexity Classification of Dial-a-Ride Problems," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 120-132, May.
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