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The capacitated team orienteering problem with incomplete service

Abstract

In this paper we study the capacitated version of the Team Orienteering Problem (TOP), that is the Capacitated TOP (CTOP) and the impact of relaxing the assumption that a customer, if served, must be completely served. We prove that the profit collected by the CTOP with Incomplete Service (CTOP-IS) may be as large as twice the profit collected by the CTOP. A computational study is also performed to evaluate the average increase of the profit due to allowing incomplete service. The results show that the increase of the profit strongly depends on the specific instance. On the tested instances the profit increase ranges between 0 and 50 %. We complete the computational study with the increase of the profit of the CTOP due to split deliveries, that is multiple visits to the same customer, and to split deliveries combined with incomplete service.

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References

  1. 1.

    Archetti, C., Bianchessi, N., Speranza, M.G.: Optimal solutions for routing problems with profits. Discret. Appl. Math. (2012). doi:10.1016/j.dam.2011.12.021

  2. 2.

    Archetti, C., Bianchessi, N., Hertz, A., Speranza, M.G.: Incomplete service and split deliveries in a routing problem with profits. Networks (to appear)

  3. 3.

    Archetti, C., Bianchessi, N., Hertz, A., Speranza, M.G.: The split delivery capacitated team orienteering problem. Networks (to appear)

  4. 4.

    Archetti, C., Hertz, A., Speranza, M.G.: Metaheuristics for the team orienteering problem. J. Heuristics 13, 49–76 (2007)

    Article  Google Scholar 

  5. 5.

    Archetti, C., Feillet, D., Hertz, A., Speranza, M.G.: The capacitated team orienteering and profitable tour problems. J. Oper. Res. Soc. 60, 831–842 (2009)

    Article  MATH  Google Scholar 

  6. 6.

    Boussier, S., Feillet, D., Gendreau, M.: An exact algorithm for team orienteering problems. 4OR Q. J. Oper. Res. 5, 211–230 (2007)

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Butt, S.E., Cavalier, T.M.: A heuristic for the multiple tour maximum collection problem. Comput. Oper. Res. 21, 101–111 (1994)

    Article  MATH  Google Scholar 

  8. 8.

    Chao, I.-M., Golden, B., Wasil, E.A.: The team orienteering problem. Eur. J. Oper. Res. 88, 464–474 (1996)

    Article  MATH  Google Scholar 

  9. 9.

    Christofides, N., Mingozzi, A., Toth, P.: The vehicle routing problem. In: Christofides, N., Mingozzi, A., Toth, P., Sandi, C. (eds.) Combinatorial Optimization, pp. 315–338. Wiley, Chichester (1979)

    Google Scholar 

  10. 10.

    Feillet, D., Dejax, P., Gendreau, M.: Traveling salesman problems with profits. Transp. Sci. 39, 188–205 (2005)

    Article  Google Scholar 

  11. 11.

    Ke, L., Archetti, C., Feng, Z.: Ants can solve the team orienteering problem. Comput. Ind. Eng. 54, 648–665 (2008)

    Article  Google Scholar 

  12. 12.

    Montemanni, R., Gambardella, L.: Ant colony system for team orienteering problem with time windows. Found. Comput. Decis. Sci. 34, 287–306 (2009)

    Google Scholar 

  13. 13.

    Souffriau, W., Vansteenwegen, P., Berghe, G.V., Van Oudheusden, D.: A path relinking approach for the team orienteering problem. Comput. Oper. Res. 37, 1853–1859 (2010)

    MathSciNet  Article  MATH  Google Scholar 

  14. 14.

    Souffriau, W., Vansteenwegen P., Berghe, G.V., Van Oudheusden, D.: The multiconstraint team orienteering problem with multiple time windows. Transp. Sci. (2011). doi:10.1287/trsc.1110.0377

  15. 15.

    Tang, H., Miller-Hooks, E.: A tabu search heuristic for the team orienteering problem. Comput. Oper. Res. 32, 1379–1407 (2005)

    Article  Google Scholar 

  16. 16.

    Tricoire, F., Romauch, M., Doerner, K.F., Hartl, R.F.: Heuristics for the multi-period orienteering problem with multiple time windows. Comput. Oper. Res. 37, 351–367 (2010)

    MathSciNet  Article  MATH  Google Scholar 

  17. 17.

    Vansteenwegen, P., Souffriau, W., Berghe, G.V., Van Oudheusden, D.: Iterated local search for the team orienteering problem with time windows. Comput. Oper. Res. 36, 3281–3290 (2009)

    Article  MATH  Google Scholar 

  18. 18.

    Vansteenwegen, P., Souffriau, W., Van Oudheusden, D.: The orienteering problem: a survey. Eur. J. Oper. Res. 209, 1–10 (2011)

    Article  MATH  Google Scholar 

  19. 19.

    Viana, A., Uchoa, E., Poggi, M.: The team orienteering problem: formulations and branch-cut and price. In: 10th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization and Systems (ATMOS ’10) (2010)

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Acknowledgments

We acknowledge the contribution of two reviewers that have helped us to improve a previous version of this paper.

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Correspondence to Claudia Archetti.

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Archetti, C., Bianchessi, N. & Speranza, M.G. The capacitated team orienteering problem with incomplete service. Optim Lett 7, 1405–1417 (2013). https://doi.org/10.1007/s11590-012-0559-4

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Keywords

  • Capacitated Team Orienteering Problem
  • Incomplete service
  • Split deliveries
  • Exact algorithms