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Annals of Operations Research

, Volume 258, Issue 2, pp 761–780 | Cite as

The multi-vehicle cumulative covering tour problem

  • David A. Flores-Garza
  • M. Angélica Salazar-Aguilar
  • Sandra Ulrich Ngueveu
  • Gilbert Laporte
Article

Abstract

This paper introduces the multi-vehicle cumulative covering tour problem whose motivation arises from humanitarian logistics. The objective is to determine a set of tours that must be followed by a fleet of vehicles in order to minimize the sum of arrival times (latency) at each visited location. There are three types of locations: mandatory, optional, and unreachable. Each mandatory location must be visited, and optional locations are visited in order to cover the unreachable locations. To guarantee the vehicle autonomy, the duration of each tour should not exceed a given time limit. A mixed integer linear formulation and a greedy randomized adaptive search procedure are proposed for this problem. The performance of the algorithm is assessed over a large set of instances adapted from the literature. Computational results confirm the efficiency of the proposed algorithm.

Keywords

Cumulative vehicle routing problem Multi-vehicle covering tour problem Minimum latency problem Humanitarian logistics 

Notes

Acknowledgments

Partial funding for this project has been provided by CONACYT (National Council of Science and Technology from Mexico), the SMI program (Soutien á la Mobilité Internationale) of the National Polytechnical Institute of Toulouse (INP-Toulouse) and the French National Research Agency through the ATHENA project under the Grant ANR-13-BS02-0006, and by the Canadian Natural Sciences and Engineering Research Council under Grant 39682-10. Thanks are due to the referees who provided valuable comments and to Há et al. (2013) for sharing their instance set with us.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Altay, N., & Green, W, I. I. I. (2006). OR/MS research in disaster operations management. European Journal of Operational Research, 175(1), 475–493.CrossRefGoogle Scholar
  2. Anaya-Arenas, A., Renaud, J., & Ruiz, A. (2014). Relief distribution networks: A systematic review. Annals of Operations Research, 223(1), 53–79.CrossRefGoogle Scholar
  3. Archer, A., & Blasiak, A. (2010). Improved approximation algorithms for the minimum latency problem via prize-collecting strolls. In Proceedings of the twenty-first annual ACM-SIAM symposium on discrete algorithms (SODA), Philadelphia, USA, pp. 429–447.Google Scholar
  4. Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, B., Raghavan, P., & Sudan, M. (1994). The minimum latency problem. In Proceedings of the twenty-sixth annual ACM symposium on theory of computing (STOC), Montreal, Canada, pp. 163–171.Google Scholar
  5. Campbell, A. M., Vandenbussche, D., & Hermann, W. (2008). Routing for relief efforts. Transportation Science, 42(2), 127–145.CrossRefGoogle Scholar
  6. Chen, P., Dong, X., & Niu, Y. (2012). An iterated local search algorithm for the cumulative capacitated vehicle routing problem. Technology for Education and Learning, Advances in Intelligent Systems and Computing, 136, 575–581.CrossRefGoogle Scholar
  7. Davoudpour, H., & Ashrafi, M. (2009). Solving multi-objective SDST flexible flow shop using GRASP algorithm. The International Journal of Advanced Manufacturing Technology, 44(7–8), 737–747.CrossRefGoogle Scholar
  8. De La Torre, L. E., Dolinskaya, I. S., & Smilowitz, K. R. (2012). Disaster relief routing: Integrating research and practice. Socio-Economic Planning Sciences, Special Issue: Disaster Planning and Logistics: Part 1, 46(1), 88–97.CrossRefGoogle Scholar
  9. Ezzine, I. O., & Elloumi, S. (2012). Polynomial formulation and heuristic based approach for the \(k\)-travelling repairman problem. International Journal of Mathematics in Operational Research, 4(5), 503–514.CrossRefGoogle Scholar
  10. Fakcharoenphol, J., Harrelson, C., & Rao, S. (2007). The \(k\)-traveling repairmen problem. ACM Transactions on Algorithms, 3(4), 40:1–40:16.CrossRefGoogle Scholar
  11. Festa, P., & Resende, M. G. C. (2009). An annotated bibliography of GRASP—Part II: Applications. International Transactions in Operational Research, 16(2), 131–172.CrossRefGoogle Scholar
  12. Galindo, G., & Batta, R. (2013). Review of recent developments in OR/MS research in disaster operations management. European Journal of Operational Research, 230(2), 201–211.CrossRefGoogle Scholar
  13. Gendreau, M., Laporte, G., & Semet, F. (1997). The covering tour problem. Operations Research, 45(4), 568–576.CrossRefGoogle Scholar
  14. Há, M. H., Bostel, N., Langevin, A., & Rousseau, L. M. (2013). An exact algorithm and a metaheuristic for the multi-vehicle covering tour problem with a constraint on the number of vertices. European Journal of Operational Research, 226(2), 211–220.CrossRefGoogle Scholar
  15. Hachicha, M., Hodgson, M. J., Laporte, G., & Semet, F. (2000). Heuristics for the multi-vehicle covering tour problem. Computers & Operations Research, 27(1), 29–42.CrossRefGoogle Scholar
  16. Hmayer, A., & Ezzine, I. (2013). CLARANS heuristic based approch for the \(k\)-traveling repairman problem. In International conference on advanced logistics and transport (ICALT), Sousse, Tunisie, pp. 535–538.Google Scholar
  17. Hodgson, M. J., Laporte, G., & Semet, F. (1998). A covering tour model for planning mobile health care facilities in Suhum District, Ghana. Journal of Regional Science, 38(4), 621–638.CrossRefGoogle Scholar
  18. Jozefowiez, N. (2011). A column generation approach for the multi-vehicle covering tour problem. In ROADEF 2011, March 2–4, Saint-Etienne, France.Google Scholar
  19. Jozefowiez, N. (2014). A branch-and-price algorithm for the multivehicle covering tour problem. Networks, 64(3), 160–168.CrossRefGoogle Scholar
  20. Kammoun, M., Derbel, H., Ratli, M., & Jarboui, B. (2015). A variable neighborhood search for solving the multi-vehicle covering tour problem. Electronic Notes in Discrete Mathematics, 47, 285–292.CrossRefGoogle Scholar
  21. Ke, L., & Feng, Z. (2013). A two-phase metaheuristic for the cumulative capacitated vehicle routing problem. Computers & Operations Research, 40(2), 633–638.CrossRefGoogle Scholar
  22. Lopes, R., Souza, V. A., & da Cunha, A. S. (2013). A branch-and-price algorithm for the multi-vehicle covering tour problem. Electronic Notes in Discrete Mathematics, 44, 61–66.CrossRefGoogle Scholar
  23. Luo, Z., Qin, H., & Lim, A. (2014). Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints. European Journal of Operational Research, 234(1), 49–60.CrossRefGoogle Scholar
  24. Lysgaard, J., & Wøhlk, S. (2014). A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem. European Journal of Operational Research, 236(3), 800–810.CrossRefGoogle Scholar
  25. Murakami, K. (2014). A column generation approach for the multi-vehicle covering tour problem. In IEEE international conference on automation science and engineering (CASE), New Taipei, Taiwan, pp. 1063–1068).Google Scholar
  26. Naji-Azimi, Z., Renaud, J., Ruiz, A., & Salari, M. (2012). A covering tour approach to the location of satellite distribution centers to supply humanitarian aid. European Journal of Operational Research, 222(3), 596–605.CrossRefGoogle Scholar
  27. Ngueveu, S. U., Prins, C., & Wolfler Calvo, R. (2010). An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Computers & Operations Research, 37(11), 1877–1885.CrossRefGoogle Scholar
  28. Oliveira, W. A., Mello, M. P., Moretti, A. C., & Reis, E. F. (2013). The multi-vehicle covering tour problem: Building routes for urban patrolling. arXiv:1309.5502.
  29. Ozsoydan, F. B., & Sipahioglu, A. (2013). Heuristic solution approaches for the cumulative capacitated vehicle routing problem. Optimization, 62(10), 1321–1340.CrossRefGoogle Scholar
  30. Ribeiro, G. M., & Laporte, G. (2012). An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem. Computers & Operations Research, 39(3), 728–735.CrossRefGoogle Scholar
  31. Sahni, S., & Gonzales, T. (1974). P-complete problems and approximate solutions. In IEEE conference record of 15th annual symposium on switching and automata theory, New York, USA, pp. 28–32.Google Scholar
  32. Salazar-Aguilar, M. A., Ríos-Mercado, R. Z., & González-Velarde, J. L. (2013). GRASP strategies for a bi-objective commercial territory design problem. Journal of Heuristics, 19(2), 179–200.CrossRefGoogle Scholar
  33. Sitters, R. (2014). Polynomial time approximation schemes for the traveling repairman and other minimum latency problems, Portland, USA, pp. 604–616. doi: 10.1137/1.9781611973402.46.
  34. Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2014). A unified solution framework for multi-attribute vehicle routing problems. European Journal of Operational Research, 234(3), 658–673.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • David A. Flores-Garza
    • 1
  • M. Angélica Salazar-Aguilar
    • 1
  • Sandra Ulrich Ngueveu
    • 2
    • 3
  • Gilbert Laporte
    • 4
  1. 1.Graduate Program in Systems EngineeringUniversidad Autónoma de Nuevo LeónSan Nicolás de los GarzaMexico
  2. 2.Univ de Toulouse, INP, LAASToulouseFrance
  3. 3.CNRSLAASToulouseFrance
  4. 4.Canada Research Chair in Distribution ManagementHEC MontréalMontrealCanada

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