Profitable mixed capacitated arc routing and related problems

Abstract

Mixed capacitated arc routing problems aim to identify a set of vehicle tours that, starting and ending at a depot node, serve a given number of links at minimum cost, while satisfying the vehicles capacity. If both profits and costs on arcs are considered, we may define the profitable mixed capacitated arc routing problem (PMCARP). In this paper we present compact flow-based models for the PMCARP, where two types of services are tackled, mandatory and optional. Adaptations of the models to fit into some other related problems are also proposed. The models are evaluated, according to their bounds quality as well as to the CPU times, over large sets of test instances. New instances have been created for some variants that have been introduced here for the first time. Results show the new models performance within CPLEX and compare, whenever available, the proposed models against other resolution methods.

This is a preview of subscription content, log in to check access.

References

  1. Aráoz J, Fernández E, Franquesa C (2009a) The clustered prize-collecting arc routing problem. Transport Sci 43:287–308

  2. Araóz J, Fernández E, Meza O (2009b) Solving the prize-collecting rural Postman problem. Eur J Oper Res 196:886–896

    Article  Google Scholar 

  3. Aráoz J, Fernández E, Zoltan C (2006) Privatized rural Postman problems. Computers Oper Res 33:3432–3449

    Article  Google Scholar 

  4. Archetti C, Corberán Á, Plana I, Sanchis JM, Speranza MG (2013) The team orienteering arc routing problem. Transport Sci. doi:10.1287/trsc.2013.0484

  5. Archetti C, Feillet D, Hertz A, Speranza MG (2010) The undirected capacitated arc routing problem with profits. Computers Oper Res 37:1860–1869

    Article  Google Scholar 

  6. Belenguer JM, Benavent E, Lacomme P, Prins C (2006) Lower and upper bound for the mixed capacitated arc routing problem. Computers Oper Res 33:3363–3383

    Article  Google Scholar 

  7. Benavent E, Campos V, Corberán A, Mota E (1992) The capacitated arc routing problem: lower bounds. Networks 22:669–690

    Article  Google Scholar 

  8. Benavent E, Corberán A, Plana I, Sanchis JM (2009) Min–max K-vehicles windy rural Postman problem. Networks 54:216–226

    Article  Google Scholar 

  9. Corberán A, Fernández E, Franquesa C, Sanchis JM (2011a) The windy clustered prize-collecting arc routing problem. Transport Sci 45:317–334

    Article  Google Scholar 

  10. Corberán A, Mejía G, Sanchis JM (2005) New results on the mixed general routing problem. Oper Res 53:363–376

    Article  Google Scholar 

  11. Corberán Á, Plana I, Rodriguez-Chía A, Sanchis JM (2013) A branch-and-cut for the maximum benefit Chinese Postman problem. Math Program 132:309–332

    Article  Google Scholar 

  12. Degraeve Z, Gochet W, Jans R (2002) Alternative formulations for a layout problem in the fashion industry. Eur J Oper Res 143:80–93

    Article  Google Scholar 

  13. Deitch R, Ladany S (2000) The one-period bus touring problem: solved by an effective heuristic for the orienteering tour problem and improvement algorithm. Eur J Oper Res 127:69–77

    Article  Google Scholar 

  14. Feillet D, Dejax P, Gendreau M (2005a) Traveling Salesman problems with profits. Transport Sci 39:188–205

    Article  Google Scholar 

  15. Feillet D, Dejax P, Gendreau M (2005b) The profitable arc tour problem: solution with a branch-and-price algorithm. Transport Sci 39:539–552

    Article  Google Scholar 

  16. Gavish B, Graves S (1978) The travelling salesman problem and related problems. In: Working Paper OR-078-78: Operations Research Center, MIT, Cambridge

  17. Gouveia L, Mourão MC, Pinto LS (2010) Lower bounds for the mixed capacitated arc routing problem. Computers Oper Res 37:692–699

    Article  Google Scholar 

  18. Hertz A, Laporte G, Nanchen-Hugo P (1999) Improvement procedures for the undirected rural postman problem. INFORMS J Comput 11:53–62

    Article  Google Scholar 

  19. Hochbaum D, Olinick E (2001) The bounded cycle-cover problem. INFORMS J Comput 13:104–119

    Article  Google Scholar 

  20. Irnich S (2010) The profitable capacitated rural Postman problem. TRISTAN 2010. Tromso, Norway, pp 408–412

  21. Jans R (2009) Solving lot-sizing problems on parallel identical machines using symmetry-breaking constraints. INFORMS J Comput 21:123–136

    Article  Google Scholar 

  22. Malandraki C, Daskin M (1993) The maximum benefit Chinese Postman problem and the maximum benefit traveling Salesman problem. Eur J Oper Res 65:218–324

    Article  Google Scholar 

  23. Pearn W, Chiu W (2005) Approximate solutions for the maximum benefit Chinese postman problem. Int J Syst Sci 36:815–822

    Article  Google Scholar 

  24. Pearn W, Wang K (2003) On the maximum benefit Chinese postman problem. OMEGA—Int J Manag Sci 31:269–273

    Article  Google Scholar 

  25. Sherali HD, Smith JC (2001) Improving discrete model representations via symmetry considerations. Manag Sci 47:1396–1407

    Article  Google Scholar 

  26. Souffriau W, Vansteenwegen P, Van den Berghe G (2011) The planning of cycle trips in the province of East Flanders. Omega 39:209–213

  27. Stenger A, Schneider M, Goeke D (2013) The prize-collecting vehicle routing problem with single and multiple depots and non-linear cost. Eur J Transp Logist 2:57–87

    Article  Google Scholar 

  28. Tang L, Wang X (2006) Iterated local search algorithm based on very large-scale neighborhood for prize-collecting vehicle routing problem. Int J Adv Manuf Technol 29:1246–1258

    Article  Google Scholar 

  29. Toth P, Vigo D (2002) The vehicle routing problem. SIAM, Philadelphia

    Google Scholar 

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

    Article  Google Scholar 

  31. Zachariadis EE, Kiranoudis CT (2011) Local search for the undirected capacitated arc routing problem with profits. Eur J Oper Res 210:358–367

Download references

Acknowledgments

Authors want to thank two anonymous referees for their comments and suggestions that have contributed to improve the content and readability of the paper. E. Benavent and Á. Corberán wish to thank the Ministerio of Economía y Competitividad (project MTM2012-36163-C06-02) of Spain and the Generalitat Valenciana (project GVPROMETEO2013-049) for their support. L. Gouveia, M.C. Mourão and L.S. Pinto wish to thank the Fundação para a Ciência e Tecnologia (projects PEsT-OE/EGE/UI0491; PEsT-OE/MAT/UI0152; PTDC/EGE-GES/121406) for their support. Project MTM2012-36163-C06-02 is funded in cooperation with the European Community Fund FEDER.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Leonor Santiago Pinto.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Benavent, E., Corberán, Á., Gouveia, L. et al. Profitable mixed capacitated arc routing and related problems. TOP 23, 244–274 (2015). https://doi.org/10.1007/s11750-014-0336-x

Download citation

Keywords

  • Routing
  • Arc routing problems
  • Profits
  • Flow-based models

Mathematics Subject Classification

  • 90B10