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Minimizing customers’ waiting time in a vehicle routing problem with unit demands

  • Systems Analysis and Operations Research
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

In this paper we study a new variant of the unit demand vehicle routing problem with the aim of minimizing the sum of customers waiting times to receive service. These kinds of problems are relevant in applications where the customers’ waiting time is essential or is more important than the vehicles’ travel time. We modify a known formulation for the multiple traveling salesman problem adapting it to the addressed problem. The derived mixed integer formulation is able to solve to optimality instances up to 40 nodes. We also develop a metaheuristic algorithm based on Iterated Greedy approach. We implement two variants of the metaheuristic algorithm using two different strategies in the constructive phase. For instances up to 40 nodes the proposed algorithms found almost all the optimal solutions and outperformed the results obtained by the formulation for instances with unknown optimal solution. In general, both versions of the metaheuristic algorithm are very fast and have a good performance too for instances ranging from 50 to 100 nodes.

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References

  1. G. Laporte, “The vehicle routing problem: an overview of exact and approximate algorithms,” Eur. J. Operat. Res. 59, 345–358 (1992).

    Article  MATH  Google Scholar 

  2. S. Kumar and R. Panneerselvam, “A survey on the vehicle routing problem and its variants,” Intell. Inform. Manag. 4, 66–74 (2012).

    Google Scholar 

  3. M. Gendreau, G. Laporte, and J. Potvin, “Metaheuristics for the capacitated VRP,” in The Vehicle Routing Problem, SIAM Monographs on Discrete Mathematics and Applications, Ed. by P. Toth and D. Vigo (SIAM, Philadelphia, 2002), Ch. 6, pp. 129–154.

    Chapter  Google Scholar 

  4. P. Toth and D. Vigo, “The granular tabu search and its application to the vehicle routing problem,” INFORMS J. Comput. 15, 333–346 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  5. C. Prins, “A simple and effective evolutionary algorithm for the vehicle routing problem,” Comput. Operat. Res. 3, 1985–2002 (2004).

    Article  MathSciNet  Google Scholar 

  6. J.-F. Cordeau, M. Gendreau, A. Hertz, G. Laporte, J.-S. Sormany, “New heuristics for the vehicle routing problem, in Logistics Systems: Design and Optimization, Ed. by A. Langevin and D. Riopel (Springer, US, 2005), pp. 279–297.

    Chapter  Google Scholar 

  7. V. Kureichik and V. Kureichik, “A genetic algorithm for finding a Salesman’s route,” J. Comput. Syst. Sci. Int. 4, 89–95 (2006).

    Article  Google Scholar 

  8. A. A. Kazharov and V. M. Kureichik, “Ant colony optimization algorithms for solving transportation problems,” J. Comput. Syst. Sci. Int. 49, 30–43 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Álvarez, S. Casado, J. González Velarde, and J. Pacheco, “A computational tool for optimizing the urban public transport: a real application,” J. Comput. Syst. Sci. Int. 49, 244–252 (2010).

    Article  MATH  Google Scholar 

  10. G. J. Araque, G. Kudva, T. Morin, and J. Pekny, “A branch-and-cut algorithm for vehicle routing problems,” Ann. Operat. Res. 50, 37–59 (1994).

    Article  MATH  Google Scholar 

  11. D. Bertsimas and D. Simchi-Levi, “A new generation of vehicle routing research: robust algorithms, addressing uncertainty,” Operat. Res. 44, 286–304 (1993).

    Article  Google Scholar 

  12. V. Campos, A. Corberan, and E. Mota, “Polyhedral results for a vehicle routing problem,” Eur. J. Operat. Res. 52, 75–85 (1991).

    Article  MATH  Google Scholar 

  13. G. Ghiani, G. Laporte, and F. Semet, “The black and white traveling salesman problem,” Operat. Res. 54, 366–378 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Haimovich and A. H. G. Rinnooy Kan, “Bounds and heuristics for capacitated routing problems,” Math. Operat. Res. 10, 527–542 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  15. A. Bompadre, M. Dror, and J. B. Orlin, “Improved bounds for vehicle routing solutions,” Discrete Optim. 3, 299–316 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  16. M. T. Godinho, L. Gouveia, and T. L. Magnanti, “Combined route capacity and route length models for unit demand vehicle routing problems,” Discrete Optim. 5, 350–372 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  17. J. N. Tsitsiklis, “Special cases of traveling salesman and repairman problems with time windows,” Networks 22, 263–282 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Fischetti, G. Laporte, and S. Martello, “The delivery man problem and cumulative matroids,” Operat. Res. 41, 1055–1064 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  19. M. Goemans and J. Kleinberg, “An improved approximation ratio for the minimum latency problem,” Math. Program. 82, 111–124 (1998).

    MathSciNet  MATH  Google Scholar 

  20. I. Méndez-Díaz, P. Zabala, and A. Lucena, “A new formulation for the traveling deliveryman problem,” Discrete Appl. Math. 156, 3223–3237 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  21. I. Ezzine and S. Elloumi, “Polynomial formulation and heuristic based approach for the k traveling repairman problem,” Int. J. Math. Operat. Res. 4, 503–514 (2012).

    Article  Google Scholar 

  22. F. Angel-Bello, A. Alvarez, and I. García, “Two improved formulations for the minimum latency problem,” Appl. Math. Model. 37, 2257–2266 (2013).

    Article  MathSciNet  Google Scholar 

  23. H. Abeledo, R. Fukasawa, A. A. Pessoa, and E. Uchoa, “The time dependent traveling salesman problem: polyhedra and algorithm,” Math. Program. Comput. 5, 27–55 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  24. A. Salehipour, K. Sörensen, P. Goos, and O. Bräysy, “An efficient GRASP + VND metaheuristic for the traveling repairman problem,” Tech. Report (University of Antwerpen, Faculty of Applied Economics, 2008).

    Google Scholar 

  25. A. Salehipour, K. Sörensen, P. Goos, and O. Bräysy, “An efficient GRASP + VND and GRASP + VNS metaheuristics for the traveling repairman problem,” 4OR: Quart. J. Operat. Res. 9, 189–209 (2011).

    Article  MATH  Google Scholar 

  26. S. U. Ngueveu, C. Prins, and R. Wolfler Calvo, “An effective memetic algorithm for the cumulative capacitated vehicle routing problem,” Comput. Operat. Res. 37, 1877–1885 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  27. M. M. Silva, A. Subramanian, T. Vidal, and L. S. Ochi, “A simple and effective metaheuristic for the minimum latency problem,” Eur. J. Operat. Res. 221, 513–520 (2012).

    Article  MATH  Google Scholar 

  28. N. Mladenovic, D. Urosevic, and S. Hanafi, “Variable neighborhood search for the travelling deliveryman problem,” 4OR: Quart. J. Operat. Res. 11, 57–73 (2012).

    Article  MathSciNet  Google Scholar 

  29. J. Fakcharoenphol, C. Harrelson, and S. Rao, “The k-traveling repairmen problem,” ACM Trans. Algorithms 3, 40 (2007).

    Article  MathSciNet  Google Scholar 

  30. Z. Luo, H. Qin, and A. Lim, “Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints,” Eur. J. Operat. Res. 234, 49–60 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  31. B. Gavish and S. C. Graves, “The travelling salesman problem and related problems,” Working Paper (Operations Research Center, Massachusetts Institute of Technology, 1978).

    Google Scholar 

  32. M. Halkidi, Y. Batistakis, and M. Vazirgiannis, “On clustering validation techniques,” J. Intel. Inform. Syst. 17, 107–145 (2001).

    Article  MATH  Google Scholar 

  33. M. L. Fisher and R. Jaikumar, “A generalized assignment heuristic for vehicle routing,” Networks 11, 109–124 (1981).

    Article  MathSciNet  Google Scholar 

  34. E. Beasley, “Route first-cluster second methods for vehicle routing,” Omega 11, 403–408 (1983).

    Article  Google Scholar 

  35. R. H. Mole, D. G. Johnson, and K. Wells, “Combinatorial analysis for route first-cluster second vehicle routing,” Omega 11, 507–512 (1983).

    Article  Google Scholar 

  36. M. Solomon, “On the worst-case performance of some heuristics for the vehicle routing and scheduling problem with time window constraints,” Networks 16, 161–174 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  37. M. Solomon, “Algorithms for the vehicle routing and scheduling problems with time window constraints,” Operat. Res. 35, 254–265 (1987).

    Article  MATH  Google Scholar 

  38. Y. A. Koskosidis, W. B. Powell, and M. M. Solomon, “An optimization-based heuristic for vehicle routing and scheduling with soft time window constraints,” Transportation Science 26, 69–85 (1992).

    Article  MATH  Google Scholar 

  39. T. Hiquebran, A. S. Alfa, J. A. Shapiro, and D. H. Gittoes, “A revised simulated annealing and cluster-first route-second algorithm applied to the vehicle routing problem,” Eng. Optimiz. 22, 77–107 (1993).

    Article  Google Scholar 

  40. A. Hamacher and C. Moll, “A new heuristic for vehicle routing with narrow time windows,” in Selected papers of the Symposium on Operations Research (SOR), Braunschweig, September 3–6, 1996 (Springer, 1997), pp. 301–306.

    Google Scholar 

  41. S.-C. Hong and Y.-B. Park, “A heuristic for bi-objective vehicle routing with time window constraints,” Int. J. Product. Econ. 62, 249–258 (1999).

    Article  Google Scholar 

  42. M. Sevaux and K. Sörensen, “Hamiltonian paths in large clustered routing problems,” in Proceedings of the EU/MEeting 2008 Workshop on Metaheuristics for Logistics and Vehicle Routing, EU/ME’08 (2008), pp. 411–417.

    Google Scholar 

  43. M. Battarra, G. Erdogan, and D. Vigo, “Exact algorithms for the clustered vehicle routing problem,” Operat. Res. 32, 58–71 (2014).

    Article  MathSciNet  Google Scholar 

  44. M. Mulvey and M. P. Beck, “Solving capacitated clustering problems,” Eur. J. Operat. Res. 18, 339–348 (1984).

    Article  MATH  Google Scholar 

  45. T. Barthelemy, “A bi-objective inventory routing problem with periodic and clustered deliveries,” Master Thesis (Universite de Nantes, France, 2012).

    Google Scholar 

  46. G. Reinelt, “TSPLIB a traveling salesman problem library,” ORSA J. Comput. 3, 376–384 (1991).

    Article  MATH  Google Scholar 

  47. A. A. Mironov, T. A. Levkina, and V. I. Tsurkov, “Minimax estimates of expectations of arc weights in integer networks with fixed node degrees,” Appl. Comput. Math. 8 (2), 216–226 (2009).

    MathSciNet  MATH  Google Scholar 

  48. A. A. Mironov and V. I. Tsurkov, “Class of distribution problems with minimax criterion,” Dokl. Phys. 39, 318 (1994).

    MathSciNet  MATH  Google Scholar 

  49. A. P. Tizik and V. I. Tsurkov, “Iterative functional modification method for solving a transportation problem,” Autom. Remote Control 73, 134 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  50. A. A. Mironov and V. I. Tsurkov, “Transportation problems with minimax criteria,” Dokl. Akad. Nauk 346, 168 (1996).

    MathSciNet  Google Scholar 

  51. A. A. Mironov and V. I. Tsurkov, “Minimax under nonlinear transportation constraints,” Dokl. Math. 64, 351 (2001).

    Google Scholar 

  52. A. A. Mironov and V. I. Tsurkov, “Open transportation models with a minimax criterion,” Dokl. Math. 64, 374 (2001).

    Google Scholar 

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Authors and Affiliations

  1. Tecnologico de Monterrey, School of Engineering and Sciences, Monterrey, Nuevo Leon, Mexico

    S. Nucamendi, Y. Cardona-Valdes & F. Angel-Bello Acosta

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  1. S. Nucamendi
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  2. Y. Cardona-Valdes
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  3. F. Angel-Bello Acosta
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Correspondence to F. Angel-Bello Acosta.

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Nucamendi, S., Cardona-Valdes, Y. & Angel-Bello Acosta, F. Minimizing customers’ waiting time in a vehicle routing problem with unit demands. J. Comput. Syst. Sci. Int. 54, 866–881 (2015). https://doi.org/10.1134/S1064230715040024

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