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Less Expensive Formulation for a Realistic Routing-Scheduling-Loading Problem (RoSLoP)

  • Juan J. González-Barbosa
  • Laura Cruz-Reyes
  • José F. Delgado-Orta
  • Héctor J. Fraire-Huacuja
  • Guadalupe Castilla-Valdez
  • Víctor J. Sosa Sosa
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 50)

Abstract

In this paper the Routing-Scheduling-Loading Problem (RoSLoP) is approached. This is a rich bin packing (BPP) and vehicle routing (VRP) problem formulated to satisfy the transportation requirements of a bottling company located in Mexico. The initial formulation of the problem uses 29 integer variables and 30 constraints making difficult to find the exact solution even for small instances. In this work it is proposed a transformation function that reduces the size of the problem formulation which allows obtaining the optimal solution of small instances using an exact algorithm. Experimental results of the performance evaluation of an approximated solution method, with regard to the optimal solution, are showed. It is important to emphasize, that this is the first time that this kind of evaluation is carried out for RoSLoP. In the experiments a set of 12 test instances were selected from the company database. The experimental evidence shows that the transformation function reduces 97% the number of customers orders. The percentage quality error for the traveled distance was 0% and for the vehicles used was 6.19%. Now these results can be used to evaluate the performance of any new approximation solution method of RoSLoP.

Keywords

Complexity Routing-Scheduling-Loading Problem (RoSLoP) Vehicle Routing Problem (VRP) Bin Packing Problem (BPP) 

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References

  1. 1.
    Toth, P., Vigo, D.: The vehicle routing problem. SIAM Monographs on Discrete Mathematics and App. Society for Industrial and Applied Mathematics (2000)Google Scholar
  2. 2.
    Dantzig, G.: On the significance of solving linear programming problems with some integer variables. Econometrica 28, 30–44 (1960)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Edmonds, J.: Covers and packings in family of sets. Bull. Amer. Math. Soc. 68, 494–499 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Dantzig, G., et al.: All shortest routes from a fixed origin in a graph. In: Theory of Graphs: International Symposium, Gordon and Breach, pp. 85–90 (1967)Google Scholar
  5. 5.
    Cruz, L., et al.: An Ant Colony System to solve Routing Problems applied to the delivery of bottled products. In: An, A. (ed.), pp. 68–77. Springer, Heidelberg (2008)Google Scholar
  6. 6.
    Dantzig, G.: Discrete-variable extremum problems. Operation Research 5, 266–277 (1957)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Shaw, P.: Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems. In: Maher, M. (ed.) 40 Conf. on Principles and Practice of Constraint Programming, pp. 417–431. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  8. 8.
    Cordeau, F., et al.: The VRP with time windows. Technical Report Cahiers du GERAD G-99-13, Ecole des Hautes Etudes Commerciales de Montreal (1999)Google Scholar
  9. 9.
    Mingozzi, A.: An exact Algorithm for Period and Multi-Depot Vehicle Routing Problems. Department of Mathematics, University of Bologna, Bologna, Italy (2003)Google Scholar
  10. 10.
    Archetti, C.: The Vehicle Routing Problem with capacity 2 and 3, General Distances and Multiple Customer Visits. Operational Research in Land and Resources Manangement, 102 (2001)Google Scholar
  11. 11.
    Thangiah, S.: A Site Dependent Vehicle Routing Problem with Complex Road Constraints. Artificial Intelligence and Robotics Lab., Slippery Rock University, U.S.A (2003)Google Scholar
  12. 12.
    Dorronsoro, B.: The VRP Web. AUREN. Language and Computation Sciences of the University of Malaga (2005), http://neo.lcc.uma.es/radi-aeb/WebVRP
  13. 13.
    Bianchi, L.: Notes on Dynamic Vehicle Routing. Technical Report IDSIA - Institut Dalle Molle di Studi sull’Intelligenza Artificiale, Switzerland (2000)Google Scholar
  14. 14.
    Jacobs, B., Goetshalckx, M.: The Vehicle Routing Problem with Backhauls: Properties and Solution Algorithms. Techincal report MHRC-TR-88-13, Georgia Institute of Technology (1993)Google Scholar
  15. 15.
    Fleischmann, B.: The Vehicle routing problem with multiple use of vehicles. Working paper, Fachbereigh Wirtschafts wissens chaften, Universitt Hamburg (1990)Google Scholar
  16. 16.
    Taillard, E.: A Heuristic Column Generation Method for the Heterogeneous Fleet VRP. Institut Dalle Moli di Studi sull Inteligenza Artificiale, Switzerland. CRI-96-03 (1996)Google Scholar
  17. 17.
    Toth, P., Vigo, D.: An Overview of Vehicle Routing Problems. SIAM Monographs on Discrete Mathematics and Applications. The Vehicle Routing Problem (2000)Google Scholar
  18. 18.
    Garey, M.R., Johnson, D.S.: Computers and Intractability, a Guide to the Theory of NP-completeness. W. H. Freeman and Company, New York (1979)zbMATHGoogle Scholar
  19. 19.
    Baase, S.: Computer Algorithms, Introduction to Design and Analysis. Editorial Addison-Wesley Publishing Company, Reading (1998)Google Scholar
  20. 20.
    Kang, J., Park, S.: Algorithms for Variable Sized Bin Packing Problem. Proc. Operational Research 147, 365–372 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Epstein, L.: Online Bin Packing with Cardinality Constraints. In: Proc. 13th European Symposium on Algorithms (2005)Google Scholar
  22. 22.
    Cruz, L., et al.: DiPro: An Algorithm for the Packing in Product Transportation Problems with Multiple Loading and Routing Variants. In: Gelbukh, A., Morales, A.F.K. (eds.), pp. 1078–1088. Springer, Heidelberg (2007)Google Scholar
  23. 23.
    Chan, W., et al.: Online Bin Packing of Fragile Objects with Application in Cellular Networks, tech. report, Hong Kong RGC Grant HKU5172/03E (2005)Google Scholar
  24. 24.
    Verweij, B.: Multiple Destination Bin Packing, tech. report, Algorithms and Complexity in Information Technology (1996)Google Scholar
  25. 25.
    Herrera, J.: Development of a methodology based on heuristics for the integral solution of routing, scheduling and loading problems on distribution and delivery processes of products. MS. thesis. Instituto Tecnológico de Ciudad Madero, México (2006)Google Scholar
  26. 26.
    Delgado, J., et al.: Construction of an optimal solution for a Real-World Routing-Scheduling-Loading Problem. Journal Research in Computing Science 35, 137–146 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Juan J. González-Barbosa
    • 1
  • Laura Cruz-Reyes
    • 1
  • José F. Delgado-Orta
    • 1
  • Héctor J. Fraire-Huacuja
    • 1
  • Guadalupe Castilla-Valdez
    • 1
  • Víctor J. Sosa Sosa
    • 2
  1. 1.Instituto Tecnológico de Ciudad Madero, 1º. de mayo s/n Col. Los MangosCiudad Madero TamaulipasMéxico
  2. 2.Centro de Investigación y de Estudios Avanzados (CINVESTAV)México

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