Advertisement

Journal of Heuristics

, Volume 19, Issue 2, pp 157–177 | Cite as

Optimizing routes and stock

  • Irma GarcíaEmail author
  • Joaquín Pacheco
  • Ada Alvarez
Article

Abstract

This work is motivated by a problem proposed to the authors by a bakery company in Northern Spain. The objective is to design the daily routes over the week in order to minimize the total traveled distance. For reducing this total distance, some flexibility in the dates of delivery is introduced, which will cause a stock. Therefore, we study the problem under the bi-objective perspective, “minimizing” simultaneously the total traveled distance and the stock. A bi-objective mixed-integer linear model for the problem is formulated and two methodologies of solution are presented. The first one is based on a series of linked variable neighborhood searches and the second one is based on NSGA-II provided of specific operators. Numerical results showing the obtained estimated Pareto front in both cases are presented.

Keywords

VRP with flexibility in delivery VNS NSGA-II 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahuja, R., Magnanti, T., Orlin, J.: Network Flows: Theory, Algorithms and Applications. Prentice Hall, Englewood Cliffs (1993) zbMATHGoogle Scholar
  2. Beasley, J.: Route–first cluster–second methods for vehicle routing. Omega 11, 403–408 (1983) CrossRefGoogle Scholar
  3. Bentley, J.: Fast algorithms for geometric traveling salesman problems. ORSA J. Comput. 4, 387–411 (1992) MathSciNetzbMATHCrossRefGoogle Scholar
  4. Caballero, R., Gonzalez, M., Guerrero, F.M., Molina, J., Paralera, C.: Solving a multiobjective location routing problem with a metaheuristic based on tabu search. Application to a real case in Andalusia. Eur. J. Oper. Res. 177(3), 1751–1763 (2007) zbMATHCrossRefGoogle Scholar
  5. Deb, K., Pratap, A., Argwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2002) CrossRefGoogle Scholar
  6. Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959) MathSciNetzbMATHCrossRefGoogle Scholar
  7. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2005) zbMATHGoogle Scholar
  8. Fisher, M., Jaikumar, R.: A generalized assignment heuristics for vehicle routing problem. Networks 11, 109–124 (1981) MathSciNetCrossRefGoogle Scholar
  9. Jozefowiez, N., Semet, F., Talbi, E.-G.: From single-objective to multiobjective vehicle routing problems: Motivations, case studies, and methods. In: Golden, B.L., Raghavan, S., Wasil, E. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges, pp. 445–471. Springer, Berlin (2008a) CrossRefGoogle Scholar
  10. Jozefowiez, N., Semet, F., Talbi, E.-G.: Multi–objective vehicle routing problems. Eur. J. Oper. Res. 189, 293–309 (2008b) MathSciNetzbMATHCrossRefGoogle Scholar
  11. Martello, S., Toth, P.: Knapsack Problems Algorithms and Computer Implementations. Wiley, New York (1990) zbMATHGoogle Scholar
  12. Or, I.: Traveling Salesman Type Combinatorial Problems and their relations to the logistics of blood banking. Dissertation, Northwestern University (1976) Google Scholar
  13. Pacheco, J., Alvarez, A., García, I., Angel-Bello, F.: Optimizing vehicle routes in a bakery company allowing flexibility in delivery dates. J. Oper. Res. Soc. (2011). doi: 10.1057/jors.2011.51 Google Scholar
  14. Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Comput. Oper. Res. 31, 1985–2002 (2004) MathSciNetzbMATHCrossRefGoogle Scholar
  15. Romero, C.: Teoría de la Decisión Multicriterio: Conceptos, Técnicas y Aplicaciones. Alianza Universidad Textos. Alianza Editorial, Madrid (1993) Google Scholar
  16. Taillard, E., Badeau, P., Gendreau, M., Potvin, J.: A tabu search heuristic for the vehicle routing problem with time windows. Transp. Sci. 31, 170–186 (1997) zbMATHCrossRefGoogle Scholar
  17. Toth, P., Vigo, D. (eds.): The Vehicle Routing Problem. SIAM. Monographs on Discrete Mathematical and Applications. SIAM, Philadelphia (2002) zbMATHGoogle Scholar
  18. Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3, 257–271 (1999) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Universidad Autónoma de Nuevo LeónNuevo LeónMexico
  2. 2.Universidad Autónoma de CoahuilaSaltilloMexico
  3. 3.Departamento de Economía AplicadaUniversidad de BurgosBurgosSpain

Personalised recommendations