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.
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References
Ahuja, R., Magnanti, T., Orlin, J.: Network Flows: Theory, Algorithms and Applications. Prentice Hall, Englewood Cliffs (1993)
Beasley, J.: Route–first cluster–second methods for vehicle routing. Omega 11, 403–408 (1983)
Bentley, J.: Fast algorithms for geometric traveling salesman problems. ORSA J. Comput. 4, 387–411 (1992)
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)
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)
Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)
Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2005)
Fisher, M., Jaikumar, R.: A generalized assignment heuristics for vehicle routing problem. Networks 11, 109–124 (1981)
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)
Jozefowiez, N., Semet, F., Talbi, E.-G.: Multi–objective vehicle routing problems. Eur. J. Oper. Res. 189, 293–309 (2008b)
Martello, S., Toth, P.: Knapsack Problems Algorithms and Computer Implementations. Wiley, New York (1990)
Or, I.: Traveling Salesman Type Combinatorial Problems and their relations to the logistics of blood banking. Dissertation, Northwestern University (1976)
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
Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Comput. Oper. Res. 31, 1985–2002 (2004)
Romero, C.: Teoría de la Decisión Multicriterio: Conceptos, Técnicas y Aplicaciones. Alianza Universidad Textos. Alianza Editorial, Madrid (1993)
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)
Toth, P., Vigo, D. (eds.): The Vehicle Routing Problem. SIAM. Monographs on Discrete Mathematical and Applications. SIAM, Philadelphia (2002)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3, 257–271 (1999)
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García, I., Pacheco, J. & Alvarez, A. Optimizing routes and stock. J Heuristics 19, 157–177 (2013). https://doi.org/10.1007/s10732-011-9182-2
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DOI: https://doi.org/10.1007/s10732-011-9182-2