Document Type: Research Paper


1 I. U. D. R., University of La Laguna, E-38271 Tenerife, Spain

2 Department C. C. I. A., University of Granada, E-18071 Granada, Spain


Transport route planning is one of the most important and frequent
activities in supply chain management. The design of information systems
for route planning in real contexts faces two relevant challenges: the
complexity of the planning and the lack of complete and precise information.
The purpose of this paper is to nd methods for the development of transport
route planning in uncertainty decision making contexts. The paper uses an
approximation that integrates a speci c fuzzy-based methodology from Soft
Computing. We present several fuzzy optimization models that address the
imprecision and/or exibility of some of its components. These models allow
transport route planning problems to be solve with the help of metaheuristics
in a concise way. A simple numerical example is shown to illustrate this


[1] E. Avineri, Soft computing applications in tra c and transport systems: a review, Advances
in Soft Computing, 1 (2005), 17-25.
[2] A. Baykasoglu and T. Gocken, Review and classi cation of fuzzy mathematical programs,
Journal of Intelligent & Fuzzy Systems, 19 (2008), 205-229.
[3] R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Management
Science, 17(B)(4) (1970), 141-164.
[4] J. M. Cadenas and J. L. Verdegay, Using fuzzy numbers in linear programming, IEEE Transactions
on Systems, Man and Cybernetics, 27(B)(6) (1997), 1017-1022.
[5] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,
Iranian Journal of Fuzzy Systems, 3(1) (2006), 1-21.
[6] R. Cheng and M. Gen, Vehicle routing problem with fuzzy due-time using genetic algorithm,
Japanese Journal of Fuzzy Theory and Systems, 7(5) (1995), 1050-1061.
[7] J. F. Cordeau, G. Laporte, M. Savelsbergh and D. Vigo, Vehicle Routing, Handbook in OR
& MS, 14(6) (2007), 367-427.
[8] M. Delgado, J. L. Verdegay and M. A. Vila, Imprecise costs in mathematical programming
problems, Control and Cybernet, 16(2) (1987), 113-121.
[9] M. Delgado, J. L. Verdegay and M. A. Vila, A general model for fuzzy linear programming,
Fuzzy Sets and Systems, 29 (1989), 21-29.
[10] M. Djadane, G. Goncalves, T. Hsu and R. Dupas, Dynamic vehicle routing problems under

exible time windows and fuzzy travel times, Proceedings of 2006 International Conference
on Service Systems and Service Management, 2 (2006), 1519-1524.

[11] C. Erbao and L. Mingyong, A hybrid di erential evolution algorithm to vehicle routing prob-
lem with fuzzy demands, Journal of Computational and Applied Mathematics, 231 (2009),
[12] K. Ganesh, A. S. Nallathambi and T. T. Narendran, Variants, solution approaches and ap-
plications for Vehicle Routing Problems in supply chain: agile framework and comprehensive
review, International Journal of Agile Systems and Management, 2(1) (2007), 50-75.
[13] M. Gendreau, G. Laporte and R. Seguin, Stochastic vehicle routing, European Journal of
Operational Research, 88(1) (1996), 312.
[14] J. Y. Guo and J. Li, A hybrid genetic algorithm to the vehicle routing problem with fuzzy
traveling time, Journal of Industrial Engineering Management, 19 (2006), 13-17.
[15] L. Hong and M. Xu, A model of MDVRPTW with fuzzy travel time and time-dependent and
its solution, Proceeding of Fifth International Conference on Fuzzy Systems and Knowledge
Discovery, 3 (2008), 473-478.
[16] L. Hong and M. Xu, Real vehicle routing and dispatching with dynamic fuzzy travel times,
Proceeding of Second International Conference on Genetic and Evolutionary Computing,
doi:10.1109/WGEC.2008.28, (2008), 32-37,
[17] J. Jia, N. Liu and R. Wang, Genetic algorithm for fuzzy logistics distribution vehicle rout-
ing problem, Proceeding International Conference on Service Operations and Logistics, and
Informatics, doi:10.1109/SOLI.2008.4686625, (2008), 1427-1432.
[18] M. Ko, A. Tiwari and J. Mehnen, A review of soft computing applicactions in supply chain
management, Applied Soft Computing, 10 (2010), 661-674.
[19] R. J. Kuo, C. Y. Chiu and Y. J. Lin, Integration of fuzzy theory and ant algorithm for vehicle
routing problem with time window, International Conference of the North American Fuzzy
Information Processing Society, 23 (2004), 925-930.
[20] C. S. Liu and M. Y. Lai, The vehicle routing problem with uncertain demand at nodes,
Transportation Research Part E: Logistics and Transportation Review, 5(4) (2009), 517-524.
[21] P. Lucic and D. Teodorovic, Vehicle routing problem with uncertain demand at nodes: the bee
system and fuzzy logic approach, In Fuzzy Sets Based Heuristics for Optimization, Springer
Verlag, Berlin, (2003), 67-82.
[22] P. Lucic and D. Teodorovic, The fuzzy ant system for the vehicle routing problem when
demand at nodes is uncertain, Journal on Arti cial Intelligence Tools (IJAIT), 16(5) (2007),
[23] M. R. Sa , H. R. Maleki and E. Zaeimazad, A note on the Zimmermann method for solving
fuzzy linear programming problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 31-45.
[24] W. R. Stewart Jr. and B. L. Golden, Stochastic vehicle routing: a comprehensive approach,
European Journal of Operational Research, 14(4) (1983), 371-385.
[25] L. Tang, W. Cheng, Z. Xhang and B. Zhong, Ant colony algorithm based on information
entropy theory to fuzzy vehicle routing problem, Proceedings ISKE, Series: Advances in Intelligent
Systems Research, 2007.
[26] D. Teodorovic and S. Kikuchi, Application of fuzzy sets theory to the saving based vehicle
routing algorithm, Civil Engineering Systems, 8 (1991), 87-93.
[27] D. Teodorovic and G. Pavkovic, The fuzzy set theory approach to the vehicle routing problem
when demand at nodes is uncertain, Fuzzy Sets and Systems, 82 (1996), 307-317.
[28] D. Teodorovi, Fuzzy logic systems for transportation engineering: the state of the art, Transportation
Research, 33(A) (1999), 337-364.
[29] F. Tillman, The multiple terminal problem with probabilistic demands, Transportation Science,
3(3) (2002), 192-204.
[30] P. Toth and D. Vigo, The vehicle routing problem, Monographs on Discrete Mathematics and
Applications, SIAM, 9 (2002).
[31] J. L. Verdegay, Fuzzy mathematical programming, In: M. M. Gupta, E. Sanchez, eds., Fuzzy
Information and Decision Processes, 1982.
[32] J. L. Verdegay, Fuzzy optimization: models, methods and perspectives, Proceding 6thIFSA-95
World Congress, (1995), 39-71.

[33] J. L. Verdegay, R. R. Yager and P. Bonissone, On heuristics as a fundamental constituent of
Soft Computing, Fuzzy Sets and Systems, 159 (2008), 846-855.
[34] R. Viertl and D. Hareter, Fuzzy information and stochastics, Iranian Journal of Fuzzy Systems,
1(1) (2004), 43-56.
[35] J. Y. Zhang and J. Li, Study on logistics distribution vehicle routing problem with fuzzy due-
time, International Conference on Management Science & Engineering, doi: 10. 1109/ICMSE.
2007. 4421866, (2007), 311-317.
[36] Y. S. Zheng and B. D. Liu, Fuzzy vehicle routing model with credibility measure and its hybrid
intelligent algorithm, Applied Mathematics and Computation, 176 (2006), 673-683.
[37] H. J. Zimmermann, Description and optimization of fuzzy system, International Journal of
general System, 2 (1976), 209-216.