
4f174a7fd39c20a
TavakkoliMoghaddam, R., Raziei, Z., Tabrizian, S. (2016). Solving a BiObjective MultiProduct Vehicle Routing Problem with Heterogeneous Fleets under an Uncertainty Condition. International Journal of Transportation Engineering, 3(3), 207225. doi: 10.22119/ijte.2016.14774Reza TavakkoliMoghaddam; Zohreh Raziei; Siavash Tabrizian. "Solving a BiObjective MultiProduct Vehicle Routing Problem with Heterogeneous Fleets under an Uncertainty Condition". International Journal of Transportation Engineering, 3, 3, 2016, 207225. doi: 10.22119/ijte.2016.14774TavakkoliMoghaddam, R., Raziei, Z., Tabrizian, S. (2016). 'Solving a BiObjective MultiProduct Vehicle Routing Problem with Heterogeneous Fleets under an Uncertainty Condition', International Journal of Transportation Engineering, 3(3), pp. 207225. doi: 10.22119/ijte.2016.14774TavakkoliMoghaddam, R., Raziei, Z., Tabrizian, S. Solving a BiObjective MultiProduct Vehicle Routing Problem with Heterogeneous Fleets under an Uncertainty Condition. International Journal of Transportation Engineering, 2016; 3(3): 207225. doi: 10.22119/ijte.2016.14774
Solving a BiObjective MultiProduct Vehicle Routing Problem with Heterogeneous Fleets under an Uncertainty Condition
Article 5, Volume 3, Issue 3, Winter 2016, Page 207225
PDF (879.14 K)
Document Type: Research Paper
DOI: 10.22119/ijte.2016.14774
Authors
Reza TavakkoliMoghaddam ^{} ^{} ^{1}; Zohreh Raziei^{2}; Siavash Tabrizian^{3}
^{1}Professor, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
^{2}M.Sc. Student, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
^{3}M.Sc. Grad., Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran
Abstract
This paper presents a novel biobjective multiproduct capacitated vehicle routing problem with uncertainty in demand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflict fuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles and shortage of products. The second objective is to minimize the shortage of products for all retailers. In order to get closer to a realworld situation, the uncertainty in the demand of retailers is applied using fuzzy numbers. Additionally, the volume of products is applied using robust parameters, because the possible value of this parameter is not distinct and belongs to a bounded uncertainty set. The fuzzyrobust counterpart model may be larger than the deterministic form or the uncertain model with one approach and it has with further complexity; however, it provides a better efficient solution for this problem. The proposed fuzzy approach is used to solve the biobjective mixedinteger linear problem to find the most preferred solution. Moreover, it is impossible to improve one of the objective functions without considering deterioration in the other objective functions. In order to show the conflict between two objective functions in an excellent fashion, a Paretooptimal solution with the εconstraint method is obtain Some numerical test problems are used to demonstrate the efficiency and validity of the presented model.
Keywords
Capacitated vehicle routing problem; Biobjective model; robust optimization; fuzzy optimization; Multiple products
References
Agra, A., Christiansen, M., Figueiredo, R., Hvattum, L. M., Poss, M. and Requejo C. (2013) “The robust vehicle routing problem with time windows”, Computers & Operations Research, Vol. 40, pp. 856866.
Bertsimas, D. and Sim, M. (2004) “The price of robustness”, Operations Research, Vol. 52, pp. 3553
Cao, E., and Lai, M. (2010) “The open vehicle routing problem with fuzzy demands”, Expert Systems with Applications, Vol. 37, pp. 2405 2411.
Chen, H.K. and Chou, H.W. (1996) “Solving multi objective linear programming problems  A generic approach”, Fuzzy Sets and Systems, Vol. 82, pp. 35–38.
Cheng, R., Gen, M., and Tozawa, T. (1995) “Vehicle routing problem with fuzzy duetime using genetic algorithms”, Japan Society for Fuzzy Theory and Systems, Vol. 7, pp. 1050 1061
 Coelho, L. C., Cordeau, J., and Laporte, G. (2012) “The inventoryrouting problem with transshipment,” Computers & Operations Research, Vol. 39, pp. 25372548
 Golden, B., Assad, A., and Dahl, R. (1984) “Analysis of a large scale vehicle routing problem with an inventory component”, Large scale systems, Vol. 7, pp. 181190.
Ghannadpour, S. F., Noori, S. and TavakkoliMoghaddam, R. (2013) “Multiobjective dynamic vehicle routing problem with fuzzy travel times and customers’ satisfaction in supply chain management”, IEEE Transactions on Engineering Management, Vol. 60, pp. 777790.
Ghannadpour, S. F., Noori, S., TavakkoliMoghaddam, R., and Ghoseiri, K. (2014) “A multiobjective dynamic vehicle routing problem with fuzzy time windows: Model, solution and application”, Applied Soft Computing, Vol. 14, pp. 504527
 Gounaris, C. E., Wiesemann, W., and Floudas C. A. (2013) “The robust capacitated vehicle routing problem under demand uncertainty”, Operations Research, Vol. 61, pp. 677693.
Gupta, R., Singh, B., and Pandey, D. (2010) “Fuzzy vehicle routing problem with uncertainty in service time”, International Journal of Contemporary Mathematical Sciences, Vol. 5, pp. 497507.
He, Y. and Xu, J. (2005) “A class of random fuzzy programming model and its application to vehicle routing problem”, World Journal of Modelling and simulation, Vol. 1, pp. 311.
Kara, I., Kara, B. Y., and Yetis, M. K. (2007) “Energy minimizing vehicle routing problem”, In Combinatorial optimization and applications, pp. 6271. Springer Berlin Heidelberg.
Kuo, R. J., Chiu, C. Y. and Lin, Y. J. (2004) “Integration of fuzzy theory and ant algorithm for vehicle routing problem with time window”, Processing of the IEEE Annual Meeting of the Fuzzy Information (NAFIPS'04), Vol. 2, pp. 925 930.
Li, H., Xu Z. and Zhou F. (2012) “A study on vehicle routing problem with fuzzy demands based on improved tabu search”, Fourth International Conference on Computational and Information Sciences (ICCIS), pp. 7376.
Li, K., Chen B., Sivakumar, A. I. and Wu, Y. (2014) “An inventory–routing problem with the objective of travel time minimization”, European Journal of Operational Research, Vol. 236, pp. 936945.
 Moin, N.H. and Salhi, S. (2007) “Inventory routing problems: a logistical overview”, Journal of Operation Research Society, Vol. 58, pp. 1185–1194.
Montemanni, R., Barta, J., Mastrolilli, M. and Gambardella L. M. (2007) “The robust traveling salesman problem with interval data”, Transportation Science, Vol. 41, pp. 366381.
Raa, B. and Aghezzaf, E. H. (2009) “A practical solution approach for the cyclic inventory routing problem”, European Journal of Operational Research, Vol. 192, pp. 429441.
Sahin, B., Yilmaz, H., Ust, Y., Guneri, A. F. and Gulsun B. (2009) “An approach for analysing transportation costs and a case study”, European Journal of Oprational Research, Vol. 93. pp.111.
SolanoCharris, E. L., Prins, C. and Santos, A. C. (2014) “A robust optimization approach for the vehicle routing problem with uncertain travel cost”, International Conference on Control, Decision and Information Technologies, pp. 098 103.
Sun, L. and Wang, B. (2015) “Robust optimization approach for vehicle routing problems with uncertainty”, Mathematical Problems in Engineering, Article in Press.
Sungur, I., Ordónez F. and Dessouky, M. (2008) “A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty”, IIE Transactions, Vol. 40, pp. 509 523.
Sungur, I., Ren, Y., Ordóñez, F., Dessouky, M. and Zhong, H. (2009) “A model and algorithm for the courier delivery problem with uncertainty”, Transportation Science, Vol. 44, pp. 193205.
Tang, J., Pan, Z., Fung, R. Y. K., and Lau, H. (2009) “Vehicle routing problem with fuzzy time windows”, Fuzzy Sets and Systems, Vol. 160, pp. 683695.
Wang, H. F., and Wen, Y. P. (2002) “Timeconstrained Chinese postman problems”, Computers & Mathematics with Applications, Vol. 44, pp. 375387.
Xu, J., Yan, F. and Li, S. (2011) “Vehicle routing optimization with soft time windows in a fuzzy random environment”, Transportation Research Part E: Logistics and Transportation Review, Vol. 47, pp. 10751091.
Yu, Y., Chen, H. and Chu, F. (2008) “A new model and hybrid approach for large scale inventory routing problems”, European Journal of Operational Research, Vol. 189, pp. 10221040.
Zheng, Y. and Liu, B. (2006) “Fuzzy vehicle routing model with credibility measure and its hybrid intelligent algorithm”, Applied Mathematics and Computation, Vol. 176, pp. 673683.
Zimmermann, H. J. (1978) “Fuzzy programming and linear programming with several objective functions”, Fuzzy Sets and Systems, Vol. 1, pp. 45–55.
StatisticsArticle View: 1,542PDF Download: 2,875