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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 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
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