Solving a bi-objective multi-product vehicle routing problem with heterogeneous fleets under an uncertainty condition

This paper presents a novel bi-objective multi-product capacitated vehicle routing problem with uncertainty indemand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflictfuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles andshortage of products. The second objective is to minimize the shortage of products for all retailers. In order to getcloser to a real-world 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 distinctand belongs to a bounded uncertainty set. The fuzzy-robust counterpart model may be larger than the deterministicform or the uncertain model with one approach and it has with further complexity; however, it provides a betterefficient solution for this problem. The proposed fuzzy approach is used to solve the bi-objective mixed-integer linearproblem to find the most preferred solution. Moreover, it is impossible to improve one of the objective functionswithout considering deterioration in the other objective functions. In order to show the conflict between two objectivefunctions in an excellent fashion, a Pareto-optimal solution with the ε-constraint method is obtained. Some numericaltest problems are used to demonstrate the efficiency and validity of the presented model.

Solving a bi-objective multi-product vehicle routing problem with heterogeneous fleets under an uncertainty condition Keywords:

Capacitated vehicle routing problem , Bi-objective model , Robust optimization , Fuzzy optimization , Multiple products