Development of a Multi-Objective Mathematical Model for a Heterogeneous Vehicle Routing Problem under Crisis

The optimal routing for transferring the wounded and relief assistance is a major problem in the event of a crisis. At this time the importance of two factors, namely time and money, in order to help and rescue the injured is doubled. This paper aims to find the most optimal route from a rescue center to the crisis center. The presented mathematical model aims to minimize the time and cost of accessing a crisis center. We also consider some assumptions, such as multiple storages, multiple paths, multiple scenarios, split delivery, multiple products, heterogeneity of the vehicles and time. Given that the values of some parameters, such as demand and time of the travel are uncertain, in which we state them in respect to the former mentioned assumptions. Considering these parameters uncertain makes them closer to the real problem. Most of the issues raised in this field have not considered all assumptions at the same time and they have considered the mentioned parameters (time and demand) as definitive. Finally, in order to find accurate answers regarding to multiple objectives of the model and different phases of parameters (i.e., time and demand), we use ε-constraint method in small-scale problems. Then because this problem is NP-hard, two meta-heuristic algorithms, namely MOHS and NSGA-II, are used to solve 15 issues large-scale problems. The results numerically show that both algorithms have high potential in producing good solutions at the right time and they are used to solve the largest and most complex issue in less than 480 seconds. This model is very suitable and uncertain with multiple objectives.