The shortage of relief vehicles capacity is a common issue throughout disastrous situations due to the abundance of injured people who need urgent medical aid. Hence, ambulances fleet management is highly important to save as many injured individuals as possible. In this regard, the present paper defines different patient groups based on their needs and characteristics. In order to provide the affected people with proper and timely medical aid, changes in their health status are also considered. A Mixed-integer Linear Programming (MILP) model is proposed to find the best sequence of routes for each ambulance and minimize the latest service completion time (SCT) as well as the number of patients whose condition gets worse because of receiving untimely medical services. Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are used to find high-quality solutions over a short time. In the end, Lorestan province, Iran, is considered as a case study to assess the model's performance and analyze the sensitivity of solutions with respect to the major parameters, which results in insightful managerial suggestions.

It is observed that the separated design of location for depots and routing for servicing customers often reach a suboptimal solution. So, solving location and routing problem simultaneously could achieve better results. In this paper, waste collection problem is considered with regard to economic and societal objective functions. A non-dominated sorting genetic algorithm (NSGA-II) is used to locate depots and treatment facilities and design the routes starting from depots to serve customers. A new mathematical model is proposed and two objective functions including economic objective (opening cost of depots and treatment facility and transportation cost) and societal objective; that is, negative impact of treatment facilities which are close to towns are addressed in this study. A straightforward order based solution representation is applied for coding solutions of the problem and clustering approach is used to generate appropriate initial solutions. Moreover, three multi-objective decomposition methods including weighted sum, goal programming, and goal attainment are applied to validate the performance of the proposed algorithm. Number of test problems are conducted and the results obtained by algorithms are compared with respect to some comparison metrics. Finally, the experimental results show that the proposed hybrid NSGA-II outperforms all decomposition methods, but the computational times for decomposition methods are less than NSGA-II.