In this paper, we consider the evacuation problem that consists of grouping and routing evacuees to safe zones. Grouping evacuees reduces congestion on roads, addresses fuel shortage and supports individuals with limited access to transportation means. We propose a mixed integer programming model where individuals with vehicles are instructed to pick up others along their route in order to evacuate the maximum number of individuals within a limited time. Since evacuation decisions and plans must be made as quickly as possible, we propose two heuristics that provide comparable solutions within a short computational time. The first heuristic is inspired from the Clarke-Wright savings heuristic for the vehicle routing problem, while the second heuristic is based on maximum bipartite matching. Computational results show that the proposed heuristics find solutions in less than a second for instances with up to 40 evacuee locations. We also present extensions of the evacuation problem that include vehicles with different capacities, that minimize the time to evacuate everyone, and that find the optimal vehicle placement.