Summary: Since the 1990s, problems regarding the evacuation of persons have been extensively studied in the literature. The proposed models can be classified into two main categories: macroscopic and microscopic models. The DSS\(\_\)Evac\(\_\)Logistic project (2015, http://projets.li.univ-tours.fr/dssvalog/?lang=en) is interested in the evacuation of people in the context of flooding, burning or seismic events for which insecurity, capacity, and time to cross roads vary over time. We consider the problem of large-scale evacuation of medium-sized cities, in situations where the evacuees must change their place of residence for a period ranging from several days to several months. As a part of this project, we assume as solved the problem of selecting a set of starting points and shelter locations. We develop discrete macroscopic models and methods that incorporate the risk and safety that are inherent in the context studied for evacuating persons. The problem that needs to be addressed is to determine the minimum overall evacuation time while minimizing the risk incurred by evacuees (i.e., maximize the amount of unharmed persons). In this context, we first propose a pseudopolynomial method, which is based on the shortest augmenting paths, without using a time-expanded network to tackle the earliest arrival flow and the quickest flow problems no-wait with time-dependent data. Then, we extend this approach to consider the safety criterion.