In this study, we propose a post-disaster assessment strategy as part of response operations in which effective and fast relief routing are of utmost importance. In particular, the road segments and the population points to perform assessment activities on are selected based on the value they add to the consecutive response operations. To this end, we develop a bi-objective mathematical model that provides damage information in the affected region by considering both the importance of population centers and road segments on the transportation network through using aerial and ground vehicles (drones and motorcycles). The first objective aims to maximize the total value added by the assessment of the road segments (arcs) whereas the second maximizes the total profit generated by assessing points of interests (nodes). Bi-objectivity of the problem is studied with the ϵ-constraint method. Since obtaining solutions as fast as possible is crucial in the post-disaster condition, heuristic methods are also proposed. To test the mathematical model and the heuristic methods, a data set belonging to Kartal district of Istanbul is used. Computational experiments demonstrate that the use of drones in post-disaster assessment contributes to the assessment of a larger area due to its angular point of view. Also, the proposed heuristic methods not only can find a high-quality approximation of the Pareto front but also mitigates the solution time difficulties of the mathematical model.