In the immediate aftermath of a disaster, local and international aid organisations deploy to deliver life-saving aid to the affected population. Yet pre-disaster road maps and road transportation models do not capture disruptions to the transportation network caused by the disaster or the dynamic changes of the situation, resulting in uncertainty and inefficiency in planning and decision-making. The integration of data in near real time on the status of the road infrastructure in the affected region can help aid organisations to keep track of the rapidly shifting conditions on the ground and to assess the implications for their logistics planning and operations. In this paper, we present a rapid graph-theoretical reachability information system based on a combination of OpenStreetMap and open humanitarian data. The system supports logistics planning in determining road access to affected communities. We demonstrate the results of our approach in a case study on the 2018 earthquake in Papua New Guinea. Our findings show the reachability of affected communities depending on the actual status of the road network, allowing for the prioritization of targeted locations and the identification of alternative routes to get there.