Two major activities in disaster response are evacuation and logistics support. Evacuation from affected areas to medical centers occurs during the initial response phase. Logistics support from supply centers to distribution centers in affected areas tends to continue for a longer time to sustain the basic needs of survivors remaining there. Minimizing delay in providing priority commodities and healthcare to the survivors can greatly improve the survival rate. As a first step toward solving the emergency-logistics problem, we developed Path-Builder, a simple, fast constructive heuristic for identifying a feasible, acceptable solution. Path-Builder is based on a greedy l-neighborhood search technique that extends the definition of neighborhood to suit the problem's special needs. The heuristic selects partial paths to append to vehicle itineraries on the basis of the vehicles' utilities. It constructs all vehicle itineraries in parallel and iteratively, trying to exploit foreseeable opportunities within the vehicles' limited neighborhood.