Given finite resources, organizations are in a constant struggle to satisfy conflicting demands for resource allocation. Finding the right number of response units needed to respond to an incident in a given area is one such problem. Different geographical areas have different characteristics that further complicate the problem. For example, Canada’s Arctic waters is a large area with many islands and where varying ice coverage conditions are the norm. These impediments complicate what would otherwise be a straightforward application of the Circle Packing or Circle Covering Problem. The authors propose to call such a problem the Impediment Induced Variable Shape Covering Problem and present the Incident Response Model that determines the minimum number of units needed to respond to an incident anywhere in a given Area of Interest within a predetermined response time while avoiding or accounting for impediments.