A multiobjective, maximal conditional covering location problem applied to the relocation of hierarchical emergency response facilities

In this research we analyze the effectiveness of the current and optimal locations of a set of existing regional assets maintained by the Department of Defense to respond to large-scale emergencies. These assets have been incrementally resourced, established, sited over the past 20 years without regard to the entire enterprise and, due to fiscal and political costs, modifications to the current structure must yield significant gains to garner approval. We formulate a multiobjective hierarchical extension of the maximal covering location problem that seeks to maximize coverage of the population within a rapid response window while minimizing modifications to the existing structure. Additionally, we prevent facilities from covering nodes located within close proximity using a modified conditional covering problem (CCP) constraint; this constraint accounts for the large impact radius that can occur in a worst-case scenario. To solve our multiobjective problem, we develop a set of non-inferior solutions using the ε-constraint method. These non-inferior solutions explicitly represent the trade-off between maximizing coverage and minimizing cost, and they offer a decision maker a set of Pareto optimal decisions to consider for implementation. Applying our model and methodology to the current set of assets, we demonstrate that, in the absence of resource constraints, we can improve coverage by more than 15%, approximately 49 million people. Furthermore, with only 23 unit relocations (less than a 30% modification of the entire structure) coverage can exceed 98%, an improvement of an additional 45 million people covered. Finally, we demonstrate additional advantages of implementing the modified CCP constraint.