The dissertation develops location-covering models considering nodal and path demand, multiple-type facilities, and unavailability of servers. The first part concentrates on the systems with demand originating from nodes and paths. Two models are proposed. The explicit model is a Quadratic Maximal Covering Location Problem and a greedy heuristic supported by simulated annealing is suggested for its solution. The implicit model is for the systems with network structure and a heuristic algorithm based on geometrical concepts is developed for its solution. A case study is presented to locate cellular base stations in Erie County, NY. The second part implements the explicit model to optimize aeromedical base locations in the state of New Mexico by considering crash nodes and crash paths. In addition, performance measures are provided for the existing aeromedical system of New Mexico. The third part addresses the problem of simultaneously locating ground ambulances, air ambulances and transfer points. Three types of coverage are considered; ground coverage, air coverage, or joint ground-air coverage through a transfer point. To analyze this complex coverage situation, two sets of models are developed, which are variations of Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). A case study, which uses crash data of New Mexico, is presented to illustrate the results. The fourth part considers the unavailability of aeromedical servers due to weather and visibility conditions. Objective is to maximize total accident coverage during the planning horizon without exceeding the specified relocation cost limit. Four different solution methods are developed based on greedy heuristic, simulated annealing and dynamic programming.