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This dissertation deals with the problem of locating inspection stations in two different scenarios: (1) in a manufacturing environment, and (2) in a network involving the transportation of hazardous materials. In the manufacturing environment problem, the location of specialized inspection stations in a serial system and in a serial-parallel system is considered. These location problems have the special characteristic that the demand for the facilities being located is from prespecified link flows and their properties. When defects are introduced in a serial manufacturing system, objectives such as minimization of total cost, maximization of yield, and minimization of undetected faulty units are all viable optimization criteria. The dissertation develops several new models for locating specialized inspection stations using such objectives. Cases considered include (1) when inspection/rework stations are to be located, (2) when inspection stations are already located but their operating modes (rework or scrap) are to be determined, and (3) when both locations and operating modes are to be determined. Exact and/or heuristic methods of solutions for these models are developed and some computational experience is reported. Serial lines have the disadvantage that the product flow is easily disrupted by a single machine malfunction anywhere on the line. One way of improving system performance is to provide some degree of redundancy at the machine level using serial-parallel systems. Extensions of some of the serial-system results to the serial-parallel systems are also presented. In the hazardous material transportation setting, the regulating agencies problem of making decisions on where to inspect trucks on the underlying transportation network is considered. In the case when each inspection station's capacity is limited, the problem can be formulated as a new capacitated facility location problem. Some heuristics and an exact branch-and-bound procedure to solve this p