Location models

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This research investigates four models for the location of facilities, such as cell phone towers, landfills, ambulances, or production and service facilities. The first problem studies the location of firms, given that a regional planner offers subsidies. While the customers purchase the good from the least expensive source and firms maximize their profits, the regional planner offers subsidies so as to stimulate economic activities and, ultimately, maximize tax income. The objective is to devise subsidy strategies that best benefit the regional planner, given that the firms and customers behave in their own best interest. The ultimate goal is to research models that include competition between regions as well. The second strand of research considers the location of emergency facilities, such as clinics and ambulances. The objective is to use the smallest possible number of health care facilities that ensure that potential customers are still covered. The notion of coverage used here is softer than in the standard models that employ a "covered - not covered" dichotomy in that customer coverage gradually decreases with increasing distance to the facility. Multi-level health care systems are the specific focus of the work. Special attention will be paid to models with congestion, a crucial feature in the location of emergency facilities. The third class of models to be researched includes location models with multiple objectives. Typical examples of such models include the location of landfills, cell phone towers, and internet kiosks in developing nations. Typical objectives include cost minimization, coverage, and disturbances due to acts of nature or deliberate destruction. Furthermore, pre- and postprocessing modules will be devised that model routing and scheduling components without their explicit inclusion in the model, as this would make most problems of realistic size unsolvable. The fourth and last class of problems to be studied are competitive location models, in which competing firms locate branches of their respective facilities. Specific attention will be paid to models that not only include the firms themselves, but also their supplier. Another important aspect that needs to be investigated is the proper inclusion of customer behavior in the competitive context.