Four communities, Amesville, Bethany, Charlestown and Drenton have obtained permission from the county, to which all four of them belong, to build hospitals to service their residents. The county is paying for the costs of building the hospitals under certain conditions. It will not pay for a single community to build a hospital. The communities will have to share hospitals. The county allows any group of two communities to build one hospital, any group of three communities may build two hospitals, and the four communities together may build three hospitals. If a community is not serviced by a hospital it has to fly its patients to a hospital further away at an extremely high cost. The four communities are connected by existing roads. The layout of the four communities is given in figure 7.1. The distances are given in ten miles, i.e., Amesville and Charlestown are connected by a 30 miles long road. The communities can build a hospital anywhere along a road, including at the site of a community.
KeywordsConvex Hull Budget Constraint Travel Cost Setup Cost Linear Programming Relaxation
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