Network Location Theory

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Network location problems involve locating one or more new facilities on a network, such as a transport network, when costs of some sort are incurred which are proportional to network travel distances between new facilities and existing facilities on the network, as well as possibly to distances between new facilities. The new facilities are to be located on the network so as to minimize an objective function. There may also be distance constraints imposing upper bounds on how far apart facilities can be. The principal approach to solving such problems in the past, when the problems have been continuous (considering all possible locations on every link) has been to exploit network structure. Recently it has been shown that many such continuous problems may be formulated as mathematical programming problems (well-defined mathematical optimization problems). This research will focus on solving continuous network location problems by exploiting connections with mathematical programming. Since the latter field is quite highly developed, the opportunities for improving our ability to solve network location problems appear very promising.