Network Location Theory

网络选址问题涉及在诸如交通网络之类的网络上定位一个或多个新设施时，所产生的某种成本与网络上新设施与网络上现有设施之间的网络旅行距离成正比，并且可能与新设施之间的距离成正比。新设施将设置在网络上，以使目标函数最小化。还可能存在距离限制，对设施之间的距离施加上限。过去，当问题是连续的(考虑每条链路上的所有可能位置)时，解决此类问题的主要方法一直是利用网络结构。最近已经表明，许多这样的连续问题可以表示为数学规划问题(明确定义的数学优化问题)。本研究将集中于利用数学规划的连通性来解决连续网络选址问题。由于后一个领域已经相当发达，提高我们解决网络选址问题的能力的机会显得非常有希望。

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.