Robust facility location
Robust facility location
复制标题
DOI：
10.1007/s001860300294
复制
发表时间：
2003-11-01
影响因子：
1.2
通讯作者：
Nickel, S
中科院分区：
文献类型：
--
作者：
Carrizosa, E;Nickel, S
设A是表示一组需求点（城镇，.）的地理坐标的平面的非空有限子集，由设施服务，其在给定区域S内的位置被寻找。假设a的单位成本是A的一个元素，如果设施位于x是S的一个元素，则与dist（x，a）-从x到a的距离-成比例，并且点a的需求由ω（a）给出，最小化总运输成本TC（ω，x）相当于解决韦伯问题。然而，在实践中，可能的情况是，需求向量ω是未知的，并且仅可以提供在上限上的估计器（ω）。此外，这种估计过程中的误差可能是不可忽略的。我们提出了一个新的模型，这种情况下：选择一个阈值B > 0代表最高的可接受的运输成本。将位置x的鲁棒性rho定义为变得不可接受所需的最小需求增加，即rho（x）= min{\\omega -（ω）over cap）\\：TC（omega，x）> B，omega大于或等于0}，并找到x最大化rho以获得最鲁棒的位置。
yLet A be a nonempty finite subset of the plane representing the geographical coordinates of a set of demand points (towns,...), to be served by a facility, whose location within a given region S is sought. Assuming that the unit cost for a is an element of A if the facility is located at x is an element of S is proportional to dist(x, a) - the distance from x to a - and that demand of point a is given by omega(a), minimizing the total transportation cost TC(omega, x) amounts to solving the Weber problem. In practice, it may be the case, however, that the demand vector omega is not known, and only an estimator (ω) over cap can be provided. Moreover the errors in such estimation process may be non-negligible. We propose a new model for this situation: select a threshold value B > 0 representing the highest admissible transportation cost. Define the robustness rho of a location x as the minimum increase in demand needed to become inadmissible, i.e. rho(x) = min{\\omega - (ω) over cap)\\ : TC(omega, x) > B, omega greater than or equal to 0} and find the x maximizing rho to get the most robust location.