This paper is concerned with two variants of the inverse uncapacitated facility location problem with service cost modifications on tree networks under the rectilinear norm. In the first variant, the aim is to modify the underlying service costs in the cheapest possible way with respect to modification bounds such that a set of predetermined facility locations becomes optimal under the new parameters. Two types of this problem are investigated. The second variant asks to modify the service costs within an associated budget until the predetermined facility locations become as close as possible to the customers. Two types of this problem are also studied. We develop exact optimal algorithms for solving the problems under investigation. By an example, the efficiency of the proposed algorithms is illustrated.

本文关注的是在线性范式下树形网络上服务成本被修改的逆失能设施定位问题的两个变体。在第一变型中，目的是相对于修改范围以最便宜的方式修改基础服务成本，以使得一组预定设施位置在新参数下变得最优。研究了两种类型的此问题。第二变体要求在相关预算内修改服务成本，直到预定设施位置变得尽可能靠近客户为止。还研究了两种类型的此问题。我们开发了精确的最佳算法来解决所研究的问题。举例说明了所提出算法的效率。