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.

本文关注的是在直线范数下对树形网络进行服务成本修正的逆非容量设施位置问题的两种变体。在第一个变体中，目标是以最便宜的方式相对于修改范围修改基础服务成本，使得一组预定的设施位置在新参数下变得最优。研究了两种类型的这个问题。第二种变体要求在相关预算内修改服务成本，直到预定的设施位置尽可能靠近客户。还研究了该问题的两种类型。我们开发精确的最优算法来解决正在研究的问题。通过一个例子，说明了所提出算法的效率。