We study the network facility location problem with constraints on the capacities of communication lines, called Restricted Facility Location Problem (RFLP). It is required to locate facilities at the vertices of a given network graph so as to simultaneously satisfy at minimum cost the demands of customers located at the vertices of the graph. We consider two statements of the problem: the multiple allocation RFLP, where the demand of a customer can be satisfied jointly by several facilities, and the single allocation RFLP, where the demand of a customer must be entirely satisfied by a single facility. We show that the single allocation RFLP is NP-hard even if the network is a simple path and strongly NP-hard if the network is a tree. The multiple allocation RFLP is weakly NP-hard on trees. For this problem, we propose a pseudopolynomial-time algorithm for the case where the network graph has constant treewidth and a linear-time algorithm for the case where the network is a simple path.

我们研究了受通信线路容量限制的网络设施位置问题，称为受限设施位置问题 (RFLP)。要求将设施定位在给定网络图的顶点处，以便同时以最小的成本满足位于图顶点的客户的需求。我们考虑该问题的两种表述：多重分配 RFLP，其中客户的需求可以由多个设施共同满足，以及单一分配 RFLP，其中客户的需求必须完全由单个设施满足。我们表明，即使网络是简单路径，单分配 RFLP 也是 NP 难的，如果网络是树，则是强 NP 难的。多重分配 RFLP 在树上是弱 NP 难的。对于这个问题，