On Exact Solvability of the Restricted Capacitated Facility Location Problem

Consider a graph G = (V,E). At the vertices of G there are consumers of some product and the possible places of its production. For each vertex i in V the demand volume b(i), the cost f(i) for opening a facility and the restriction a(i) on the facility’s capacity are given. For each edge e in E, there are given the cost of the transportation of the product unit ce and the maximum quantity qe of a product that can be transported along this edge. It is required to place the facilities in a way they satisfy all demand with minimal total cost of opening facilities and delivering the product to consumers. We propose a pseudo-polynomial time algorithm solving the problem with restrictions on facility and edge capacities on a tree graph, and discuss a polynomial time algorithm solving the problem with restrictions on edge capacities in the case of a line graph given.