The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network.

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...

We consider cost sharing for a class of facility location games, where the strategy spaceof each player consists of the bases of a player-specific matroid defined on the set of re-sources. We assume that resources have nondecreasing load-dependent costs and player-specific delays. Our model includes the important special case of capacitated facility loca-tion problems, where...

We consider a generalized version of the rooted Connected Facility Location Problem (ConFL) with capacities and prizes on clients as well as capacity constraints on potential facilities. Furthermore, we are interested in selecting and connecting the most profitable client subset (i.e. a prize collecting variant) instead of mandatorily connecting all clients. Connected Facility Location Problems...

This research develops a clustering-based location-allocation method to the Capacitated Facility Location Problem (CFLP), which provides an approximate optimal solution to determine the location and coverage of a set of facilities to serve the demands of a large number of locations. The allocation is constrained by facility capacities – different facilities may have different capacities and the...

This paper presents an extension of the capacitated facility location problem (CFLP), in which the general setup cost functions and multiple facilities in one site are considered. The setup costs consist of a fixed term (site setup cost) plus a second term (facility setup costs). The facility setup cost functions are generally non-linear functions of the size of the facility in the same site. T...

The Soft-Capacitated Facility Location Problem, where each facility is composed of a variable number of fixed-capacity production units, has been recently studied in several papers, especially in the metric case. In this paper, we only consider the general problem where connection costs do not systematically satisfy the triangle inequality property. We show that an adaptation of the set coverin...

This paper concerns a dynamic multi-commodity capacitated facility location problem in supply chain, where different products flow throughout different layers of supply chain over a time horizon to meet customers’ demand. The capacity and the location of facilities need to be changed for supply chain to operate efficiently and respond quickly to demand changes. Relocating facilities or changing...

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We consider the polyhedral approach to solving the capacitated facility location problem. The valid inequalities considered are the knapsack, ow cover, e ective capacity, single depot, and combinatorial inequalities. The ow cover, e ective capacity, and single depot inequalities form subfamilies of the general family of submodular inequalities. The separation problem based on the family of subm...