We study the two-level uncapacitated facility location (TUFL) problem. Given two types of facilities, which we call y-facilities and z-facilities, the problem is to decide which facilities of both types to open, and to which pair of y- and z-facilities each client should be assigned, in order to satisfy the demand at maximum profit. We first present two multi-commodity flow formulations of TUFL and investigate the relationship between these formulations and similar formulations of the one-level uncapacitated facility location (UFL) problem. In particular, we show that all nontrivial facets for UFL define facets for the two-level problem, and derive conditions when facets of TUFL are also facets for UFL. For both formulations of TUFL, we introduce new families of facets and valid inequalities and discuss the associated separation problems. We also characterize the extreme points of the LP-relaxation of the first formulation. While the LP-relaxation of a multi-commodity formulation provi...

Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure. The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with constant capacity K for all plants. These facet inequalities depend on K and thus differ fundamentally from the valid inequalities for the uncapacitated version of the problem. We also introduce a second formulation for a model with indivisible cus-tomer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.

. In the operation of communication and computer networks, it may become desirable or necessary to add a new function to the network through the placement of the corresponding electronic device within certain existing user locations. This will involve deciding which user locations will have devices placed at them as well as deciding an assignment of users to device locations. The objective when adding the new function is to choose these locations and assignments such that the combined cost of placing the devices and routing users to their assigned device locations is minimized. This problem, which we call the device placement problem, is closely related to the simple plant location problem and the p-median problem. Like these problems, the device placement problem is NP-hard, and thus it is highly unlikely that efficient methods for solving this problem to optimality exist. We discuss and test several heuristic methods for the device placement problem, as well as a very efficient meth...

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this paper we consider a restricted version of the problem of locating "access facilities", or concentration points, to permit economical connection of users to resources. This problem has been already studied [16]. Actually, we consider only one resource that does not have a important place in the optimization problem. This assumption leads to a strong relation with the problem of finding a minimum r-rooted 2-height spanning tree, giving as result conceptually easy heuristics, that are easilly implemented as well. In the next section we describe in details the restricted concentrator location problem, and some related problems often found in the literature. In section

Sensor networks proved to be a useful research tool in the field of environmental monitoring. While first sensor deployments consisted of a relatively small number of static nodes, mobile sensor devices have attracted growing interest for large-scale sensing applications in recent years. In this paper, we present Ikarus, a novel participatory sensing application having orders of magnitude more users than existing approaches. The Ikarus system exploits sensor data collected during cross-country flights by paraglider pilots to study thermal effects in the atmosphere. Based on first experiences gained from this approach, we identify three key aspects that are crucial for the success of participatory sensing applications: incentives for participation, the ability to deal with faulty data, and concise data representation. 1.