What approximation ratio can we achieve for the Facility Location problem if whenever a client u connects to facility v, opening cost of v is at most θ times service u? We show that this and many other problems are particular case Activation Edge-Cover problem. Here given multigraph G=(V,E), set R⊆V terminals, thresholds {tue,tve} each uv-edge e∈E. The goal find an assignment a={av:v∈V} nodes m...

Facility location problem involves locating a facility to optimize some performance measures. Location of a public facility to serve the community, such as a fire station, significantly affects its service quality. Main objective in locating a fire station is to minimize the response time, which is the time duration between receiving a call and reaching the place of incident. In metropolitan ar...

We study various models for the one-dimensional multi-stage facility location problems with transient agents, where a agent arrives in some stage and stays number of consecutive stages. In problems, we need to serve each one their stages by determining at stage. first model, assume there is no cost moving across focus on optimal algorithms minimize both social objective, defined as total distan...

Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made the development of models for facility location under uncertainty a high priority for researchers i...

There has been a number of facility location problems dealing with the introduction of the equity issue in the travel distances distribution. In this paper we analyze a new aspect of equity concerning the distribution of the arrival times of customers. Given a depot and a set of demand points generating flow which also represent potential locations, we consider a discrete two-stage location pro...

This paper considers minimax regret 1-sink location problems in dynamic path networks. A dynamic path network consists of an undirected path with positive edge lengths and constant edge capacity and the vertex supply which is nonnegative value, called weight, is unknown but only the interval of weight is known. A particular assignment of weight to each vertex is called a scenario. Under any sce...

In this paper we study a simple vulnerability-based stochastic dependency model of link failures in a network prone to disasters. Under this model, we study the problem of locating k facilities to maximize the expected demand serviced within a given distance, and show its equivalence to the well-studied maximum k-facility location problem. In the special case when there is no distance constrain...