We consider a single-facility location problem, where agents are positioned on the real line and partitioned into multiple disjoint districts. The goal is to choose (where public facility be built) so as minimize total distance of from it. This process distributed: positions in each district first aggregated representative for district, then one representatives chosen location. indirect access ...

This paper studies a reliable facility location problem with facility protection that aims to hedge against random facility disruptions by both strategically protecting some facilities and using backup facilities for the demands. An Integer Programming model is proposed for this problem, in which the failure probabilities of facilities are site-specific. A solution approach combining Lagrangian...

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...

With increasing production costs and constraints, demand has increased for manufacturers to minimize maintenance cost and product transport time. We address some aspects of this problem by examining how to choose the optimal layout of stations (machines or buffers) in a production facility based on how the station layout affects the maintenance and product transport times. Specifically, we cons...

in this study, we discuss the capacitated facility location-allocation problem with uncertain parameters in which the uncertainty is characterized by given finite numbers of scenarios. in this model, the objective function minimizes the total expected costs of transportation and opening facilities subject to the robustness constraint. to tackle the problem efficiently and effectively, an effici...

In the Nearest Neighbor problem (NN), the objects in the database that are nearer to a given query object than any other objects in the database have to be found. In the conceptually inverse problem, Reverse Nearest Neighbor problem (RNN), objects that have the query object as their nearest neighbor have to be found. Reverse Nearest Neighbors queries have emerged as an important class of querie...

We consider the online variant of facility location, in which demand points arrive one at a time and we must maintain a set of facilities to service these points. We provide a randomized onlineO(1)-competitive algorithm in the case where points arrive in random order. If points are ordered adversarially, we show that no algorithm can be constant-competitive, and provide an O(logn)-competitive a...

In the Universal Facility Location problem we are given a set of demand points and a set of facilities. The goal is to assign the demands to facilities in such a way that the sum of service and facility costs is minimized. The service cost is proportional to the distance each unit of demand has to travel to its assigned facility, whereas the facility cost of each facility i depends on the amoun...

Facility location games have been a topic of major interest in economics, operations research and computer science, starting from the seminal work by Hotelling. Spatial facility location models have successfully predicted the outcome of competition in a variety of scenarios. In a typical facility location game, users/customers/voters are mapped to a metric space representing their preferences, ...

In out last lecture, we discussed the LP Rounding technique for producing approximation algorithms. The idea behind LP Rounding is to write the problem as an integer linear program, relax its integrality restraints to efficiently solve the general linear program, and then move the LP solution to a nearby integral point in the feasible solution space. The difficulty of this process lies in the r...