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Gilbert Laporte - One of the best experts on this subject based on the ideXlab platform.
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Multi-level Facility Location problems
European Journal of Operational Research, 2018Co-Authors: Camilo Ortiz-astorquiza, Ivan Contreras, Gilbert LaporteAbstract:Abstract We conduct a comprehensive review on multi-level Facility Location problems which extend several classical Facility Location problems and can be regarded as a subclass within the well-established field of hierarchical Facility Location. We first present the main characteristics of these problems and discuss some similarities and differences with related areas. Based on the types of decisions involved in the optimization process, we identify three different categories of multi-level Facility Location problems. We present overviews of formulations, algorithms and applications, and we trace the historical development of the field.
Mohammad Mahdian - One of the best experts on this subject based on the ideXlab platform.
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Approximation Algorithms for Metric Facility Location Problems
SIAM Journal on Computing, 2006Co-Authors: Mohammad Mahdian, Jiawei ZhangAbstract:In this paper we present a 1.52-approximation algorithm for the metric uncapacitated Facility Location problem, and a 2-approximation algorithm for the metric capacitated Facility Location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for the corresponding problem, and our soft-capacitated Facility Location algorithm achieves the integrality gap of the standard linear programming relaxation of the problem. Furthermore, we will show, using a result of Thorup, that our algorithms can be implemented in quasi-linear time.
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Universal Facility Location
Lecture Notes in Computer Science, 2003Co-Authors: Mohammad Mahdian, Martin PalAbstract: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 amount of demand assigned to that Facility and is given by a cost function f i (.). We present a (7.88 + e)-approximation algorithm for the Universal Facility Location problem based on local search, under the assumption that the cost functions f i are nondecreasing. The algorithm chooses local improvement steps by solving a knapsack-like subproblem using dynamic programming. This is the first constant-factor approximation algorithm for this problem. Our algorithm also slightly improves the best known approximation ratio for the capacitated Facility Location problem with non-uniform hard capacities.
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ESA - Universal Facility Location
Algorithms - ESA 2003, 2003Co-Authors: Mohammad Mahdian, Martin PalAbstract: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 amount of demand assigned to that Facility and is given by a cost function f i (·). We present a (7.88 + e)-approximation algorithm for the Universal Facility Location problem based on local search, under the assumption that the cost functions f i are nondecreasing. The algorithm chooses local improvement steps by solving a knapsack-like subproblem using dynamic programming. This is the first constant-factor approximation algorithm for this problem. Our algorithm also slightly improves the best known approximation ratio for the capacitated Facility Location problem with non-uniform hard capacities.
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improved approximation algorithms for metric Facility Location problems
Lecture Notes in Computer Science, 2002Co-Authors: Mohammad Mahdian, Jiawei ZhangAbstract:In this paper we present a 1.52-approximation algorithm for the uncapacitated metric Facility Location problem. This algorithm uses an idea of cost scaling, a greedy algorithm of Jain, Mahdian and Saberi, and a greedy augmentation procedure of Charikar, Guha and Khuller. We also present a 2.89-approximation for the capacitated metric Facility Location problem with soft capacities.
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a new greedy approach for Facility Location problems
Symposium on the Theory of Computing, 2002Co-Authors: Kamal Jain, Mohammad Mahdian, Amin SaberiAbstract:We present a simple and natural greedy algorithm for the metric uncapacitated Facility Location problem achieving an approximation guarantee of 1.61. We use this algorithm to find better approximation algorithms for the capacitated Facility Location problem with soft capacities and for a common generalization of the k-median and Facility Location problems. We also prove a lower bound of 1+2/e on the approximability of the k-median problem. At the end, we present a discussion about the techniques we have used in the analysis of our algorithm, including a computer-aided method for proving bounds on the approximation factor.
Moshe Tennenholtz - One of the best experts on this subject based on the ideXlab platform.
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Multiunit Facility Location Games
Mathematics of Operations Research, 2019Co-Authors: Omer Ben-porat, Moshe TennenholtzAbstract:Facility Location games have been a topic of major interest in economics, operations research, and computer science, starting from the seminal work by Hotelling [Hotelling H (1929) Stability in com...
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WINE - Shapley Facility Location Games
Web and Internet Economics, 2017Co-Authors: Omer Ben-porat, Moshe TennenholtzAbstract: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, and each player picks a point (Facility) in that space. In most Facility Location games considered in the literature, users are assumed to act deterministically: given the facilities chosen by the players, users are attracted to their nearest Facility. This paper introduces Facility Location games with probabilistic attraction, dubbed Shapley Facility Location games, due to a surprising connection to the Shapley value. The specific attraction function we adopt in this model is aligned with the recent findings of the behavioral economics literature on choice prediction. Given this model, our first main result is that Shapley Facility Location games are potential games; hence, they possess pure Nash equilibrium. Moreover, the latter is true for any compact user space, any user distribution over that space, and any number of players. Note that this is in sharp contrast to Hotelling Facility Location games. In our second main result we show that under the assumption that players can compute an approximate best response, approximate equilibrium profiles can be learned efficiently by the players via dynamics. Our third main result is a bound on the Price of Anarchy of this class of games, as well as showing the bound is tight. Ultimately, we show that player payoffs coincide with their Shapley value in a coalition game, where coalition gains are the social welfare of the users.
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Shapley Facility Location Games
arXiv: Computer Science and Game Theory, 2017Co-Authors: Omer Ben-porat, Moshe TennenholtzAbstract: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, and each player picks a point (Facility) in that space. In most Facility Location games considered in the literature, users are assumed to act deterministically: given the facilities chosen by the players, users are attracted to their nearest Facility. This paper introduces Facility Location games with probabilistic attraction, dubbed Shapley Facility Location games, due to a surprising connection to the Shapley value. The specific attraction function we adopt in this model is aligned with the recent findings of the behavioral economics literature on choice prediction. Given this model, our first main result is that Shapley Facility Location games are potential games; hence, they possess pure Nash equilibrium. Moreover, the latter is true for any compact user space, any user distribution over that space, and any number of players. Note that this is in sharp contrast to Hotelling Facility Location games. In our second main result we show that under the assumption that players can compute an approximate best response, approximate equilibrium profiles can be learned efficiently by the players via dynamics. Our third main result is a bound on the Price of Anarchy of this class of games, as well as showing the bound is tight. Ultimately, we show that player payoffs coincide with their Shapley value in a coalition game, where coalition gains are the social welfare of the users.
Mark S Daskin - One of the best experts on this subject based on the ideXlab platform.
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strategic Facility Location a review
European Journal of Operational Research, 1998Co-Authors: Susan Hesse Owen, Mark S DaskinAbstract:Abstract Facility Location decisions are a critical element in strategic planning for a wide range of private and public firms. The ramifications of siting facilities are broadly based and long-lasting, impacting numerous operational and logistical decisions. High costs associated with property acquisition and Facility construction make Facility Location or reLocation projects long-term investments. To make such undertakings profitable, firms plan for new facilities to remain in place and in operation for an extended time period. Thus, decision makers must select sites that will not simply perform well according to the current system state, but that will continue to be profitable for the Facility's lifetime, even as environmental factors change, populations shift, and market trends evolve. Finding robust Facility Locations is thus a difficult task, demanding that decision makers account for uncertain future events. The complexity of this problem has limited much of the Facility Location literature to simplified static and deterministic models. Although a few researchers initiated the study of stochastic and dynamic aspects of Facility Location many years ago, most of the research dedicated to these issues has been published in recent years. In this review, we report on literature which explicitly addresses the strategic nature of Facility Location problems by considering either stochastic or dynamic problem characteristics. Dynamic formulations focus on the difficult timing issues involved in locating a Facility (or facilities) over an extended horizon. Stochastic formulations attempt to capture the uncertainty in problem input parameters such as forecast demand or distance values. The stochastic literature is divided into two classes: that which explicitly considers the probability distribution of uncertain parameters, and that which captures uncertainty through scenario planning. A wide range of model formulations and solution approaches are discussed, with applications ranging across numerous industries.
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Invited Review Strategic Facility Location: A review
1998Co-Authors: Susan Hesse Owen, Mark S DaskinAbstract:Facility Location decisions are a critical element in strategic planning for a wide range of private and public firms. The ramifications of siting facilities are broadly based and long-lasting, impacting numerous operational and logistical decisions. High costs associated with property acquisition and Facility construction make Facility Location or reLocation projects long-term investments. To make such undertakings profitable, firms plan for new facilities to remain in place and in operation for an extended time period. Thus, decision makers must select sites that will not simply perform well according to the current system state, but that will continue to be profitable for the Facility’s lifetime, even as environmental factors change, populations shift, and market trends evolve. Finding robust Facility Locations is thus a diAcult task, demanding that decision makers account for uncertain future events. The complexity of this problem has limited much of the Facility Location literature to simplified static and deterministic models. Although a few researchers initiated the study of stochastic and dynamic aspects of Facility Location many years ago, most of the research dedicated to these issues has been published in recent years. In this review, we report on literature which explicitly addresses the strategic nature of Facility Location problems by considering either stochastic or dynamic problem characteristics. Dynamic formulations focus on the diAcult timing issues involved in locating a Facility (or facilities) over an extended horizon. Stochastic formulations attempt to capture the uncertainty in problem input parameters such as forecast demand or distance values. The stochastic literature is divided into two classes: that which explicitly considers the probability distribution of uncertain parameters, and that which captures uncertainty through scenario planning. A wide range of model formulations and solution approaches are discussed, with applications ranging across numerous industries. ” 1998 Elsevier Science B.V. All rights reserved.
Martin Pal - One of the best experts on this subject based on the ideXlab platform.
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Universal Facility Location
Lecture Notes in Computer Science, 2003Co-Authors: Mohammad Mahdian, Martin PalAbstract: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 amount of demand assigned to that Facility and is given by a cost function f i (.). We present a (7.88 + e)-approximation algorithm for the Universal Facility Location problem based on local search, under the assumption that the cost functions f i are nondecreasing. The algorithm chooses local improvement steps by solving a knapsack-like subproblem using dynamic programming. This is the first constant-factor approximation algorithm for this problem. Our algorithm also slightly improves the best known approximation ratio for the capacitated Facility Location problem with non-uniform hard capacities.
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ESA - Universal Facility Location
Algorithms - ESA 2003, 2003Co-Authors: Mohammad Mahdian, Martin PalAbstract: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 amount of demand assigned to that Facility and is given by a cost function f i (·). We present a (7.88 + e)-approximation algorithm for the Universal Facility Location problem based on local search, under the assumption that the cost functions f i are nondecreasing. The algorithm chooses local improvement steps by solving a knapsack-like subproblem using dynamic programming. This is the first constant-factor approximation algorithm for this problem. Our algorithm also slightly improves the best known approximation ratio for the capacitated Facility Location problem with non-uniform hard capacities.
