scholarly journals Nash Welfare in the Facility Location Problem

2021 ◽  
Author(s):  
Alexander Lam
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem ◽  
Maximum Cost ◽  
Total Cost ◽  
Strategic Behaviour ◽  
Fairness And Efficiency ◽  
Facility Placement

In most facility location research, either an efficient facility placement which minimizes the total cost or a fairer placement which minimizes the maximum cost are typically proposed. To find a solution that is both fair and efficient, we propose converting the agent costs to utilities and placing the facility/ies such that the product of utilities, also known as the Nash welfare, is maximized. We ask whether the Nash welfare's well-studied balance between fairness and efficiency also applies to the facility location setting, and what agent strategic behaviour may occur under this facility placement.

scholarly journals Facility Location Problem with Capacity Constraints: Algorithmic and Mechanism Design Perspectives

2020 ◽  
Vol 34 (02) ◽  
pp. 1806-1813 ◽  
Author(s):  
Haris Aziz ◽  
Hau Chan ◽  
Barton Lee ◽  
Bo Li ◽  
Toby Walsh
Keyword(s):  
Mechanism Design ◽  
Facility Location ◽  
Location Problem ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Solution Quality ◽  
Maximum Cost ◽  
Fixed Parameter Tractable ◽  
Fixed Parameter ◽  
The One

We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the corresponding optimization problem, where the goal is to locate facilities to minimize either the total cost to all agents or the maximum cost of any agent is NP-hard. However, we show that the problem is fixed-parameter tractable, and the optimal solution can be computed in polynomial time whenever the number of facilities is bounded, or when all facilities have identical capacities. We then consider the problem from a mechanism design perspective where the agents are strategic and need not reveal their true locations. We show that several natural mechanisms studied in the uncapacitated setting either lose strategyproofness or a bound on the solution quality %on the returned solution for the total or maximum cost objective. We then propose new mechanisms that are strategyproof and achieve approximation guarantees that almost match the lower bounds.

scholarly journals An Improved Voronoi-Diagram-Based Algorithm for Continuous Facility Location Problem under Disruptions

2018 ◽  
Vol 10 (9) ◽  
pp. 3099 ◽  
Author(s):  
Jiguang Wang ◽  
Yucai Wu
Keyword(s):  
Supply Chain ◽  
Facility Location ◽  
Voronoi Diagram ◽  
Location Problem ◽  
Facility Location Problem ◽  
Research Problem ◽  
Future Research ◽  
Total Cost ◽  
Disruption Risk ◽  
The Impact

The classical location models implicitly assume that the facilities, once built, will always operate as planned. However, some of the facilities may become unavailable from time to time due to disruptions which highlight the urgent need to effectively manage supply chain disruptions in spite of their low probability of occurrence. Therefore, it is critical to take account of disruptions when designing a resilient supply chain network so that it performs well as a whole even after an accidental disruption. In this paper, a stylized facility location problem is considered in a continuous plane which is solved through an improved Voronoi-diagram-based algorithm under disruption risks. The research problem is to minimize the total cost in normal and failure scenarios. Furthermore, the impact of misestimating the disruption probability is also investigated. The results numerically show that although the estimated disruption probability has a significant impact on the facilities configuration, it has a minor impact on the total quantity of facilities and the expected total cost. Therefore, this paper proposes that the decision-maker should moderately overestimate disruption risk based on the “pessimistic principle”. Finally, the conclusion considers managerial insights and proposes potential areas for future research.

scholarly journals On a Leasing Variant of the Online Connected Facility Location Problem

2018 ◽  
Author(s):  
Murilo Santos De Lima ◽  
Mário César San Felice ◽  
Orlando Lee
Keyword(s):  
Facility Location ◽  
Optimization Model ◽  
Location Problem ◽  
Facility Location Problem ◽  
Scaling Factor ◽  
Total Cost ◽  
Connected Facility Location ◽  
Time Periods

In the leasing optimization model, resources are leased for K different time periods, instead of being acquired for unlimited duration. The goal is to use these temporary resources to maintain a dynamic infrastructure that serves n requests while minimizing the total cost. We propose and study a leasing variant of the online connected facility location problem, which we call the online connected facility leasing problem. In this problem each client that arrives must be connected to a temporary facility, which in turn must be connected to a root facility using permanent edges. We present an algorithm that is O(K · lg n)-competitive if the scaling factor is M = 1.  

scholarly journals Dispersing Obnoxious Facilities on a Graph

Algorithmica ◽  
2021 ◽  
Author(s):  
Alexander Grigoriev ◽  
Tim A. Hartmann ◽  
Stefan Lendl ◽  
Gerhard J. Woeginger
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Unit Length ◽  
Facility Location Problem ◽  
Np Hard ◽  
Obnoxious Facilities ◽  
Rational Parameter ◽  
Polynomially Solvable

AbstractWe study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance $$\delta$$ δ from each other. We investigate the complexity of this problem in terms of the rational parameter $$\delta$$ δ . The problem is polynomially solvable, if the numerator of $$\delta$$ δ is 1 or 2, while all other cases turn out to be NP-hard.

Fuzzy facility location problem with preference of candidate sites

2007 ◽  
Vol 158 (17) ◽  
pp. 1922-1930 ◽  
Author(s):  
Hiroaki Ishii ◽  
Yung Lung Lee ◽  
Kuang Yih Yeh
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem
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