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 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 Approach for Distributed Drones

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 118 ◽  
Author(s):  
Jared Lynskey ◽  
Kyi Thar ◽  
Thant Oo ◽  
Choong Hong
Keyword(s):  
Energy Consumption ◽  
Facility Location ◽  
Location Problem ◽  
Average Distance ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Traveling Salesman ◽  
Future Research ◽  
Shortest Route ◽  
Initial Location

Currently, industry and academia are undergoing an evolution in developing the next generation of drone applications. Including the development of autonomous drones that can carry out tasks without the assistance of a human operator. In spite of this, there are still problems left unanswered related to the placement of drone take-off, landing and charging areas. Future policies by governments and aviation agencies are inevitably going to restrict the operational area where drones can take-off and land. Hence, there is a need to develop a system to manage landing and take-off areas for drones. Additionally, we proposed this approach due to the lack of justification for the initial location of drones in current research. Therefore, to provide a foundation for future research, we give a justified reason that allows predetermined location of drones with the use of drone ports. Furthermore, we propose an algorithm to optimally place these drone ports to minimize the average distance drones must travel based on a set of potential drone port locations and tasks generated in a given area. Our approach is derived from the Facility Location problem which produces an efficient near optimal solution to place drone ports that reduces the overall drone energy consumption. Secondly, we apply various traveling salesman algorithms to determine the shortest route the drone must travel to visit all the tasks.

scholarly journals An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Ľuboš Buzna ◽  
Michal Koháni ◽  
Jaroslav Janáček
Keyword(s):  
Approximation Algorithm ◽  
Facility Location ◽  
Location Problem ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Exact Algorithm ◽  
General Purpose ◽  
Median Problem ◽  
Discrete Facility Location ◽  
Number Of Customers

We present a new approximation algorithm to the discrete facility location problem providing solutions that are close to the lexicographic minimax optimum. The lexicographic minimax optimum is a concept that allows to find equitable location of facilities serving a large number of customers. The algorithm is independent of general purpose solvers and instead uses algorithms originally designed to solve thep-median problem. By numerical experiments, we demonstrate that our algorithm allows increasing the size of solvable problems and provides high-quality solutions. The algorithm found an optimal solution for all tested instances where we could compare the results with the exact algorithm.

scholarly journals Continuous facility location on graphs

2021 ◽  
Author(s):  
Tim A. Hartmann ◽  
Stefan Lendl ◽  
Gerhard J. Woeginger
Keyword(s):  
Facility Location ◽  
Unit Length ◽  
Facility Location Problem ◽  
Covering Problem ◽  
Fixed Parameter Tractable ◽  
Unit Fractions ◽  
Fixed Parameter ◽  
Minimum Number ◽  
Polynomially Solvable ◽  
Interior Points

AbstractWe study a continuous facility location problem on undirected graphs where all edges have unit length and where the facilities may be positioned on the vertices as well as on interior points of the edges. The goal is to cover the entire graph with a minimum number of facilities with covering range $$\delta >0$$ δ > 0 . In other words, we want to position as few facilities as possible subject to the condition that every point on every edge is at distance at most $$\delta $$ δ from one of these facilities. We investigate this covering problem in terms of the rational parameter $$\delta $$ δ . We prove that the problem is polynomially solvable whenever $$\delta $$ δ is a unit fraction, and that the problem is NP-hard for all non unit fractions $$\delta $$ δ . We also analyze the parametrized complexity with the solution size as parameter: The resulting problem is fixed parameter tractable for $$\delta <3/2$$ δ < 3 / 2 , and it is W[2]-hard for $$\delta \ge 3/2$$ δ ≥ 3 / 2 .

scholarly journals Solving the Bilevel Facility Location Problem under Preferences by a Stackelberg-Evolutionary Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
José-Fernando Camacho-Vallejo ◽  
Álvaro Eduardo Cordero-Franco ◽  
Rosa G. González-Ramírez
Keyword(s):  
Evolutionary Algorithm ◽  
Facility Location ◽  
Location Problem ◽  
Classical Problem ◽  
Facility Location Problem ◽  
Mixed Integer ◽  
Solution Quality ◽  
Customer Preferences ◽  
Customer Order ◽  
Numerical Experimentation

This research highlights the use of game theory to solve the classical problem of the uncapacitated facility location optimization model with customer order preferences through a bilevel approach. The bilevel model provided herein consists of the classical facility location problem and an optimization of the customer preferences, which are the upper and lower level problems, respectively. Also, two reformulations of the bilevel model are presented, reducing it into a mixed-integer single-level problem. An evolutionary algorithm based on the equilibrium in a Stackelberg’s game is proposed to solve the bilevel model. Numerical experimentation is performed in this study and the results are compared to benchmarks from the existing literature on the subject in order to emphasize the benefits of the proposed approach in terms of solution quality and estimation time.

scholarly journals Solving k-obnoxious facility location problem on a plane

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Utpal Kumar Bhattacharya
Keyword(s):  
Linear Programming ◽  
Facility Location ◽  
Upper Bound ◽  
Location Problem ◽  
Distance Measure ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Problem Area ◽  
Obnoxious Facility Location ◽  
Obnoxious Facility

 In this paper k-obnoxious facility location problem has been modeled as a pure planner location problem.  Area restriction concept has been incorporated by inducting a convex polygon in the constraints set. A linear programming iterative algorithm for k- obnoxious facility locations has been developed. An upper bound has been incorporated in the algorithm to get the  optimal solution. Also the concept of upper bound has reduced  the number of linear programming problems to solved in the algorithm. Rectilinear distance norm has been considered as the distance measure as it is more appropriate to the various realistic situations. 

Generating optimal and near-optimal solutions to facility location problems

2020 ◽  
Vol 47 (6) ◽  
pp. 1014-1030
Author(s):  
Richard L Church ◽  
Carlos A Baez
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Spatial Optimization ◽  
Problem Instance ◽  
Optimal Solutions ◽  
Discrete Location ◽  
Classic Approach

There is a decided bent toward finding an optimal solution to a given facility location problem instance, even when there may be multiple optima or competitive near-optimal solutions. Identifying alternate solutions is often ignored in model application, even when such solutions may be preferred if they were known to exist. In this paper we discuss why generating close-to-optimal alternatives should be the preferred approach in solving spatial optimization problems, especially when it involves an application. There exists a classic approach for finding all alternate optima. This approach can be easily expanded to identify all near-optimal solutions to any discrete location model. We demonstrate the use of this technique for two classic problems: the p-median problem and the maximal covering location problem. Unfortunately, we have found that it can be mired in computational issues, even when problems are relatively small. We propose a new approach that overcomes some of these computational issues in finding alternate optima and near-optimal solutions.

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