scholarly journals Aggregation and non aggregation techniques for large facility location problems: A survey

2015 ◽  
Vol 25 (3) ◽  
pp. 313-341 ◽  
Author(s):  
Chandra Irawan ◽  
Said Salhi
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem ◽  
Location Problems ◽  
Objective Functions ◽  
Facility Location Problems ◽  
Aggregation Techniques ◽  
Number Of Customers

A facility location problem is concerned with determining the location of some useful facilities in such a way so to fulfil one or a few objective functions and constraints. We survey those problems where, in the presence of a large number of customers, some form of aggregation may be required. In addition, a review on conditional location problems where some (say q) facilities already exist in the study area is presented.

scholarly journals Globally Optimal Facility Locations for Continuous-Space Facility Location Problems

2021 ◽  
Vol 11 (16) ◽  
pp. 7321
Author(s):  
Xuehong Gao ◽  
Chanseok Park ◽  
Xiaopeng Chen ◽  
En Xie ◽  
Guozhong Huang ◽  
...  
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem ◽  
Exact Method ◽  
Global Minimizer ◽  
Location Problems ◽  
Continuous Space ◽  
Facility Location Problems ◽  
Facility Locations ◽  
Higher Dimensional

The continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- and higher-dimensional continuous-space facility location problems when the Manhattan distance is considered. Before we propose the exact method, we start with the continuous-space single-facility location problem and obtain the global minimizer for the problem using a statistical approach. Then, an exact method is developed to determine the globally optimal solution for the two- and higher-dimensional continuous-space facility location problem, which is different from the previous clustering algorithms. Based on the newly investigated properties of the minimizer, we extend it to multi-facility problems and transfer the continuous-space facility location problem to the discrete-space location problem. To illustrate the effectiveness and efficiency of the proposed method, several instances from a benchmark are provided to compare the performances of different methods, which illustrates the superiority of the proposed exact method in the decision-making of the continuous-space facility location problems.

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 Facility location via continuous optimization with discontinuous objective functions

2007 ◽  
Vol 48 (3) ◽  
pp. 315-325 ◽  
Author(s):  
J. Ugon ◽  
S. Kouhbor ◽  
M. Mammadov ◽  
A. Rubinov ◽  
A. Kruger
Keyword(s):  
Global Optimization ◽  
Facility Location ◽  
Continuous Optimization ◽  
Optimization Methods ◽  
Optimization Method ◽  
Location Problems ◽  
Objective Functions ◽  
Global Optimization Method ◽  
Facility Location Problems ◽  
Real World Application

AbstractFacility location problems are one of the most common applications of optimization methods. Continuous formulations are usually more accurate, but often result in complex problems that cannot be solved using traditional optimization methods. This paper examines theuse of a global optimization method—AGOP—for solving location problems where the objective function is discontinuous. This approach is motivated by a real-world application in wireless networks design.

scholarly journals Solving Classic Discrete Facility Location Problems Using Excel Spreadsheets

2021 ◽  
Author(s):  
Michael J. Brusco
Keyword(s):  
Facility Location ◽  
Operations Management ◽  
Location Problem ◽  
Set Covering ◽  
Location Problems ◽  
Discrete Location ◽  
Facility Location Problems ◽  
Location Models ◽  
Optimal Subset ◽  
Discrete Facility Location

There are a variety of discrete facility location models that have practical relevance for operations management and management science courses. Integer linear programming (ILP) is the standard technique for solving such problems. An alternative approach that is often conceptually appealing to students is to pose the problem as one of finding the best possible subset of p facilities out of n possible candidates. I developed an Excel workbook that allows students to interactively evaluate the quality of different subsets, to run a VBA macro that finds the optimal subset, or to solve an ILP formulation that finds the optimal subset. Spreadsheets are available for five classic discrete location models: (1) the location set-covering problem, (2) the maximal covering location problem, (3) the p-median problem, (4) the p-centers problem, and (5) the simple plant location problem. The results from an assignment in a master’s-level business analytics course indicate that the workbook facilitates a better conceptual understanding of the precise nature of the discrete facility location problems by showing that they can be solved via enumeration of all possible combinations of p subsets that can be drawn from n candidate locations. More important, students directly observe the superiority of ILP as a solution approach as n increases and as p approaches n/2.

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.

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