scholarly journals Optimization of the Weighted Multi-Facility Location Problem Using MS Excel

Algorithms ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 191
Author(s):  
Petr Němec ◽  
Petr Stodola ◽  
Miroslav Pecina ◽  
Jiří Neubauer ◽  
Martin Blaha
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Dimensional Space ◽  
Continuous Optimization ◽  
Facility Location Problem ◽  
Benchmark Instances ◽  
Hardware Configuration ◽  
Complex Optimization ◽  
Excel Solver ◽  
Office Software

This article presents the possibilities in solving the Weighted Multi-Facility Location Problem and its related optimization tasks using a widely available office software—MS Excel with the Solver add-in. To verify the proposed technique, a set of benchmark instances with various point topologies (regular, combination of regular and random, and random) was designed. The optimization results are compared with results achieved by a metaheuristic algorithm based on simulated annealing principles. The influence of the hardware configuration on the performance achieved by MS Excel Solver is also examined and discussed from both the execution time and accuracy perspectives. The experiments showed that this widely available office software is practical for solving even relatively complex optimization tasks (Weighted Multi-Facility Location Problem with 100 points and 20 centers, which consists of 40 continuous optimization variables in two-dimensional space) with sufficient quality for many real-world applications. The method used is described in detail and step-by-step using an example.

scholarly journals Optimization of the Multi-Facility Location Problem Using Widely Available Office Software

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 106
Author(s):  
Petr Němec ◽  
Petr Stodola
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem ◽  
Optimal Location ◽  
Evolutionary Method ◽  
Office Software ◽  
User Knowledge ◽  
Annealing Method

Multi-facility location problem is a type of task often solved (not only) in logistics. It consists in finding the optimal location of the required number of centers for a given number of points. One of the possible solutions is to use the principle of the genetic algorithm. The Solver add-in, which uses the evolutionary method, is available in the Excel office software. It was used to solve the benchmark in 4 levels of difficulty (from 5 centers for 25 points to 20 centers for 100 points), and one task from practice. The obtained results were compared with the results obtained by the metaheuristic simulated annealing method. It was found that the results obtained by the evolutionary method are sufficiently accurate. Their accuracy depends on the complexity of the task and the performance of the HW used. The advantage of the proposed solution is easy availability and minimal requirements for user knowledge.

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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