A Spatial Optimization Approach for Solving a Multi-facility Location Problem with Continuously Distributed Demand

2020 ◽  
pp. 113-135 ◽  
Author(s):  
Jing Yao ◽  
Alan T. Murray
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem ◽  
Spatial Optimization ◽  
Optimization Approach

scholarly journals A Robust Optimization Approach to the Multiple Allocation p-Center Facility Location Problem

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 588 ◽  
Author(s):  
Bo Du ◽  
Hong Zhou
Keyword(s):  
Robust Optimization ◽  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem ◽  
Optimization Approach ◽  
Robust Solutions ◽  
Demand Node ◽  
Uncertainty Sets ◽  
Ellipsoidal Uncertainty ◽  
Multiple Allocation

In this study, we apply a robust optimization approach to a p-center facility location problem under uncertainty. Based on a symmetric interval and a multiple allocation strategy, we use three types of uncertainty sets to formulate the robust problem: box uncertainty, ellipsoidal uncertainty, and cardinality-constrained uncertainty. The equivalent robust counterpart models can be solved to optimality using Gurobi. Comprehensive numerical experiments have been conducted by comparing the performance of the different robust models, which illustrate the pattern of robust solutions, and allocating a demand node to multiple facilities can reduce the price of robustness, and reveal that alternative models of uncertainty can provide robust solutions with different conservativeness.

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.

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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