MINLP for Obnoxious Facility Location Problem on a Simplified 2-D Non-Convex Set

2018 ◽  
Vol 35 (1) ◽  
pp. 41-54
Author(s):  
Junghee Kim ◽  
Namsuk Cho
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Convex Set ◽  
Facility Location Problem ◽  
Obnoxious Facility Location ◽  
Obnoxious Facility

OBNOXIOUS FACILITY LOCATION: COMPLETE SERVICE WITH MINIMAL HARM

2000 ◽  
Vol 10 (06) ◽  
pp. 581-592 ◽  
Author(s):  
BOAZ BEN-MOSHE ◽  
MATTHEW J. KATZ ◽  
MICHAEL SEGAL
Keyword(s):  
Data Structure ◽  
Facility Location ◽  
Efficient Solution ◽  
Location Problem ◽  
Facility Location Problem ◽  
Efficient Algorithms ◽  
Minimal Distance ◽  
Rectangular Region ◽  
Obnoxious Facility Location ◽  
Obnoxious Facility

We present efficient algorithms for several instances of the following facility location problem. Place k obnoxious facilities, with respect to n given demand sites and m given regions, where the goal is to maximize the minimal distance between a demand site and a facility, under the constraint that each of the regions must contain at least one facility. We also present an efficient solution to the following planar problem that arises as a subproblem. Given n transmitters, each of range r, construct a compact data structure that supports coverage queries, i.e., determine whether a query polygonal/rectangular region is fully covered by the transmitters.

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. 

A Computational Method for the Solution of Optimizing Facility Location Problem in the Non-Convex Set

2014 ◽  
Vol 1073-1076 ◽  
pp. 1376-1379
Author(s):  
Tao Yang ◽  
Ju Zhou
Keyword(s):  
Fixed Point ◽  
Facility Location ◽  
Location Problem ◽  
Convex Set ◽  
Facility Location Problem ◽  
Fixed Point Problem ◽  
Computational Method ◽  
Point Problem ◽  
Distribution Centers ◽  
Fire Stations

Facility location problems arise for planning and stationing serve centers including waste disposal sites, hospitals, distribution centers, post offices, and fire stations. The single facility location problem can be modeled by a fixed point problem. Commonly the definition set of variables are requested as a convex set. In real world applications, the collection of feasible sites to locate always is non-convex set. The contribution of this paper is to apply the theorem of existence of the solution of fixed point problem to discuss the facility location problem in non-convex definition set of variables and obtain the computational result. Numerical example shows that the numerical method by tracing the homotopy pathway with predictor-corrector is an effective method to solving the facility location problem and a global optimal solution can be obtained.

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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