3 research outputs found
The obnoxious facilities planar p-median problem
In this paper we propose the planar obnoxious p-median problem. In the
p-median problem the objective is to find p locations for facilities that
minimize the weighted sum of distances between demand points and their closest
facility. In the obnoxious version we add constraints that each facility must
be located at least a certain distance from a partial set of demand points
because they generate nuisance affecting these demand points. The resulting
problem is extremely non-convex and traditional non-linear solvers such as
SNOPT are not efficient. An efficient solution method based on Voronoi diagrams
is proposed and tested. We also constructed the efficient frontiers of the test
problems to assist the planers in making location decisions
Mixed planar and network single-facility location problems
We consider the problem of optimally locating a single facility anywhere in a network to serve both on-network and off-network demands. Off-network demands occur in a Euclidean plane, while on-network demands are restricted to a network embedded in the plane. On-network demand points are serviced using shortest-path distances through links of the network (e.g., on-road travel), whereas demand points located in the plane are serviced using more expensive Euclidean distances. Our base objective minimizes the total weighted distance to all demand points. We develop several extensions to our base model, including: (i) a threshold distance model where if network distance exceeds a given threshold, then service is always provided using Euclidean distance, and (ii) a minimax model that minimizes worst-case distance. We solve our formulations using the “Big Segment Small Segment” global optimization method, in conjunction with bounds tailored for each problem class. Computational experiments demonstrate the effectiveness of our solution procedures. Solution times are very fast (often under one second), making our approach a good candidate for embedding within existing heuristics that solve multi-facility problems by solving a sequence of single-facility problems. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(4), 271–282 2016
New local searches for solving the multi-source Weber problem
This paper presents three new heuristic approaches for the solution of the multisourceWeber
problem in the plane: a constructive heuristic that finds a good starting solution,
a decomposition approach which uses Delaunay triangulation, and a new efficient neighborhood
structure based on the single facility limited distance median problem. A new heuristic
incorporating all these approaches provided high quality solutions in reasonable computing
time. We conclude that these heuristics successfully compete with the metaheuristic based
methods found in the literature improving ten best known solutions. The ideas here may be
extended to a variety of other continuous location as well as data mining problems