A Multi-level continuous minimax location problem with regional demand

Download
index.pdf
2017
Faridyahyaei, Amin
Show full item record
71
views
31
downloads
The minimax facility location problem seeks for the optimal locations of the facilities in the plane so that the maximum Euclidean distance between the demanding entities (given points in the plane) and their corresponding nearest facilities is minimized. In the solutions, remote entities (irrespective of their weights) tend to pull the facilities toward themselves which may result in larger distances for the other entities. In this thesis, we consider a multi-level minimax location problem which allows some of the entities to be covered in outer levels and thereby reducing their impact on the facility locations. We assume that associated with each entity, there is a weight which represents its importance, e.g., weights might represent populations if the entities are districts or cities. Additionally, we consider entities as regions in the plane consisting of an infinite number of points, therefore, this problem is a multi-level version of the minimax location problem with continuous demand. Based on the nature of the problem, the farthest point of each region to its nearest facility is important and Euclidean distance is utilized in distance calculations. In this thesis, firstly, we model the single and multi-facility versions of the considered problem as mixed integer second order cone programming (MISOCP) problems. Secondly, we perform computational experiments on artificially generated instances to see the limits of the mathematical programming formulations. Then, we propose several heuristics and compare them with the MISOCP formulations in terms of solution quality and computational time. Finally, all these solution approaches are tested on the case study of Istanbul. 
Maxima and minima., Facility management., Mathematical optimization.
http://etd.lib.metu.edu.tr/upload/12621325/index.pdf
https://hdl.handle.net/11511/26679
Graduate School of Natural and Applied Sciences, Thesis

Suggestions

Solution approaches for single-source capacitated multi facility weber problem
Damgacıoğlu, Haluk; İyigün, Cem; Department of Industrial Engineering (2014)
Single Source Capacitated Multi Facility Location Problem (SSCMFLP) is a continuous location-allocation problem such that determining the locations of p facilities in the plane and allocations of n demand points to only one facility by considering the capacity restriction of each facility so as to minimize total transportation cost to satisfy n demand points from p facilities. In addition to Mixed Integer Non-Linear Programming formulation of the problem in the literature, we give a new formulation for the ...
The Weber problem in congested regions with entry and exit points
Farham, Mohammad Saleh; Süral, Haldun; İyigün, Cem (2015-10-01)
The Weber problem is about finding a facility location on a plane such that the total weighted distance to a set of given demand points is minimized. The facility location and access routes to the facility can be restricted if the Weber problem contains congested regions, some arbitrary shaped polygonal areas on the plane, where location of a facility is forbidden and traveling is allowed at an additional fixed cost. Traveling through congested regions may also be limited to certain entry and exit points (o...
A minisum location problem with regional demand considering farthest Euclidean distances
DİNLER, DERYA; Tural, Mustafa Kemal (2016-06-01)
We consider a continuous multi-facility location-allocation problem that aims to minimize the sum of weighted farthest Euclidean distances between (closed convex) polygonal and/or circular demand regions, and facilities they are assigned to. We show that the single facility version of the problem has a straightforward second-order cone programming formulation and can therefore be efficiently solved to optimality. To solve large size instances, we adapt a multi-dimensional direct search descent algorithm to ...
Generalization of restricted planar location problems : unified meta-heuristics for single facility case
Farham, Mohammad Saleh; Süral, Haldun; İyigün, Cem; Department of Industrial Engineering (2013)
A planar single facility location problem, also known as the Fermat–Weber problem, is to find a facility location such that the total weighted distance to a set of given demand points is minimized. A variation to this problem is obtained if there is a restriction coming from congested regions. In this study, congested regions are considered as arbitrary shaped polygonal areas on the plane where location of a facility is forbidden and traveling is charged with an additional fixed cost. The traveling fixed cost ...
The planar hub location problem: a probabilistic clustering approach
İyigün, Cem (Springer Science and Business Media LLC, 2013-12-01)
Given the demand between each origin-destination pair on a network, the planar hub location problem is to locate the multiple hubs anywhere on the plane and to assign the traffic to them so as to minimize the total travelling cost. The trips between any two points can be nonstop (no hubs used) or started by visiting any of the hubs. The travel cost between hubs is discounted with a factor. It is assumed that each point can be served by multiple hubs.
Citation Formats
A. Faridyahyaei, “A Multi-level continuous minimax location problem with regional demand,” M.S. - Master of Science, Middle East Technical University, 2017.
METU IIS - Integrated Information Service open@metu.edu.tr