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A Multi-level continuous minimax location problem with regional demand
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Date
2017
Author
Faridyahyaei, Amin
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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.
Subject Keywords
Maxima and minima.
,
Facility management.
,
Mathematical optimization.
URI
http://etd.lib.metu.edu.tr/upload/12621325/index.pdf
https://hdl.handle.net/11511/26679
Collections
Graduate School of Natural and Applied Sciences, Thesis
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A. Faridyahyaei, “A Multi-level continuous minimax location problem with regional demand,” M.S. - Master of Science, Middle East Technical University, 2017.