Paper Info
Title
Placing a finite size facility with a center objective on a rectangular plane with barriers
Abstract
This paper addresses the finite size 1-center placement problem on a rectangular plane in the presence of barriers. Barriers are regions in which both facility location and travel through are prohibited. The feasible region for facility placement is subdivided into cells along the lines of Larson and Sadiq [R.C. Larson, G. Sadiq, Facility locations with the Manhattan metric in the presence of barriers to travel, Operations Research 31 (4) (1983) 652–669]. To overcome complications induced by the center (minimax) objective, we analyze the resultant cells based on the cell corners. We study the problem when the facility orientation is known a priori. We obtain domination results when the facility is fully contained inside 1, 2 and 3-cornered cells. For full containment in a 4-cornered cell, we formulate the problem as a linear program. However, when the facility intersects gridlines, analytical representation of the distance functions becomes challenging. We study the difficulties of this case and formulate our problem as a linear or nonlinear program, depending on whether the feasible region is convex or nonconvex. An analysis of the solution complexity is presented along with an illustrative numerical example.
Year
DOI
Venue
2007
10.1016/j.ejor.2005.08.029
European Journal of Operational Research
Keywords
Field
DocType
1-Center placement,Finite size facility location,Barrier,Rectangular plane
Minimax,Mathematical optimization,Regular polygon,Facility location problem,Feasible region,Linear programming,Numerical analysis,1-center problem,Function representation,Mathematics
Journal
Volume
Issue
ISSN
179
3
0377-2217
Citations 
PageRank 
References 
7
0.53
5
Authors
3
Name
Order
Citations
PageRank
Avijit Sarkar1112.02
Rajan Batta284989.39
Rakesh Nagi344345.82