Article ID: | iaor20031318 |
Country: | Netherlands |
Volume: | 111 |
Issue: | 1 |
Start Page Number: | 89 |
End Page Number: | 110 |
Publication Date: | Mar 2002 |
Journal: | Annals of Operations Research |
Authors: | Dearing P.M., Segars R. |
This paper considers planar location problems with rectilinear distance and barriers, where the objective function is any convex, nondecreasing function of distance. Such problems have a non-convex feasible region and a non-convex objective function. A modification of the barriers is developed based on properties of the rectilinear distance. It is shown that the original problem with barriers is equivalent to the problem with modified barriers. A particular modification is given that reduces the feasible region and permits its partitioning into convex subsets on which the objective function is convex. A solution algorithm based on the partitioning is the subject of a companion paper.