Locating Facilities on the Manhattan Metric with Arbitrarily Shaped Barriers and Convex Forbidden Regions

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Abstract
This paper considers two planar facility location problems while employing the Manhattan travel metric. We first consider the p-median problem in the presence of arbitrarily shaped barriers and convex forbidden regions. For this problem we establish that the search for an optimal solution can be restricted to a finite set of easily identifiable points. Next, we consider the stochastic queue median problem in the presence of arbitrarily shaped barriers. A procedure to obtain a global optimum solution for this problem is established. The results of the paper are illustrated via numerical examples. Finally, we comment on a connection between network location problems and planar location problems which use the Manhattan travel metric.
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