  Approximating distance is one of the key challenge in a facility location
problem. Several algorithms have been proposed, however, none of them focused
on estimating distance between two concave regions. In this work, we present an
algorithm to estimate the distance between two irregular regions of a facility
location problem. The proposed algorithm can identify the distance between
concave shape regions. We also discuss some relevant properties of the proposed
algorithm. A distance-sensitive capacity location model is introduced to test
the algorithm. Moreover, sSeveral special geometric cases are discussed to show
the advantages and insights of the algorithm.
