Heuristic procedures for the m-partial cover problem on a plane

The m-partial cover problem on a plane is defined as follows: given npoints located at cartesian coordinates (x_j, y_j) (j=1,…,n) each with an associated weight w_j, a critical distance R and an integer number m, determine the location of m centres so that the sum of the weights of those points lying within distance R of at least one centre is maximised. Five heuristic procedures to solve the m-partial cover problem are presented and computational experience reported. The use of the procedures for some related problems is discussed.