Location models with groups of demand points

In this paper we investigate the location of a new facility in an area where demand is generated by groups of demand points. The group-distance between the facility and a group of demand points is determined in three ways: the closest point in the group, the farthest one, and the average distance to all members in the group. Three objectives are considered: minisum (minimize the sum of weighted group-distances to the group), minimax, and maximin. Two of the nine resulting possible models (maximal group-distance using minisum objective, and average group-distance using minimax objective) are analyzed in the paper. These problems can be solved by standard mathematical programming methods. Special algorithms designed for large problems are proposed and computational experience reported.