The multi-facility min-max Weber problem

An algorithm is presented to solve the problem of the locating a given number of facilities on the plane amongst given customers so that the maximum weighted distance from any facility to the customers it services is minimised. The algorithm successfully overcomes the allocation aspects of this problem by generating partitions of customers using a method originally designed for graph colouring embedded within a modified bisection search. Problems of 50 customers and three facilities can be solved in entirely acceptable computer times.