The minimum equitable radius location problem with continuous demand

We analyze the location of p facilities satisfying continuous area demand. Three objectives are considered: (i) the p-center objective (to minimize the maximum distance between all points in the area and their closest facility), (ii) equalizing the load service by the facilities, and (iii) the minimum equitable radius – minimizing the maximum radius from each point to its closest facility subject to the constraint that each facility services the same load. The paper offers three contributions: (i) a new problem – the minimum equitable radius is presented and solved by an efficient algorithm, (ii) an improved and efficient algorithm is developed for the solution of the p-center problem, and (iii) an improved algorithm for the equitable load problem is developed. Extensive computational experiments demonstrated the superiority of the new solution algorithms.