Refinement systems currently select the best rule refinements from a set of conflicting and alternative refinements by using heuristics. This paper presents a new operations research approach for the selection of optimal rule refinements. The problem analysis and the description of the optimization are performed using two well-defined examples. The analysis of the refinement selection problem leads to the conclusion that a binary linear maximization problem is to be solved by a operations research procedure. The mathematical solution of the refinement selection problem is a milestone in the history of rule refinement.