This Paper proposes a mathematical model to solve the cell formation problem with exceptional elements, Exceptional elements are bottleneck machines and exceptional parts that span two or more manufacturing cells. The model suggests whether it is cost-effective to eliminate an EE (by machine duplication or part subcontracting), or whether the intercellular transfer caused by the EE should remain in the cell formation. It provides an optimal solution for resolving the interaction created by EE in the initial cell formation solution. In addition, the model recognizes potentially advantageous mixed strategies ignored by previous approaches.