Novel efficient relaxation reference method for part-machine clustering with assignment of duplicated machines

In a Cell Formation (CF) problem, minimizations of the numbers of Exceptional Elements (EEs) and Void Elements (VEs) are usually considered. However, conventional methods for solving the CF problem do not always give the efficient solutions in which both EEs and VEs are reduced. Moreover, eliminating EEs by adding duplicated machines always has to be reconsidered after forming the manufacturing cells. In this research, a new efficient relaxation reference method is presented in order to complete these critical issues. Based on a perfect grouping concept, EEs and VEs are both eliminated orderly. The efficient relaxation reference method can be applied to generate efficient solutions of part-machine clustering and allows the decision maker to assign duplicated machines for the CF problem simultaneously.