This article develops efficient p-median mathematical formulations for solving the machine-part grouping problem (MPGP) in group technology manufacturing and compares the performance of the formulations with that of existing p-median ones. In spite of the successful applications of MPGP that have been reported in the literature, existing p-median formulations have been restricted to small to medium-sized MPGP since they attempt to find the optimal solution over the entire feasible region of the constraint set without any prior knowledge about the median machines. Our formulations lead to rapid implementation of the model by introducing the idea of a candidate set of median machines, which consists of the machines that have a high possibility of serving as medians or seed machines for grouping. The candidate set of median machines plays the role of medians known in advance and enables the model to be implemented with the feasible region of a reduced constraint set. Furthermore, our alternative formulation can attack large-size MPGPs efficiently. Computational results show the comparative advantage of the formulations in terms of computation time and solution quality over existing p-median ones.
