PMP approach for solving the binary static multi-objective generalised cell formation problem

The p-median problem (PMP) approach has been used as an effective alternative for solving small-to-medium-sized single-objective cell formation (SOCF) problems. Cell load balancing is an important consideration in multi-objective cell formation (MOCF) problems for reflecting realistic manufacturing factors. However, few cell formation (CF) studies using the conventional PMP approach with the binary machine-part incidence matrix (MPIM) alone have considered multiple objectives including cell load balancing because the conventional binary MPIM can only indicate whether parts are processed on particular machines. In this study, we emphasise the importance of cell load balancing even in binary MPIM-based multi-objective generalised cell formation (MOGCF) problems with alternative process plans for parts and demonstrate that the binary MPIM-based CF without consideration of cell load balancing can lead to inferior solutions. This study shows that the PMP approach can effectively solve large-sized MOGCF problems by considering the minimisation of cell load imbalance and inter-cellular part moves, which result in inefficient cells. Our PMP approach first solves the SOCF problem and then attempts to satisfy conflicting multiple objectives ex post facto with a subsequent heuristic procedure. The computational results show that the proposed PMP approach is very effective for large-sized MOGCF problems.