A Bender's algorithm of decomposition used for the parallel machine problem of robotic cell

The present research addresses the single transportation robot used to alleviate problems of robotic cell scheduling of the machines. For the purpose of minimizing the make‐span, a model of mixed‐integer linear programming (MILP) has been suggested. Since the inefficiency exists in NP‐hard, a decomposition algorithm posed by Bender was utilized to alleviate the problem in real life situations. The proposed algorithm can be regarded as an efficient attempt to apply optimality Bender's cuts regarding the problem of parallel machine robotic cell scheduling in order to reach precise resolutions for medium and big sized examples. The numerical analyses have demonstrated the efficiency of the proposed solving approach.