Using tool life models to minimize processing time on a flexible machine

Economic tool life models are presented for machines with finite capacity tool magazines and variable processing speed capability. Single and multiple part models for minimizing the total throughput time are formulated as nonlinear, integer programs (NLIP). An algorithm is presented for the NLP relaxation and a marginal analysis approach for solving the NLIP is detailed, giving an optimal tool loading policy as well as the processing speeds for each of the part types so as to minimize the makespan. A numerical example illustrates the procedures.