An exact solution to the TLP problem in an NC machine

This paper considers a job sequencing problem for a single numerical controlled machining center. It is assumed that all the considered jobs must be processed on a single machine provided with a tool magazine with C positions, that no job requires more than C tools to be completely machined and that the tools may be loaded and unloaded from the tool magazine only when the machining operations for each job are completed. The decisional problem is referred to as the tool loading problem (TLP) and it determines the jobs machining sequence as well as the tools to load in the machine tool magazine before the machining operations on each job may start. In industrial cases where the tool switching time is both significant relative to job processing time and proportional to the number of tool switches, the performance criterion is the minimization of the number of tool switches. This paper demonstrates that the TLP is a symmetric sequencing problem. The authors enrich a branch-and-bound algorithm proposed in literature for the TLP with the new symmetric formulation. Computational experiments show the significant improvement obtained by the novel symmetric formulation of the TLP.