Models Arising from a Flexible Manufacturing Machine, Part I: Minimization of the Number of Tool Switches

TLDR

The study addresses job scheduling on flexible manufacturing machines in metalworking, where each of N jobs requires up to C tools and missing tools necessitate costly tool switches. The objective is to minimize the total number of tool switches by determining the optimal job sequence and tool placement. The authors model tool switching as a significant cost and present procedures that compute equilibrium solutions where no unilateral change in job order or tool placement can improve performance.

Abstract

This paper considers a job scheduling problem for a flexible manufacturing machine. This problem arises in the metal working industry when numerical controlled (N/C) machines are used to manufacture parts (jobs). Assume that each of N jobs must be processed on a machine that has positions for C tools, but no job requires more than C tools. If the requisite tools are not on the machine, then one or more tool switches must occur before the job can be processed. The problem consists of finding the sequence in which to process the jobs and the tools to place on the machine before each job is processed. This paper considers one performance criterion: minimize the total number of tool switches. This criterion is adequate for situations where the tool switching time is proportional to the number of tool switches. In our model, we assume that the time needed to switch tools is significant relative to the job processing time. A feasible solution is in “equilibrium” if better performance cannot be attained by changing either the job sequence or the tool placement specified by the solution unilaterally. Procedures that find an equilibrium are presented in this paper.