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.
This paper deals with a job scheduling problem for a flexible manufacturing machine. We consider the same manufacturing environment described in a companion study (Part I), but we use a different performance criterion: to minimize the total number of instants at which tools are switched. This performance criterion is appropriate when the switching time is roughly constant and independent of the number of tool switches. We show that this scheduling problem generalizes the classical bin packing problem, and we present a non-LP-based branch-and-bound procedure that terminates with an optimal solution. We extend this procedure to the case of K machines in sequence.
We present a new family of shortest-route methods, which reduce an upper bound on running time, and make empirical comparisons for a certain class of networks. These methods also allow for exploitation of structure by pruning arcs and/or nodes.
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