Equipment Location in Machining Transfer Lines with Multi-spindle Heads

The considered problem appears when a machining line must be configured. It is necessary to define the number of workstations and the number of spindle heads at each workstation to be put in the line in order to produce a given part. This problem is known to be $\mathcal{NP}$ -hard and, as a consequence, the solution time increases exponentially with the size of the problem. A number of pre-processing procedures are suggested in this article in order to decrease the initial problem size and thus shorten the solution time. A new algorithm for calculating a lower bound on the number of required equipment is also presented. A numerical example is given.