Simultaneous determination of the cutting speed and lot size values in machining systems

This paper presents an iterative procedure for the simultaneous determination of the cutting speed and lot size values in machining systems. These values are determined by differentiating the total cost consisting of machining and lot sizing costs. Additional conditions are presented that help identify a local optimum if one is found. The usefulness of the algorithm is that it could provide a lower cost solution than separate procedures for determining cutting speed and lot sizes. The multiple item case is also examined with the necessary feasibility condition introduced as a constraint and the lot size and cutting speed values determined by using the Lagrangian technique. The cases of both negligible and non-negligible setup times are considered. Computational experience with different cutting tool materials is presented for both the single and the multiple item cases.