A new bounding mechanism for the CNC machine scheduling problems with controllable processing times

In this study, we determine the upper and lower bounds for the processing time of each job under controllable machining conditions. The proposed bounding scheme is used to find a set of discrete efficient points on the efficient frontier for a bi-criteria scheduling problem on a single CNC machine. We have two objectives; minimizing the manufacturing cost (comprised of machining and tooling costs) and minimizing makespan. The technological restrictions of the CNC machine along with the job specific parameters affect the machining conditions; such as cutting speed and feed rate, which in turn specify the processing times and tool lives. Since it is well known that scheduling problems are extremely sensitive to processing time data, system resources can be utilized much more efficiently by selecting processing times appropriately.