Scheduling with tool changes to minimize total completion time under controllable machining conditions

Scheduling under controllable machining conditions has been studied for some time. Scheduling with tool changes, particularly due to tool wear, has just begun to receive attention. Though machining conditions impact tool wear and induce tool change, the two issues have not been considered together. We address for the first time the problem of scheduling a computer numerically controlled (CNC) machine subject to tool changes and controllable machining conditions; our objective is to minimize the total completion time of a given set of jobs. We establish an important result that helps us identify feasible settings of machining parameters such as feed rate and cutting speed. However, the problem at hand remains intractable, even when a single setting is used. In the general case, we are able to solve the problem exactly for up to 30 jobs using a mixed integer linear programming formulation. For larger problems, we turn to approximate solution via heuristics. We examine a number of different schemes. The best of these schemes are used in a problem space genetic algorithm; this produces quality solutions in a time-efficient manner, as is evidenced from an extensive computational study conducted by us.