Scheduling with tool changes to minimize total completion time

Abstract

In the literature, scheduling models do not consider the unavailability of tools. The tool management literature separately considers tool loading problem when tool changes are due to part mix. However in manufacturing settings tools are changed more often due to tool wear. In this research, the problem of scheduling a set of jobs to minimize total completion time on a single CNC machine is considered where the cutting tool is subject to wear. We show that this problem is NP-hard in the strong sense. We discuss the behavior of SPT heuristic and show that its worst case performance ratio is bounded above by a constant. A pseudo-polynomial dynamic programming formulation is provided to solve the problem optimally. Furthermore, heuristic algorithms are developed including dispatching heuristics and local search algorithms. It is observed that the performance of SPT rule gets worse as the tool change time increases and tool life decreases. The best improvement over the SPT rule’s performance is achieved by the proposed genetic algorithm with problem space search.