Optimization-based scheduling of a machining center

A machining center is an advanced NC (numerical control) machine that has the capability to perform a variety of operations on a part by automatically changing the cutting tools. Because of the versatile processing capabilities, a machining center is often a production bottleneck, and effective scheduling can result in significant improvement of system performance. The problem, however, is very difficult since many factors such as machine setups, pallets, tool magazine, and the possible tool overlapping among different part types, have to be considered. This paper presents an optimization-based approach for the scheduling of a machining center with two pallets. A novel “separable” problem formulation that considers the above mentioned factors is presented. Lagrangian relaxation is applied to decompose the problem into simple subproblems, which are efficiently solved without encountering complexity difficulties. The subgradient method is then used to update the multipliers. Preliminary testing results indicate that the approach is effective, and the algorithm provides a valuable tool for solving standalone machining center scheduling problems