Sheet-Metal Shop Scheduling Considering Makespan and Flow Time Criteria

Sheet-metal parts typically follow a unidirectional flow in the sheet-metal shop. In the first cutting stage, a large sheet is cut to different unfolded parts with a laser cutting machine. To avoid waste material different parts are combined on a sheet. Next, the 2D parts are transformed to 3D products with air bending. In this bending stage, time- consuming set-ups between production layouts are reduced as much as possible. Separate optimisation of cutting and air bending causes the optimisation benefits to counteract one another. Integrated models have been proposed for both single- and multiple-machine classes, but calculation times are too high and avoidable changeovers still occur. In this paper, by applying variable neighbourhood search with a number of different starting solutions, local optima of good quality are determined for minimising the makespan and the total flow time for both the single-machine and the multi-machine classes. Because the two performance measures are important for a good production plan, bicriteria optimisation by means of a simultaneous and a hierarchical approach, is also considered. Compared to the mathematical programming models for the combined cutting and bending operations, both quality and required computation time are improved for several real-life instances.