Melt scheduling to trade off material waste and shipping performance

The ingot formation or ‘melt’ process is the first step in many steel-making operations. This process involves melting steel and alloys in the desired chemical composition, then pouring it into a variety of ingot molds. Complex technological and resource constraints can make the planning and scheduling of such processes extremely challenging. In this paper, we report our experience in developing solution methods for this ‘melt scheduling’ problem at BethForge, a division of the Bethlehem Steel Corporation, and a manufacturer of custom-made heavy steel forgings. We describe the main issues associated with generic melt-scheduling problems as well as constraints that are specific to BethForge. The problem at BethForge is particularly challenging, because of the need to keep the ingot at a high temperature before forging, their large product variety, and the need to consider trade-offs between two conflicting objectives. We first formulate the base melt-scheduling problem as a mixed-integer program. We then decouple the scheduling decisions into two levels and develop a local search algorithm based on Storer and Wu's problem space neighborhood. Our aim is to generate a family of efficient schedules that allow decision makers to balance the trade-off between two criteria. Computational experiments are performed using data from BethForge. The melt-scheduling procedure developed here has been implemented and installed at BethForge. It has made fundamental improvement in their melt-scheduling process.