Using a facility location algorithm to determine optimum cast bloom lengths

The dimensions of a bloom, which is a rectangular piece of steel, are critical for efficiently and effectively rolling the bloom into a finished structured shape (I-beam) for sale to the customer. To achieve maximum productivity and yield, the bloom size (thickness, width and length) to be rolled on a finishing mill into a structural shape must be determined by steel deformation experts. Suppose, for a particular finishing mill, these ‘rolled’ blooms are all produced from a ‘cast’ bloom of the same cross-section but with many different lengths. It is necessary to consolidate the many ‘cast’ bloom length-metallurigcal grade combinations to a number that can be managed by the casting operation and bloom stockyard without significantly impacting productivity and yield. An uncapacitated facility location problem formulation and algorithm were used to solve this problem. The way in which this approach was used to solve a real-world application is discussed.