A set covering approach to metallurgical grade assignment

Early in 1986 Bethlehem Steel Corporation installed two continuous slab caster machines to modernize the steelmaking facilities at two of its major plants. The installation of this equipment, at a total cost of about half a billion dollars, required accompanying production planning and control systems (PPC) in order to function efficiently. The PPC module responsible for assigning metallurgical grades to customer orders uses a minimum cardinality set covering approach which not only minimizes the number of metallurgical grades required to satisfy a given collection of customer orders, but also is able to ‘show preference’ to priority orders. The algorithm, OPTSOL is used in a two-pass mode to quickly generate very good solutions to these large scale (up to 1000 zero-one variables and 2500 constraints) problems. When compared to the traditional method of grade assignment, this approach has the potential to significantly improve caster productivity and to reduce semi-finished inventory.