Steel Scrap Purchasing Optimization and Supply Management

A mixed integer non-linear optimization problem has been developed to aid in purchasing scrap steel. The model, which includes about 600 real-valued variables, 200 integers, and over 800 possible constraint equations, uses industrial data, actual market prices and supplier information to perform calculations. Prices, quality and supplier information are input or read into the model, along with selections of constraints and a production plan. The model has been in use by production personnel. To date, the caseby-case solution of the optimization problem has led to suggestions for improved steel blends and has indicated a potential for savings in monthly scrap purchases. Introduction The production of steel is dominated by the use of iron ore and recycled steel scrap. Recycled steel scrap is available on the open market as a commodity. The scrap commodity is purchased periodically to ensure that overall production targets are met. Recycled steel scrap is used primarily in electric arc furnaces (EAF) where it is blended and melted, batch-wise, to produce steel that is cast into solid shapes that are then rolled, treated, and shipped to customers. Producing families of steel grades with recycled steel scrap to meet customer requirements in a timely fashion is a key aspect of EAF operation. Purchased steel scrap is the most important feedstock material for an EAF, contributing significantly to production costs. Steel scrap can be used in different proportions to achieve desired physical and chemical properties of the finished product in order to meet customer requirements. The economical use of recycled steel scrap is governed by many factors including the prevailing market price and availability from each scrap supplier (e.g. cars vs. refrigerators) and the content of constituents such as copper, tin, sulfur and phosphorus. Limiting or controlling the level of these constituents is of primary concern to meet requirements such as hardness and weldability and to ensure that steel material properties are uniform across the cast piece. Since the price and quality of purchased scrap fluctuate, a periodic adjustment is required to the relative usage rate for each batch of steel made in a particular period of time. The determination of the steel scrap usage rates results in an optimization programming problem that seeks to minimize scrap purchase costs plus operating costs. Figure 1 shows that the solution of the programming problem should indicate which scrap supplier to purchase from, what scrap type to use, and in what lot quantities, in order to fill customer orders and to maintain desired inventory levels for the steel producer. Model Description An approximate cost equation can be developed for optimization by considering cost of steel scrap and the cost of electrical energy used to melt it in an EAF. The cost of scrap is directly related to market pricing and availability as well as internal inventory holding costs. Market prices are determined through monthly negotiations with local scrap suppliers. Internal inventory holding costs for a particular commodity like shredded scrap account for the opportunity costs of purchasing a similar commodity on the open market. Energy costs are focused on approximating the electricity use for each scrap type. Electricity use will vary with the quality of the scrap type, its density and how it was prepared by the supplier prior to its use in an EAF. Purchase costs and energy use costs can be related to the amounts of scrap used through Equation (1). The expression in Equation (1) is the economic objective function for the scrap blending optimization problem and is an estimate of the total operating cost c [$]. The purchase cost cp [$] in Equation (1) includes the costs incurred for adding m [kg] of each scrap type i to an EAF batch j to meet production demand. In addition to the amount of scrap added to each batch produced, the cost cp is related to the amount of scrap purchased from a particular supplier, the amount taken from inventory, and the integer decision variables used to choose the source and the pricing option for the scrap. ∑ ∑∑ = = = × + = J