Mathematical model of steel consumption minimization considering the two-stage billets cutting

Abstract

Purpose. To achieve a decrease in energy and resource costs in the multi-stage production of rolled products within a given plan through the development of appropriate mathware. Methodology. The multi-stage problem mathware for producing rolling steel products is developed on the basis of system approach applying fundamental principles of the optimization and operation research theory. Realization of the developed mathematical model allows discovering such a strategy of using steel during the whole manufacturing process, which minimizes not only the steel waste at the moment of its casting in a mold, but also the offcuts in the process of cutting the obtained ingots into the billets. Findings. A mathematical task model is built to minimize the amount of steel for producing a certain order of size of one cast volume only. The developed model specifies the possibility to pre-evaluate the billet optimal size, based on the necessary cutting along the final product length, appropriate for the certain billet form of section, and ingot weight limits. Originality. A mathematical model is provided for the optimal metal distribution process when implementing the plan of manufacturing rolling products. The model, in contrast to the existing ones, shifts the emphasis on forming the optimal ingot weight, which has a pre-calculated optimal cutting plan. Practical value. The use of the developed mathematical optimization model (minimizing the amount of steel for producing a certain order) as part of an automated decision support system for management of rolling production will reduce the number of cutting machine changeover and minimize resources use and stock balance.