Simultaneous optimization of slab permutation scheduling and heat controlling for a reheating furnace

In this report, for a reheating furnace, which is employed in one of the processes for producing steel sheets from slabs, we propose a modelling method that simultaneously optimizes both the permutation scheduling of slabs and the heat controlling of the furnace. The proposed modelling scheme is based on a hybrid model composed of a nonlinear advection equation that expresses the behavior of the slab temperature and a discrete model for feeding slabs. The model predictive control problem of this model, which will be reduced to a mixed integer programming problem, is formulated by discretizing the advection equation in time and space by means of the method of characteristics and spatially piecewise-linearizing the nonlinear term. It is shown by numerical simulations that the proposed model predictive control method is very effective from the viewpoint of the control performance and the computational burden. (C) 2013 Elsevier Ltd. All rights reserved.