Modeling and real-time heating control of a reheating furnace using an advection equation

This paper proposes a novel modeling scheme for optimal control of a reheating furnace, where permutation scheduling of slabs inserted into the furnace and control of continuous dynamics on slabs inside the furnace are simultaneously optimized. This modeling introduces an advection equation and allows us to reduce the number of the binary decision variables in the resulting mixed integer programming (MIP) problem. Consequently, in comparison with [Fujii et al., 2010, in Proc. IEEE MSC], a decrease in the computational burden of solving the optimal control problem is accomplished.