Hierarchical approach to steel production scheduling under a global energy constraint

This paper presents a model for the optimization of productivity in a steel plant comprised of four arc furnaces and three continuous casting machines and subject to a global limitation on the power supplied to the furnaces. The furnaces produced in batch mode and require a given amount of energy at each fusion phase in a production cycle. The problem is to define the starting time and duration of each phase for each production cycle, in combination with a power schedule which meets the energy requirements of the different furnaces and a global power supply limit for the whole plant, in order to minimize the due date of the last production cycle. This scheduling problem is formulated as a nonstandard optimization problem, combining an optimal control problem and a mathematical programming problem. A two-level algorithm is proposed, which yields a suboptimal solution through a sequence of linear programming problems. The optimality of solutions produced with the approach is established in the cases of one cycle and for steady-state operations.