Optimal control for steel annealing processes as hybrid systems

This paper formulates and solves an optimal control problem for steel annealing manufacturing processes involving one or more furnaces integrated with plant-wide planning and scheduling operations. We use a hybrid system framework to capture the tradeoff between metallurgical quality requirements and timely product delivery. The resulting nonconvex and nondifferentiable problem is solved by decomposing it into several smaller and simpler constrained convex optimization subproblems. Although the number of such subproblems appears to be combinationally large in the number N of jobs to be completed, we use a recently developed approach for identifying at most 2N-1 such problems and provide some explicit numerical results.