(736b) Plant-Wide Coordination for the Energy-Efficient Scheduling of an Integrated Steel Production Process

In this work, we present a coordination method to synchronize the schedules of two consecutive production sections in an integrated steel plant: meltshop and hot rolling mill.  The meltshop produces steel slabs, which are stored in a slab yard, and then have to be reheated before being processed by the hot rolling mill. A well-coordinated schedule allows some slabs from the melt shop to be charged directly into the reheating furnace of the hot rolling mill. This operational technique, called hot charging, leads to substantial energy savings and productivity increase but is challenging in terms of production planning and scheduling.

            A review detailing the different hot charging techniques and corresponding integrated production scheduling approaches can be found in Tang [5]. The problem of generating an overall production schedule satisfying both meltshop and hot strip mill constraints has been tackled using AI methods (expert systems, random heuristic search and constraint satisfaction problems), multi agent methods [4] or operations research methods. Our work is based on the approach proposed by Xu [6][7], consisting of a bi-level coordination framework in which the lower-level optimizers are the meltshop and hot rolling mill schedulers while the upper-level focuses only on the bottleneck of the two processes. The advantage of this approach is that it reuses two existing independent optimization modules for the meltshop and the hot rolling mill, without having to develop a monolithic model which would be intractable. The Meltshop Optimizer (MSO) is based on the decomposition strategy presented in Harjunkoski & Grossmann [3] which includes multiple MILP optimization steps using continuous-time formulation and global precedence variables. The Hot Strip Mill Optimizer (HSO) is based on the approach presented by Biondi & Saliba [1] which uses a combination of optimization steps and algorithmic rules in order to build and sequence rolling programs. The upper-level coordinator considers only the bottleneck of the process, namely the continuous casting and hot strip mill stages, and is therefore called intersection model. The coordination objective is to maximize the hot charging ratio by reducing the slab storage times in the slab yard.

            An important challenge of this coordination framework is that the intersection model considers only the production stages of the bottleneck of the process. For this reason it is not guaranteed that the schedule proposed by this simplified model would be feasible when considering the constraints of all upstream and downstream production stages. Xu [6][7] proposed an iterative framework in which logical and integer cuts are progressively added to the intersection model, in order to remove from the search space the job sequences and machine assignments that are not feasible for the lower level schedulers. In this work we show that the potential inability of the sub-optimizers to follow the desired master schedule is not caused by infeasible job sequences but instead by an unrealistic timing of the jobs that doesn’t correspond to the normal process operation and throughput capacity. The problem comes from the difficulty to generate a realistic continuous casting schedule without considering explicitly the upstream steel-making stages. Our approach is to use the information contained in an initial overall solution obtained by a first call of the MSO and HSO schedulers. From this feasible solution, we extract knowledge about the meltshop process in terms of load balancing of the casters and casting production capacity. Based on this data we then generate automatically additional constraints to the intersection model, which lead to a more realistic master schedule.

            For a better evaluation of hot charging, the inner structure of rolling programs and casting sequences are considered in the intersection model. The hot charging condition for each slab (whether the waiting time of the slab is lower than a certain time limit) can be represented by a binary variable. This model extension doesn’t add much complexity to the earlier heatgroup/program based model since the assignment, precedence and timing decision variables are maintained. The shifting algorithm, a linear shift of the hot rolling mill schedule in order to guarantee feasibility, is also modified to take into account this deeper granularity of the mathematical model. The coordination framework has been tested on several real-world large-scale instances, and the results show the benefits of the proposed model developments in terms of hot charging ratio.

References:

(1)   Biondi, M., Saliba, S. and Harjunkoski, I., 2011, Production Optimization and Scheduling in a Steel Plant: Hot Rolling Mill, 18th IFAC World Congress Milano (Italy)

(2)   Cowling, P. I. and Rezig, W. (2000) Integration of continuous caster and hot strip mill planning for steel production. Journal of Scheduling, 3 (4), 185-208.

(3)   Harjunkoski and I. E. Grossmann, 2001, A Decomposition Approach for the Scheduling of a Steel Plant Production, Computers & Chemical Engineering, 25, pp. 1647-1660

(4)   Ouelhadj D. 2003, A Multi Agent system for the integrated dynamic scheduling of steel production, PhD Thesis, University of Nottingham.

(5)   Tang, L., Liu, J., Rong, A. and Yang, Z., 2001, A review of planning and scheduling systems and methods for integrated steel production, European Journal of Operational Research, Vol.133, Issue 1, pp.1-20

(6)   Xu, C., 2013, Coordination and Decomposition of Large-Scale Planning and Scheduling Problems with Application to Steel Production, Thesis, Technische Universität Dortmund.

(7)   Xu, C., Sand, G., Harjunkoski, I., Engell, S., 2012, A new heuristic for plant-wide schedule coordination problems: The intersection coordination heuristic, Journal of Computers & Chemical Engineering, Vol. 42, 11 July 2012, pp. 152–167