(715a) Adaptive Scheduling of Steelmaking and Continuous Cast Process Under Uncertainty

Steelmaking and continuous casting (SCC) is widely used in industry to convert raw iron ore and scrap iron into various steel products. SCC comprises three major processing stages: steelmaking, refining and continuous casting. Each of them involves high-energy, high-temperature, complex processes which require heavy investment and operation costs. The optimal scheduling of these processes would result in reduced energy consumption and costs, increased profits and an improved refining-casting-delivery schedule. In practice, SCC process scheduling is complicated because of the interacting and sequential nature of the processes, and strict material, flow time, quality and delivery time constraints. Furthermore, additional complexity is introduced into the scheduling exercise when one accounts for the uncertainty associated with a large host of parameters involved, such as demand fluctuation and processing time uncertainty.

Tang, et al (1998) presented a linear programming model approach to develop a production schedule for SCC. Their technique consisted of a just-in-time approach based on meeting product demand as well as ensuring continuity in process operations. Atighehchian, et al (2009) proposed an algorithm that treats the SCC scheduling process as a hybrid flow shop scheduling exercise and solves it using a combination of ant colony optimization and nonlinear optimization. The stochastic SCC scheduling process can be dealt with in two ways: reactive scheduling and preventive scheduling. Reactive scheduling deals with uncertainties pertaining to unforeseen product cancellations or breakdowns during operation, whereas preventive scheduling deals with uncertainties pertaining to processing time, product demand and prices. Rodrigues, et al (1996) presented a mixed integer linear programming formulation for reactive scheduling using state task network representation and a rolling horizon approach. Ye, et al (2014) compared two approaches for dealing with product demand uncertainty during the SCC process: static robust optimization and two-stage stochastic optimization framework, and compared the quality of solutions obtained from both approaches.

The focus of this work is to generate adaptive scheduling policy for the SCC process when there is uncertainty in ladle processing time. The proposed method is based on multistage adaptive optimization using a linear decision rule based solution technique. Compared to static robust optimization techniques, the proposed method generates less conservative, yet robust schedule solution, which is adjustable based on the observed uncertainty realizations. The proposed solution framework handles two types of objectives: a risk-averse objective function which leads to adaptive robust optimization and a risk-neutral objective function which leads to adaptive stochastic optimization. The optimal solution is a set of linear decision rules for adaptive decision variables, rather than the exact values. Accordingly, realized uncertainties until a particular decision stage are plugged into the linear decision rules, and then, the values for decision variables are determined for the next stage. Moreover, since the decision rules are linear, the problem size is a polynomial function of the number of stages. Therefore, this approach is a good candidate for large scale SCC scheduling problems.

The proposed methods were tested through several case studies. Although the adaptive robust and adaptive stochastic solution give different objective values, the scheduling solutions given by both models are robust and feasible for all possible uncertainty realizations. However, the adaptive robust solution is more conservative than the adaptive stochastic solution. Hence, the adaptive stochastic optimization method is found to be preferable for SCC scheduling under uncertainty.

References

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