(179b) Medium-Term Production Scheduling of a Large-Scale Steelmaking Continuous Casting Process Under Demand and Processing Time Uncertainty

Scheduling of steelmaking-continuous casting (SCC) processes is of major importance in iron and steel operations since the SCC process is often a bottleneck in iron and steel production.[1] Li et al.[2] developed a novel and effective unit-specific event based continuous time formulation for this process and extended the rolling-horizon approach[3-4] to decompose the entire MILP problem. The computational results show that the extended rolling horizon approach reduced the computational time and generated the same or better feasible solution than that without using the rolling horizon approach. This proposed model assumes that all the parameters are deterministic in nature.

However, several uncertainties such as demand fluctuation, and processing time uncertainty frequently happen during the realistic operations. In the presence of these uncertainties, the nominal schedule may often be suboptimal or even become infeasible. In general, two approaches can be used to address those uncertainties: reactive scheduling and preventative scheduling.[5] While reactive scheduling is a process to revise the generated schedule from nominal parameters when a disruption has occurred during the actual execution of the schedule, preventive scheduling seeks to accommodate future uncertainty at the scheduling stage. The uncertainty can be explicitly taken into account through preventive approaches such as two-stage stochastic programming, parametric programming, fuzzy programming, chance constraint programming, robust optimization techniques, and conditional value at risk.[5] Among these approaches, uncertain parameters are often represented by scenarios or non-scenarios. The detailed reviews on planning and scheduling under uncertainty can be referred to Li and Ierapetritou[6] and Verderame et al. [5].

In steelmaking and continuous casting process, reactive scheduling is often used for handling different types of disruptions such as machine breakdowns, rush orders, defect problems, and order cancellations.[7-9] Hou and Li[9] investigated comprehensively various disturbances in steel production dynamic environment and their effects. To address those disturbances, they proposed a general repair procedure and basic repair steps to provide an effective decision support for theory and practice of the integrated steel production rescheduling. Yu et al.[10] used fuzzy programming approach to address uncertain processing time in the steelmaking and continuous casting production process. The uncertain processing time was denoted by triangular fuzzy number.

In this paper, we first employ the robust optimization framework from Lin et al.,[11] Janak et al.,[12] Li et al.,[13] and Li et al.[14] to develop a deterministic robust counterpart optimization model for demand and processing time uncertainty during the steelmaking and continuous casting operations. The robust solution from the robust optimization framework is guaranteed to be feasible for the nominal parameters. The computational results show that the obtained schedule is more robust than the nominal schedule.

While the robust optimization framework aims at finding a single schedule that is immune to all the possible uncertainty realizations within a uncertainty set, two/multi-stage stochastic programming method provides flexibility of implementing different operational decisions after the realization of uncertainty. In this paper, a two-stage stochastic programming framework was also studied for the scheduling of steelmaking and continuous operations under demand and processing time uncertainty. Scenario based stochastic programming method was applied to the problem under investigation. To make the resulted stochastic programming problem computationally tractable, a novel scenario reduction method[15-16] has been applied to reduce the huge number of scenarios to a small set of representative realizations. The selected scenarios are incorporated into the stochastic programming model, which is further reformulated into its deterministic equivalent model and solved. Results demonstrate that the robust optimization-based solution is of comparable quality to the two-stage stochastic programming based solution.

References

[1] Tang, L. X., Lih, P. B., Liu, J. Y., Fang, L. Steel-making process scheduling using lagrangian relaxation, Int. J. Prod. Res., 2002, 40, 55-70.

[2] Li, J., Xiao, X., Tang, Q. H., Floudas, C. A. Production scheduling of a large-scale steelmaking continuous casting process via unit-specific event-based continuous-time models: Short-term and medium-term scheduling, Ind. Eng. Chem. Res., 2012, 51, 7300-7319.

[3] Lin, X., Floudas, C. A., Modi, S., Juhasz, N. M. Continuous-time optimization approach for medium-range production scheduling of a multiproduct batch plant, Ind. Eng. Chem. Res., 2002, 41, 3884-3906.

[4] Janak S. L., Floudas C. A., Kallrath J., Vormbrock N. Production scheduling of a large-scale industrial batch plant. II. Reactive scheduling, Ind. Eng. Chem. Res., 2006, 45, 8234-8252.

[5] Verderame, P. M., Elia, J. A., Li, J., & Floudas, C. A. Planning and scheduling under uncertainty: A review across multiple sections, Ind. Eng. Chem. Res., 2010, 49, 3993-4017.

[6] Li, Z., Ierapetritou, M. Processing scheduling under uncertainty: Review and challenges, Computers and Chemical Engineering, 2008, 32, 715-727.

[7] Tang, L. X., Wang, X. P. A predictive reactive scheduling method for color-coating production in steel industry, The International Journal of Advanced Manufacturing, 2008, 35, 633-645.

[8] Worapradya, K., Buranathiti, T. Production rescheduling based on stability under uncertainty for continuous slab casting, Proceedings of ASIMMOD, January 22-23, Bangkok, Thailand, 2009, 170-176.

[9] Hou, D. L., Li, T. K. Analysis of ramdom disturbances on shop floor in modern steel production dynamic environment. Procedia Engineering, 2012, 29, 663-667.

[10] Yu, S. P., Pang, X. F., Chai, T. Y., Zheng, B. L. Scheduling of steelmaking and continuous casting process under processing time uncertainty. Control and Decision, 2009, 24, 10, 1-6.

 [11] Lin, X., Janak, S. L., Floudas, C. A. A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty. Computers and Chemical Engineering, 2004, 28, 1069-1085.

 [12] Janak, S. L., Lin, X., Floudas, C. A. A new robust optimization approach for scheduling under uncertainty. II. Uncertainty with known probability distribution. Computers and Chemical Engineering, 2007, 31, 171-195.

[13] Li, Z., Ding, R., Floudas, C. A. A comparative theoretical and computational study on robust counterpart optimization: I. Robust linear optimization and robust mixed-integer linear optimization. Industrial and Engineering Chemistry Research, 2011, 50, 10567-10603.

[14] Li, Z., Tang, Q., Floudas, C. A. A comparative theoretical and computational study on robust counterpart optimization: II. Probabilistic guarantees on constraint satisfaction. Industrial and Engineering Chemistry Research, 2012, 51, 6769-6788.

[15] Li, Z., Floudas, C. A. Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: I. Single reduction via mixed integer linear optimization, Computers and Chemical Engnineering, Under review, 2013a.

[16] Li, Z., Floudas, C. A. Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: II. Sequential reduction, To be submitted, 2013b.