The operational planning and the medium-term scheduling of a chemical plant are interrelated activities dealing with the allocation of plant resources. Operational planning typically occurs over a time horizon of between one to three months and determines the daily production targets for the plant in question. Medium-term scheduling occurs over a time horizon of between two to four weeks and deals in greater detail with the allocation of plant resources such as process units. Given the production targets supplied by the operational planning model, the medium-term scheduling model attempts to determine when certain units should be utilized and the sequencing of these units. In order to ultimately generate a final production profile which is immune to uncertainty in demand, price, and processing time, a planning and scheduling framework needs to explicitly model uncertainty.

The effective integration of operational planning and medium-term scheduling under uncertainty has proven to be a formidable task. Shah [1] and Kallrath [2] both presented excellent reviews highlighting the challenges surrounding the integration of planning and scheduling. Floudas and Lin [3,4] outlined the various objectives and modeling aspects surrounding the scheduling of chemical plants, and Li and Ierapetritou [5] have presented a review of process scheduling under uncertainty. The main approaches for optimizing under uncertainty are stochastic programming, fuzzy programming, stochastic dynamic programming, and robust optimization. The work of Lin et al. [6] and Janak et al. [7] has laid the foundation for a robust optimization approach toward addressing uncertainty within the field of planning and scheduling.

In order to address the objective of providing a production profile which is immune to various forms of uncertainty, the integrated operational planning and medium-term scheduling framework developed by Verderame and Floudas [8] has been extended in order to take into account uncertainty at both the planning and scheduling level using in part the techniques presented by Lin et al. [6] and Janak et al. [7]. The novel Planning with Production Disaggregation Model, as well as the medium-term scheduling model developed by Janak et al. [9] have been reformulated into their respective robust counterparts for both bounded uncertainty and uncertainty with known distribution. The rolling horizon framework, which allows for the two-way interaction between the planning and scheduling levels, also has been modified so as to take into account the presence of uncertainty. It will be demonstrated through an industrial case study of a large-scale, multiproduct and multipurpose batch plant capable of producing hundreds of different products that the extended planning and scheduling framework is capable of providing a daily production profile which is immune to various forms of uncertainty.

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[2] Kallrath, J. Planning and Scheduling in the Process Industry. OR Spectrum, 2002, 24, 219.

[3] Floudas, C.A.; Lin, X. Continuous-time versus Discrete-time Approaches for Scheduling of Chemical Processes: A review. Comp. Chem. Eng. 2004, 28, 2109.

[4] Floudas, C.A.; Lin, X. Mixed Integer Linear Programming in Process Scheduling: Modeling, Algorithms, and Applications. Annals of Operations Research. 2005, 139, 131.

[5] Li, Zukui; Ierapetritou, M. Process scheduling under uncertainty: Review and Challenges. Comp. Chem. Eng. 2008, 32, 715.

[6] Lin, X.; Janak, S.L.; Floudas, C.A. A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty. Comp. Chem. Eng. 2004, 28, 1069.

[7] Janak, S.L.; Lin, X.; Floudas, C.A. A new robust optimization approach for scheduling under uncertainty: II. Uncertainty with known probability distribution. Comp. Chem. Eng. 2007, 31, 171.

[8] Verderame, P.M.; Floudas, CA. Integrated Operational Planning and Medium-term Scheduling of Large-Scale Industrial Batch Plants. Ind. Eng. Chem. Res. Accepted for Publication.

[9] Janak, S.L.; Floudas, C.A.; Vormbrock, N. Production Scheduling of a Large-Scale Industrial Batch Plant. I. Short-Term and Medium-Term Scheduling. Ind. Eng. Chem. Res. 2006, 25, 8234.