(545f) Optimal Design and Scheduling of Multipurpose Batch Plants Under Uncertainty

Due to its necessary flexibility, batch processing mode is predominant in the commercial manufacture of many chemicals of high value and low volume, or products which require complex synthesis procedures [1]. Meanwhile, the special characteristics of batch processes introduce considerable complexities to the systematic design of batch plants. It is known that efficient designs cannot be achieved without taking into account the detailed planning and scheduling. Hence, the integration of design and scheduling is desired [2]. Assuming the demand pattern is stable, a campaign mode operation is often employed for the design of batch plants [3]. In this work, rather than looking at a deterministic case, we assume that the batch plant is exposed to the uncertainty of demand variations from external markets and supply delays from external suppliers. In general, inventories can serve as buffers in dealing with uncertainties. Moreover, adding intermediate storages can increase the efficiency of equipment utilization, thus achieving more economical designs for batch plants. Therefore, when determining the optimal inventory levels for storage tanks of chemicals, we need to look at two aspects. One is the working inventory to satisfy the external demands as well as the internal consumptions. The other is the safety stock to hedge against the unexpected demand variations. A body of research closely related to this work is the multi-echelon stochastic inventory theory, which is originally developed for the supply chain management. By using the guaranteed service approach, one is allowed to model the inventory allocation across the entire system [4-6]. Applications of this approach were reported in studying continuous chemical process networks [7], but how to capture the stochastic nature of demand variations and supply delays within batch plants remains a challenge. While multiproduct plants are easier to model, most of the batch products are manufactured in multipurpose facilities [8]. Thus, in this work, we address the design of multipurpose batch plants and the first step is to establish a unified framework to account for the planning, scheduling and inventories.

By dividing the multipurpose batch plant system into macrostructure (connections between stages) and microstructure (a series of basic processing tasks within a stage) [3], we are able to derive a multi-stage network which can serve as the basis for the integration of planning, scheduling and stochastic inventory management for the design of batch plants. To approach this aggregated problem, we propose a single MINLP model that simultaneously determines the batch sizing, equipment assignments, production schedules, purchases and sales as well as the working and safety inventory profiles. This model exhibits multi-tradeoffs among decision variables from all problem levels, thus seamlessly integrate the planning, scheduling and stochastic inventory management. While this basic model contains multi-linear and concave terms, which would be computationally intractable for large-size problems, we reformulate the model to an MINLP with only square root and linear terms by exploiting the problem properties and using general linearization methods. In order to obtain global optimal solutions with modest computational times, we further develop a tailored branch-and-refine algorithm based on successive piecewise linear approximations. At last, examples are presented to illustrate the application of the model and the performance of the proposed algorithm.

References

[1]        S. Papageorgaki and G. V. Reklaitis, "Optmal Design of Multipurpose Batch Plants. 1. Problem Formulation," Industrial & Engineering Chemistry Research, vol. 29, pp. 2054-2062, Oct 1990.

[2]        A. P. Barbosapovoa and S. Macchietto, "Detailed Design of Multipurpose Batch Plants," Computers & Chemical Engineering, vol. 18, pp. 1013-1042, Nov-Dec 1994.

[3]        N. Shah and C. C. Pantelides, "Optimal Long-Term Campaign Planning and Design of Batch Operations," Industrial & Engineering Chemistry Research, vol. 30, pp. 2308-2321, Oct 1991.

[4]        S. C. Graves and S. P. Willems, "Optimizing the Supply Chain Configuration for New Products," Management Science, vol. 51, pp. 1165-1180, Aug 2005.

[5]        F. Q. You and I. E. Grossmann, "Integrated Multi-Echelon Supply Chain Design with Inventories Under Uncertainty: MINLP Models, Computational Strategies," Aiche Journal, vol. 56, pp. 419-440, Feb 2010.

[6]        F. Q. You and I. E. Grossmann, "Mixed-Integer Nonlinear Programming Models and Algorithms for Large-Scale Supply Chain Design with Stochastic Inventory Management," Industrial & Engineering Chemistry Research, vol. 47, pp. 7802-7817, Oct 2008.

[7]        F. Q. You and I. E. Grossmann, "Stochastic Inventory Management for Tactical Process Planning Under Uncertainties: MINLP Models and Algorithms," AIChE Journal, vol. 57, pp. 1250-1277, May 2011.

[8]        D. W. T. Rippin, "Batch Process Systems Engineering: A Retrospective and Prospective Review," Computers & Chemical Engineering, vol. 17, pp. S1-S13, 1993.