The αBB Approach in Batch Design under Uncertainty
In this chapter, we address the batch design under uncertainty problems via the αBB global optimization framework. Section 18.1 reviews the previous research work in this area. Section 18.2 introduces the problem definition, presents the mathematical formulations, and highlights the need for global optimization. Section 18.3 presents the important theoretical properties that set the foundation for the global optimization framework, and introduces three different lower bounding formulations. Section 18.4 provides the algorithmic steps of the modified αBB global optimization approach. Section 18.5 introduces an illustrative example that identifies the characteristics of the three different lower bounding problems presented in section 18.3. Section 18.6 presents the formulation for mixed-product campaign and treats the unlimited intermediate storage (UIS) case. Section 18.7 presents computational studies for multiproduct batch plant design under uncertainty. Finally, section 18.8 provides a comparison with other types of underestimating problems. The material presented in this chapter is based on the work of Harding and Floudas (1997).
KeywordsGlobal Solution Uncertain Parameter Quadrature Point Uncertain Demand Batch Plant
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