New approach for quantifying process feasibility: Convex and 1‐D quasi‐convex regions

Ierapetritou, Marianthi G.

doi:10.1002/aic.690470616

Cited by 50 publications

(30 citation statements)

References 16 publications

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“…More detailed approximation of feasible region shape was motivated in part by the fact that deterministic approaches to solving the feasibility problem may underestimate feasibility for complex and nonconvex feasible regions [101]. Goyal and Ierapetritou [102] present a Simplicial Approximation Approach [103] to determine the feasible region, which can help to address the issue of underestimating process feasibility.…”

Section: Operational Envelopes For Feasibility Analysismentioning

confidence: 99%

Mathematical Tools for the Quantitative Definition of a Design Space

Rogers

Ierapetritou

2016

Methods in Pharmacology and Toxicology

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This chapter focuses on the application of process modeling to determination of design space for pharmaceutical manufacturing processes. The first two sections define design space and related terms from a regulatory perspective and discuss how these apply in practice during pharmaceutical process development. In Sect. 3, a variety of mathematical techniques that can be used to guide design space development are introduced. An emphasis is placed on the use of feasibility analysis and the relationship between process feasibility and design space. Statistical techniques, including latent variable and Bayesian methods, are also discussed in detail. For methods that have been reported in the literature for pharmaceutical manufacturing applications, an overview of the relevant case studies is provided. If methods have not yet been applied to pharmaceutical processes, potential applications for these techniques are indicated. To illustrate the applicability of these concepts to pharmaceutical manufacturing processes, a brief case study is presented in Sect. 4. A discussion of design space verification and issues related to scale-up is provided in Sect. 5. Finally a brief summary of the concepts presented and their potential role in design space development for pharmaceutical processes is given in Sect. 6. This chapter is intended to provide readers with an understanding of mathematical techniques that can be used during process development to assist in the determination of process design space. An overview of the problem formulation and solution approaches for each method are presented. More detailed mathematical developments for each technique are available in the references provided. Table 1 provides a list of symbols that are used throughout this chapter, while Table 2 describes acronyms used within this chapter.

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Section: Operational Envelopes For Feasibility Analysismentioning

confidence: 99%

Mathematical Tools for the Quantitative Definition of a Design Space

Rogers

Ierapetritou

2016

Methods in Pharmacology and Toxicology

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“…16,17 Further extensions include stochastic flexibility, 18,19 where the uncertain parameters are described by a joint probability distribution function; flexibility analysis of dynamic systems 20 ; flexible design with confidence intervals and process variability 21,22 ; new flexibility measure from constructing feasible polytopes in the parameter space 23 ; simplicial approximation of feasibility limits 24 ; and flexibility analysis via parametric programming. 25 More recent works focus on data-driven approaches for flexibility analysis.…”

Section: Historical Perspectivementioning

confidence: 99%

On the relation between flexibility analysis and robust optimization for linear systems

2016

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Flexibility analysis and robust optimization are two approaches to solving optimization problems under uncertainty that share some fundamental concepts, such as the use of polyhedral uncertainty sets and the worst-case approach to guarantee feasibility. The connection between these two approaches has not been sufficiently acknowledged and examined in the literature. In this context, the contributions of this work are fourfold: (1) a comparison between flexibility analysis and robust optimization from a historical perspective is presented; (2) for linear systems, new formulations for the three classical flexibility analysis problems-flexibility test, flexibility index, and design under uncertainty-based on duality theory and the affinely adjustable robust optimization (AARO) approach are proposed; (3) the AARO approach is shown to be generally more restrictive such that it may lead to overly conservative solutions; (4) numerical examples show the improved computational performance from the proposed formulations compared to the traditional flexibility analysis models.

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“…Alternatively, chance of feasible operation can be reflected by the size of the feasible operating region. Flexibility metrics, such as flexibility index (FI G ) [9,11], resiliency index (RI) [25] and feasible convex hull ratio (FCHR) [26], reflect the degree of system flexibility by estimating the size of the feasible operating space using various types of polygons (or hyper-polygons for system with higher dimensionality). These metrics have different advantages and disadvantages for system evaluation [27].…”

Section: Feasibility and Flexibilitymentioning

confidence: 99%