Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty

Grossmann, Ignacio E.; Apap, Robert M.; Calfa, Bruno A.; García-Herreros, Pablo; Zhang, Qi

doi:10.1016/j.compchemeng.2016.03.002

Cited by 171 publications

(45 citation statements)

References 79 publications

(100 reference statements)

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“…For the nominal design, T i is kept at its upper boundary to ensure higher vapor pressure P i at the sublimation interface, and thus, to accelerate the sublimation process according to Equations (13) and (15). In the beginning, P c is set to 9.6 Pa to achieve a higher sublimation speed and is decreased gradually to compensate for the influence of the decreasing height of the frozen layer following Equation (16). However, with the existence of (imprecise) parameter uncertainties, the variation of temperature at the sublimation interface will lead to significant violations of the critical temperature which is necessary for maintaining the quality of dried API product.…”

Section: Resultsmentioning

confidence: 99%

“…Traditional methods for propagating and quantifying model uncertainties are probabilistic and frequently used in robust process design. Here, the interested reader is referred to [9,11,13,16,30,35,37] and references therein. The general structure of the original probability-based robust process design reads as:…”

Section: Probability-based Robust Optimizationmentioning

confidence: 99%

“…Although uncertainties in process models and parameters are considered, and are frequently incorporated in robust process design concepts [9][10][11][12][13], the applied algorithms are commonly based on perfect uncertainty measures, i.e., using specific probability density functions (PDFs). In addition to probability-based concepts for robust process design, scenario-based methods exist [14][15][16]. Simulation studies seek the worst-case scenario for which the process is optimized, even when the worst-case scenario rarely occurs in reality, and thus, lead to robust but extremely conservative designs with considerable performance losses.…”

Section: Introductionmentioning

confidence: 99%

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Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

Xie

Schenkendorf

2019

Processes

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Model-based concepts have been proven to be beneficial in pharmaceutical manufacturing, thus contributing to low costs and high quality standards. However, model parameters are derived from imperfect, noisy measurement data, which result in uncertain parameter estimates and sub-optimal process design concepts. In the last two decades, various methods have been proposed for dealing with parameter uncertainties in model-based process design. Most concepts for robustification, however, ignore the batch-to-batch variations that are common in pharmaceutical manufacturing processes. In this work, a probability-box robust process design concept is proposed. Batch-to-batch variations were considered to be imprecise parameter uncertainties, and modeled as probability-boxes accordingly. The point estimate method was combined with the back-off approach for efficient uncertainty propagation and robust process design. The novel robustification concept was applied to a freeze-drying process. Optimal shelf temperature and chamber pressure profiles are presented for the robust process design under batch-to-batch variation.Processes 2019, 7, 509 2 of 14 operating mode when producing active pharmaceutical ingredients (APIs) and drugs [18], i.e., all materials are charged before the start of processing and discharged at the end of processing. Thus, slight experimental deviations or the degradation of the process equipment might result in batch-to-batch variation [18][19][20]. The source of batch-to-batch variation is difficult to predict, but can be quantified with process analytical technology (PAT) and multivariate statistical analysis [19,20]. In the literature, it is well-known that batch-to-batch variation causes severe problems in pharmaceutical manufacturing, drug quality, clinical studies, and therapeutics [6,17,21,22]. To lower batch-to-batch variation in pharmaceutical, and to improve QbD measures, analyzing the effect of measurement noise and batch-to-batch variation is essential. The adverse effect of batch-to-batch variation in pharmaceutical manufacturing is studied experimentally for various processing steps, e.g., fermentation, crystallization, and (nanomaterial) formulation [17,19,23]. In model-based process design, in turn, recent studies try to analysis and control batch-to-batch variation effects too [24,25]. For instance, in the case of model-based process design, model parameters can be derived for each batch data set separately. When each batch run is fit individually, batch-to-batch variation leads to different sets of model parameter estimates and parameter uncertainties. Please note that the variability in the model parameters is not exclusively the result of measurement noise, but the joint effect of measurement errors and slight differences in the experimental settings and the raw materials of the batches [6,17]. Thus, simulation studies should consider imprecise uncertainties [26-28] as well. These imprecise uncertainties cannot be described via a single PDF, but via a set of PDFs that is known as the a...

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Section: Resultsmentioning

confidence: 99%

Section: Probability-based Robust Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

Xie

Schenkendorf

2019

Processes

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“…Flexible design strategies have been applied to several processes including distillation columns [12], air separation units [255], polygeneration systems [73], and supply chain networks [256], with details given in a review by Grossmann et al [257]. In other work, Grossmann et al also provide a review on the use of mathematical programming techniques for optimal process design under uncertainty [21].…”

Section: Economic Criteriamentioning

confidence: 99%

Modeling and Simulation of Energy Systems: A Review

2018

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Energy is a key driver of the modern economy, therefore modeling and simulation of energy systems has received significant research attention. We review the major developments in this area and propose two ways to categorize the diverse contributions. The first categorization is according to the modeling approach, namely into computational, mathematical, and physical models. With this categorization, we highlight certain novel hybrid approaches that combine aspects of the different groups proposed. The second categorization is according to field namely Process Systems Engineering (PSE) and Energy Economics (EE). We use the following criteria to illustrate the differences: the nature of variables, theoretical underpinnings, level of technological aggregation, spatial and temporal scales, and model purposes. Traditionally, the Process Systems Engineering approach models the technological characteristics of the energy system endogenously. However, the energy system is situated in a broader economic context that includes several stakeholders both within the energy sector and in other economic sectors. Complex relationships and feedback effects exist between these stakeholders, which may have a significant impact on strategic, tactical, and operational decision-making. Leveraging the expertise built in the Energy Economics field on modeling these complexities may be valuable to process systems engineers. With this categorization, we present the interactions between the two fields, and make the case for combining the two approaches. We point out three application areas: (1) optimal design and operation of flexible processes using demand and price forecasts, (2) sustainability analysis and process design using hybrid methods, and (3) accounting for the feedback effects of breakthrough technologies. These three examples highlight the value of combining Process Systems Engineering and Energy Economics models to get a holistic picture of the energy system in a wider economic and policy context.

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“…This includes contributions in supply chain planning under uncertainty (Gupta and Maranas, 2003), multi-echelon supply chain network design under uncertainty (Tsiakis et al, 2001), and dynamic operability analysis of process supply chain systems (Mastragostino and Swartz, 2014). An overview of twostage stochastic programming formulations, solution approaches, and process systems applications is given in Grossmann et al (2016).…”

Section: Flexible Design Under Uncertaintymentioning

confidence: 99%

The Optimal Design of a Distillation System for the Flexible Polygeneration of Dimethyl Ether and Methanol Under Uncertainty

et al. 2018

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Two process designs for the separation section of a flexible dimethyl ether and methanol polygeneration plant are presented, as well as an optimization method which can determine the optimal design under market uncertainty quickly and to global optimality without loss of model fidelity. The polygeneration plant produces a product mixture that is either mostly dimethyl ether or mostly methanol depending on market conditions by using a classic two-stage dimethyl ether production catalytic reaction route in which the second stage is bypassed when the market demand is such that methanol production is more favorable than dimethyl ether. The downstream distillation sequence is designed to purify the products to desired specifications despite the wide variability in feed condition that corresponds to the upstream reaction system operating either in DME-rich or methanol-rich mode. Because the optimal design depends on uncertain market conditions (realized as the percentage of the time in which the plant operates in either DME-rich or methanol-rich mode), this uncertainty is considered in the formulation of the optimal design problem. The results show that using one set of flexible distillation columns for two different objectives is superior to the "traditional" approach of using two different sets of distillation columns which are each optimized for one specific operating condition. Different approaches to design under uncertainty were considered, with a scenario-based two-stage stochastic formulation with a uniform distribution of the uncertain parameter recommended as the preferred formulation.

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Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty

Cited by 171 publications

References 79 publications

Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

Modeling and Simulation of Energy Systems: A Review

The Optimal Design of a Distillation System for the Flexible Polygeneration of Dimethyl Ether and Methanol Under Uncertainty

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