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Overview of Scheduling Methods for Pharmaceutical Production 367
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time might constrain the production, and incorporating these constraints is essential
to generate an implementable schedule. In some chemical or biopharmaceutical
production, products are generated in batches, and different batches of the same
products/intermediates cannot be mixed, which demands multiple storage vessels
for storing these batches. Furthermore, if batching decisions are considered, the size
of the storage vessels will influence batch sizes. If enough vessels of sufficient sizes
are available, then we can assume unlimited storage policy; else, the storage policy
is limited, and the multistage production schedule is influenced by both the number
and size of the available storage vessels. Another important factor is storage time,
which is often important for pharmaceutical processes due to the low shelf life of
the intermediate products. Accounting for the waiting time in the processing units
is also important and might be used instead of an actual storage vessel in case of
limited availability. For further information on modelling of the storage constraints
in a multistage facility, the interested reader can refer to Sundaramoorthy et al. [19]
5 Illustrative Example
In this section, we demonstrate the applicability of the abovementioned discretetime scheduling models through some case studies. The instances are designed to
demonstrate the modelling of changeovers and utility (resource) constraints and the
efficacy of discrete-time models. We have solved all the instances using the FICO
Xpress Optimization Suite and the “mmxprs” module version 2.8.1 on an Intel Core
i7 (2.3 GHz) unit with 32GB RAM [43], and the model characteristics for each of
these instances are provided in Table 1.
For the first two instances, we consider a production facility involving two
production stages and four units: two units per stage. Ten batches need to be
processed in this facility, and unlimited storage policy is assumed. Data for this
example is taken from Sundaramoorthy et al. [19] and modified accordingly (Figs.
2 and 3).
Two different instances ofthis example are considered. In thefirst instance, wedo
not consider changeover times, while in the second, we find the optimum schedule
incorporating changeover times. The objective is to minimize the makespan. The
resultant optimal schedules for these two instances are shown in Fig. 2a and b.
Table 1 Model statistics for the instances
Objective Makespan minimization Makespan minimization Cost minimization
Constraints 604 10,659 51,831
Continuous variables 1 1 99
Binary variables 890 890 80,661
Computational time (s) 0.1 3 2309
Instance 1 Instance 2 Instance 3
368 S. Misra and C. T. Maravelias
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Fig. 2 Gantt chart of optimal solutions for Instances 1 and 2
Fig. 3 Gantt chart and utility profiles of optimal solutions for Instance 3. (a) Optimum schedule;
(b) consumption and availability of utility (EL) required for batch execution; (c) consumption of
utility (CW) required for changeover
Overview of Scheduling Methods for Pharmaceutical Production 369
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We next present a large size instance, in which 20 batches are to be scheduled.
Each batch is to be processed in two stages, and each stage has two dedicated units
in which the batches can be processed. We also consider utility requirements and
illustrate the effect of limited utility on the optimum schedule. We assume that
the processing of each batch requires electricity (EL) in both stages. Furthermore,
it is assumed that each changeover among batches incurs cost and requires the
consumption of cleaning water (CW), which is assumed to be a nonrenewable utility
with initial inventory of 130 tons. The cost of CW is assumed to be included in the
changeover cost. The objective is to minimize the total (processing +changeover +
utility) cost.
Figure 3 shows the Gantt chart and utility profiles of the optimum solution for
the third instance. Figure 3b depicts the engagements of EL utility that coincide
with the processing of batches, whereas Fig. 3c illustrates the consumption profile
of CW utility, which is triggered by the changeovers. This example demonstrates
how the intricacies related to changeover time cost and utility requirements can be
modeled. Nevertheless, as the computational requirements increase with problem
size, advanced solution methods may be necessary to solve large industrial-scale
instances. A set of such solution methods, including tightening methodologies
and reformulation techniques applicable to multistage, multiproduct production
environment, are described in Merchan et al. [20] and Lee and Maravelias [21, 22].
6 Conclusion
This chapter provides an overview of discrete-time batch scheduling models that can
be used to schedule chemical and biopharmaceutical manufacturing environments.
Concepts and techniques regarding the formulation of such models are discussed,
starting from the single-unit problem and building up to problems in multiproduct
multistage facilities. The structure of the discrete-time models remains almost the
same from a single-unit to multiunit multistage problems, and complex decisions
related to batching, changeover, and shared resources can be easily modeled.
Furthermore, as the time grid is explicit, time-sensitive nuances such as time varying
resource availability, intermediate orders can also be easily incorporated into the
model. We showed, through a medium-size case study of a multiproduct multistage
facility, how the aforementioned features can be incorporated.
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Applications of Optimization with Xpress-MP.
Model-Based Risk Assessment of mAb
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Developability
M. Karlberg, A. Kizhedath, and J. Glassey
Monoclonal antibodies were already one of the fastest growing sectors of biopharmaceutical industry [1]. Recent research on the significant benefits of various
antibodies in reducing the risks of fatality or reducing the symptoms of COVID19, e.g., tocilizumab and sarilumab (Cortegiani et al. 2021), inevitably increases
the importance of the rapid discovery of mAbs and the development of efficient
manufacturing processes. Research reports frequently concentrated on the rapid
discovery of new mAbs, but the developability and the manufacturability of mAbs
were less explored until recently [1–4]. Thischapter adopts the framework of quality
by design (QbD), concentrating particularly on the model-based risk assessment
of mAb developability. A case study highlights specific areas where advanced
modelling approaches can contribute to speeding up the manufacturability and
developability of mAbs and demonstrates the benefits and the challenges of this
approach.
1 Quality by Design
The QbD paradigm was introduced in 2004 and is a systematic approach that aligns
with the Process Analytical Technology (PAT) principles and aims to build quality
into the product through product and process understanding (US FDA 2004). The
framework is especially useful for the process development of mAbs, which consists
of many different steps (unit operations). A typical mAb process can be divided into
two parts: the upstream (USP) or the cell culture processing where the mAbs are
expressed and the downstream (DSP) or purification where the mAbs are isolated
M. Karlberg · A. Kizhedath · J. Glassey ()
School of Engineering, Newcastle University, Newcastle upon Tyne, UK
e-mail: jarka.glassey@ncl.ac.uk
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
A. Fytopoulos et al. (eds.), Optimization of Pharmaceutical Processes, Springer
Optimization and Its Applications 189, https://doi.org/10.1007/978-3-030-90924-6_14
373
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Fig. 1 General outline of the QbD methodology. The process design space is shown as the dashed
box where the effects of process parameters and raw material input (blue box) on the product
quality are characterised.Steps highlighted in red indicate risk assessment of either product quality
attributes, process parameters or raw materials. The green box indicates the availability of clinical
data which can be used to better define the QTPP
and contaminants removed. Typically, a mAb process will consist of between 15 and
20 different unit operations which must be individually characterised, e.g. finding
the optimal process parameters that deliver consistent drug quality and safety of
use [5]. The major steps of a QbD implementation to develop and characterise a
product/process are illustrated in Fig. 1. It is important to note that these are a subset
of steps involved in the whole QbD process. For more details on QbD, including
important aspects such as Critical Material Attributes (CMAs), which will not be
discussed in this contribution in detail, please refer to Rathore [6] and Lawrence et
al. [7].
1.1 Quality Target Product Profile
The implementation of QbD starts by defining the Quality Target Product Profile
(QTPP) which forms the basis of the design for the development and contains
information about the drug quality criteria such as delivery mechanisms, intended
use and route of administration for the intended product to ensure clinical safety and
efficacy. The QTPP is generated from knowledge that is based on literature research,
clinical trials and existing experience from industry or academia [8, 9]. For mAbs,
the QTPP relates to the product’s intended use and properties that can affect patients
and needs to be clearly stated to avoid adverse effects in patients.
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Issues with the lack of efficacy, adverse effects and/or high manufacturing
costs have led to the withdrawal or discontinuation of several mAb products
(Kizhedath et al. 2017). It is thus important that QTPPs include antigen binding,
pharmacokinetics, effector function, stability and half-life of the mAb [6, 10].
However, much of this information does not become available until later when
clinical data has been obtained. Thus, instead, many aspects of the QTPP are
based on prior knowledge in early process development of a mAb. Recently, the
computational prediction and simulation of the mAb structure have been shown
to be a valuable tool for mAb design due to their ability to provide estimates of
behaviour and protein stability which can aid in more accurate QTPP specification
[11, 12].
1.2 Critical Quality Attributes and Risk Assessment
QTPP provides the basis for the identification of Critical Quality Attributes (CQAs)
from a list of Quality Attributes (QAs) using risk-based analysis. This is in
accordance with the ICH Q9 guideline to investigate properties that might affect
product quality. The CQAs are physical, chemical or biological properties of the
drug product that need to be within appropriate ranges to ensure the desired
product quality. These ranges, similar to the generation of QTPP, are obtained
through literature research, clinical data and previous experience, but they are
also updated during process development as new information from characterisation
studies becomes available. The most frequently used method for risk assessment
in industries is Failure Mode and Effect Analysis (FMEA) where the impact of
different unit operations in the process on the QAs is listed. Each effect is ranked
according to a Severity rating (S), an Occurrence rating (O) and a Detectability
rating (D). A final Risk Priority Number (RPN) is calculated by multiplying the
ratings which are then ranked to identify the effects that potentially affect the
product quality and efficacy [13, 14]. Tailored risk assessment methods have also
been proposed for biopharmaceuticals by Zalai et al. (2013). In their work, the
authors argued that traditional methods do not consider the “complexity” of how
a process might affect the product or the “uncertainty” which includes the quality
of the input material as a possible source of risk and which need to be added as
additional factors to the risk assessment.
Once the CQAs have been selected, a process design space is defined by
screening process parameters (PPs) for each of the unit operations that have a
significant effect on the CQAs. PPs that have a significant impact on the CQAs are
called Critical Process Parameters (CPPs) and are identified and controlled using
the following steps:
1. Similar to identification of CQAs, risk analysis methods, such as FMEA, are used
to reduce the large number of PPs to those that may affect CQAs.
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2. Systematic experimental studies using Design of Experiments (DoE) over a
range of PP settings are carried out in small scale to obtain experimental data
for process characterisation to identify CPPs and their optimal ranges. This is
referred to as the control space.
3. Multivariate data analysis (MVDA) is used for the implementation of appropriate
real-time monitoring and control strategies needed for the defined CQAs and
CPPs to ensure product quality. Movement outside of the defined control space
would cause the product quality to drop below that of the desired quality stated
in the QTPP.
The use of statistical DoE is preferred over univariate analysis in process
development of pharmaceuticals as it can generate qualitative and quantitative
information about important process parameters and their impact on the product
quality [15]. Response Surface Modelling (RSM) and leverage plots are often used
to analyse the DoE data to investigate the significance of PPs on the explored
CQAs as well as to define allowed ranges for the identified CPPs [16]. Various
experimental designs exist, and selecting an appropriate design is critical in order
to maximise the information gained from the experiments. Kumar et al. [17]
compared different experimental designs for the DoE of downstream unit operations
to demonstrate how these affect the response surface of each unit operation [17].
Tai et a l. [ 18] showed that a well-chosen experimental design can lead to diverse
and informative data about the system and when combined with high-throughput
experimentation techniques, it can be a powerful tool in defining the process design
space.
The fundamental principle of the QbD framework is to increase process understanding in terms of the effect that PPs have on product quality. Zurdo [19]
suggested that the QbD framework needed to be extended to incorporate product
understanding in terms of the developability of the pharmaceutical which would
include manufacturability, safety, pharmacology and biological activity. The author
argued that by using in silico risk assessment tools based on structural features of
the mAbs and historic development data, predictions concerning manufacturability
of an mAb could be made. In a later publication, two case studies were presented
where structural properties of mAbs were successfully linked to CQAs related
to aggregation and half-life [4]. Such tools can add great value to early process
development of mAbs when implementing the QbD framework where little is
known about both the process and product. Thus, a more in-depth investigation of
Quantitative Structure-Activity Relationship (QSAR) framework and its potential
benefits for QbD integration is explored here.
2 Advanced Modelling Approaches in QbD
The QSAR framework relates structural properties and features (also known as
descriptors) of a compound to biological or physicochemical activity [20, 21].
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This methodology was first introduced by Hammet in the 1930s and was later
refined by Hansch and Fujita and has become a standard tool for small-molecule
drug discovery [22]. A method derived from QSAR, referred to as Quantitative
Sequence-Activity Modelling (QSAM), has been introduced in recent years and
focuses on relating structural descriptors of proteins, peptides and nucleic acids to
activity [23]. The only difference between QSAR and QSAM is the development of
descriptors, whereas the guidelines for the predictive model development remain the
same. Given the complex protein structure of mAbs, the QSAM methodology for
descriptor generation will be of more relevance, and the workflow described below
will therefore focus more on protein-based rather than small molecule-based QSAR.
2.1 Descriptor Generation
One of the most important steps in QSAR is the numerical representation of
structures of the pharmaceuticals so that they can be used in correlation studies
with prediction outputs of interest. For proteins, such as mAbs, two approaches
to generate descriptors are discussed here: (1) descriptors generated from the amino
acid primary sequence and (2) descriptors generated from three-dimensional models
of the mAbs. It has been shown that a combination of both physicochemical and 3D
structure descriptors works best and also ensures that the model is not overly reliant
on a single type of a descriptor [24].
2.2 Amino Acid Composition-Based Descriptor Generation
Extensive research has been carried out to develop new informative descriptors for
peptides and proteins generated from their primary sequence [25]. This was first
introduced by Sneath [26] who derived amino acid descriptors for the 20 naturally
occurring amino acids from qualitative data. Later on, Kidera et al. [27] used 188
properties of the 20 naturally occurring amino acids, which were converted into
ten orthogonal new descriptors to describe the amino acids. Later, the Z-scale,
which consists of three new amino acid descriptors derived by applying PCA to
29 physiochemical properties [28, 29], was introduced. Other amino acid scales,
which were also derived through PCA, include the extended Z-scale and T-scale
[30, 31]. Other descriptors include the so-called isotropic surface area (ISA) and
the electronic charge index (ECI), which are derived from the 3D structures of the
amino acids [32]. All these descriptors were tested and performed well in respective
studies on small peptides. In a two-part review by van Westen et al. [33, 34],
many of the existing amino acid scales were benchmarked and compared. The
authors demonstrated that the different scales described different physiochemical
and topological properties which is useful when deciding on which scales to use [33,
34]. Doytchinova et al. [35] applied the Z-scale’s descriptors to successfully predict
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