Simulation based Decision Support System for ...
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Simulation based Decision Support System for Pharmaceutical Quality Control Laboratory Miguel Alexandre Ramos Lopes Thesis to obtain the Master of Science Degree in Mechanical Engineering Supervisors: Prof. Susana Margarida da Silva Vieira Dr. Rui Montenegro Val-do-Rio Pinto Examination Committee Chairperson: Prof. Paulo Jorge Coelho Ramalho Oliveira Supervisor: Prof. Susana Margarida da Silva Vieira Members of the Committee: Prof. Carlos Baptista Cardeira Doutor Filipe Andr ´ e Prata Ata´ ıde May 2017
Transcript of Simulation based Decision Support System for ...
Simulation based Decision Support System forPharmaceutical Quality Control Laboratory
Miguel Alexandre Ramos Lopes
Thesis to obtain the Master of Science Degree in
Mechanical Engineering
Supervisors: Prof. Susana Margarida da Silva VieiraDr. Rui Montenegro Val-do-Rio Pinto
Examination Committee
Chairperson: Prof. Paulo Jorge Coelho Ramalho OliveiraSupervisor: Prof. Susana Margarida da Silva Vieira
Members of the Committee: Prof. Carlos Baptista CardeiraDoutor Filipe Andre Prata Ataıde
May 2017
The truth is, most of us discover where we are heading when we arrive- Bill Watterson
Acknowledgments
Firstly, I wish to thank my supervisors, Prof. Susana Vieira and Dr. Rui Pinto, for theguidance and insightful counselling they provided throughout the course of this work.
I also extend my gratitude to Prof. Joao Sousa and Hovione Farmaciencia S.A. forproviding me the opportunity to conduct my Thesis on a such an engaging context,covering an applied research topic that I’ve grown deeply found of. A special thanksgoes to the Knowledge Management team members, past and present, for their com-panionship and invaluable insights. Moreover, the effort of the Innovation team to keepme hydrated should not go unmentioned.
I am grateful for the unconditional support my parents have always provided me, asentiment that extends to the rest of my family. A special mention to my little sisterSara, a true source of inspiration and someone I always look-up to.
Thanks to gang - Zeze, Ayala and Leonor - and all the wonderful people I wasfortunate enough to have met over the last year - specially Marghe, Simo, Marti, Maria& Giulia and Marco for all the great times we had.
Lastly, shout out to my mates at IST - specially Ricardo and Miguel - for their cama-raderie over the last five years.
Abstract
The pharmaceutical industry is undergoing times of upheaval. Recent disruptive trends have resulted in
an unprecedented conjuncture that has prompted pharmaceutical companies to pursue new standards
of operational excellence. Pharma 4.0, an archetype of Industry 4.0, promises to introduce a productivity
leap across the industry’s key focus areas - drug discovery, development, manufacturing and marketing
- sparked by the dissemination of embedded technologies and higher levels of distributed intelligence,
connected and supported by the Internet of Things.
In the strive towards optimization, the main focus has been devoted to logistics and manufacturing
operations. The coupled relationship between production and Quality Control related activities has been
overlooked, resulting in a great untapped potential for improvement on the Quality Control front, that can
come to fruition under Pharma 4.0. In this spirit, a data-driven decision support system was implemented
in the form of discrete event simulation model of a Quality Control Laboratory, developed with the aim
of assisting laboratory managers in the tasks of resource planning and scheduling. Considering a new,
state of the art facility as a case study, crucial workflows were modelled and vectors for improvement
pinpointed. A simulation study was conducted to gather insight into the expected performance of the
future laboratory, using the model as a testing platform to benchmark alternative Governance Models,
scheduling heuristics and resource allocation policies.
Keywords
Quality Control Laboratory, Process Modelling, Planning, Scheduling, Discrete Event Systems, Simula-
tion
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Contents
1 Introduction 1
1.1 Pharmaceutical Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Pharmaceutical Supply Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Quality Control in the Pharmaceutical Industry . . . . . . . . . . . . . . . . . . . . 6
1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Quality Control Laboratory Management 9
2.1 Laboratory Resource Planning and Scheduling . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Proposed Solution and Expected Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Modelling Workflows and Data Processing 15
3.1 Analytical Work Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Process Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1 In-Process Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Product Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Method Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Information Sources & Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Quality Control Laboratory Simulation Model 27
4.1 Discrete Event Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Simulation Study Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.3 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.1 Demand Forecasting and Sample Arrival Rate . . . . . . . . . . . . . . . . . . . . 30
4.3.2 Analyst Staff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3.3 Analytical Equipment & Generic Analysis Workflow . . . . . . . . . . . . . . . . . . 43
4.4 Model Framework Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.5 Model Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5 Simulation Study 49
5.1 Model Validation Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6 Conclusion 59
6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
A Arrival of Samples: Clusters & Distributions 65
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List of Figures
1.1 Yearly FDA approved NCEs and R&D investment totals (1997-2015) . . . . . . . . . . . . 3
1.2 Overview of the Integrated Pharmaceutical Supply Chain . . . . . . . . . . . . . . . . . . 5
2.1 Representation of available information and uncertainty in planning and scheduling with
respect to time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1 Black box representation of a Quality Control laboratory . . . . . . . . . . . . . . . . . . . 15
3.2 BPMN Core Notation Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 BPMN representation of In-Process Control Workflow . . . . . . . . . . . . . . . . . . . . 20
3.4 BPMN representation of Product Stability Analysis Workflow . . . . . . . . . . . . . . . . . 21
3.5 BPMN representation of Validation Workflow . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.6 Relative Frequency of Occurring Combinations of Analytical Tests on IPC Samples . . . . 23
3.7 Relative Frequency of Occurring Combinations of Analytical Tests on FP Samples . . . . 24
4.1 DES Time Advancement in Single Server Queueing Systems . . . . . . . . . . . . . . . . 28
4.2 Monthly Workload Levels - IPC Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3 Monthly Workload Levels, per Sample Type . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.4 Summary Statistics: IPC Samples Received per Weekday . . . . . . . . . . . . . . . . . . 34
4.5 IPC Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . . 36
4.6 IPC Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots . . . 36
4.7 IPC Samples, High Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . 37
4.8 COL Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . 38
4.9 COL Samples, Low Monthly Workload: Batch Size Empirical Cumulative Distribution . . . 38
4.10 COL Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots . . 39
4.11 COL Samples, Moderate Monthly Workload: Batch Size Empirical Cumulative Distribution 39
4.12 COL Samples,High Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . 40
4.13 COL Samples,High Monthly Workload: Batch Size Empirical Cumulative Distribution . . . 40
4.14 High-level Sample Generator Framework Representation . . . . . . . . . . . . . . . . . . 41
4.15 BPMN representation of the Generic Analysis Workflow . . . . . . . . . . . . . . . . . . . 44
4.16 Simio Implementation of the Generic Equipment Model . . . . . . . . . . . . . . . . . . . 45
4.17 High-level QCL Simulation Model Flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.18 3D Renders of the QCL Simulation Model Implemented in Simio . . . . . . . . . . . . . . 46
4.19 QCL Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
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5.1 Sample Generator Framework - Number of Incoming Samples: Simulation Input Data
Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Comparison of Governance Model’s Mean Time in System, per Sample Type . . . . . . . 51
5.3 Comparison of Mean Time in System for IPC samples, per Analytical Test . . . . . . . . . 54
5.4 Effect of Qmax on Mean Time in System, per Sample Type . . . . . . . . . . . . . . . . . . 56
A.1 Monthly Workload Levels - FA Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
A.2 FA Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . . 65
A.3 FA Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots . . . 66
A.4 FA Samples, High Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . . 66
A.5 Monthly Workload Levels - FP Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
A.6 FP Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . . 67
A.7 FP Samples, Low Monthly Workload: Batch Size Empirical Cumulative Distribution . . . . 67
A.8 FP Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots . . . 68
A.9 FP Samples, Moderate Monthly Workload: Batch Size Empirical Cumulative Distribution . 68
A.10 Monthly Workload Levels - IN Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
A.11 IN Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots . . . 69
A.12 Monthly Workload Levels - MS Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
A.13 MS Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . . 70
A.14 MS Samples, Low Monthly Workload: Batch Size Empirical Cumulative Distribution . . . . 70
A.15 MS Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots . . . 71
A.16 MS Samples, Moderate Monthly Workload: Batch Size Empirical Cumulative Distribution 71
A.17 MS Samples,High Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . . 72
A.18 MS Samples,High Monthly Workload: Batch Size Empirical Cumulative Distribution . . . . 72
A.19 Monthly Workload Levels - RM Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
A.20 RM Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . . 73
A.21 RM Samples, Low Monthly Workload: Batch Size Empirical Cumulative Distribution . . . 73
A.22 RM Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots . . . 74
A.23 RM Samples, Moderate Monthly Workload: Batch Size Empirical Cumulative Distribution 74
A.24 RM Samples,High Monthly Workload: Density Histogram, Q−Q & P − P plots . . . . . . 75
A.25 RM Samples,High Monthly Workload: Batch Size Empirical Cumulative Distribution . . . . 75
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List of Tables
3.1 Quantitative Analysis of the Number of Analytical Tests Performed on Unique Samples,
per Sample Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1 Arrival Process Properties per Sample Type . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Analyst Work-shifts Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Common Core Analysis Process Steps - Work Environment & Required Resources . . . . 43
4.4 Processing times’ distributions (Tr(a, b, c): Triangular pdf; U(a, b): Uniform pdf); time in
arbitrary units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5 QC Branches and their allocated Sample Types . . . . . . . . . . . . . . . . . . . . . . . . 47
5.1 Mean relative difference in TiS between free-for-all and structured GMs . . . . . . . . . . 52
5.2 Structured Governance Models - Analyst Breakdown per Branch/Work-shift (Scheduled
Utilization %) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3 Free-for-All Governance Models - Analyst Breakdown per Branch/Work-shift (Scheduled
Utilization %) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.4 Planned Equipment Pool Size per Device Variant . . . . . . . . . . . . . . . . . . . . . . . 53
5.5 Equipment Usage Rate % (maximum number of concurrent equipments in use) . . . . . . 55
5.6 Relative difference in mean TiS between SPTF, LPTF and FIFO heuristics . . . . . . . . . 57
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Acronyms
API Application Program Interface
AC Analytical Chemistry
API Active Pharmaceutical Ingredient
BPMN Business Process Modelling Notation
CDMO Contract Development and Manufacturing Organization
COL Change of Line
CMO Contract Manufacturing Organization
DES Discrete Event Systems
DSC Differential Scanning Calorimetry
ERP Enterprise Resource Planning
EMA European Medicines Agency
FA Fast Analysis
FDA Food and Drug Administration
FIFO First In First Out
FP Final Product
GC Gas Cromatography
GLP Good Laboratory Practice
GM Governance Model
GMP Good Manufacturing Practice
IN Intermediate
IPC In-process Control
HPLC High Performance Liquid Cromatography
KF Karl Fischer Titration
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LIMS Laboratory Information Management System
LP Linear Programming
LPTF Longest Processing Time First
NCE New Chemical Entity
PSA Particle Size Analysis
QC Quality Control
QCL Quality Control Laboratory
RM Raw Material
SC Supply Chain
SPTF Shortest Processing Time First
TiS Time in System
WHO World Health Organization
XRPD X-Ray Powder Diffraction
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Chapter 1
Introduction
The pharmaceutical industry is undergoing times of upheaval. Recent disruptive trends, such as the
declining return of investment on the discovery of new drugs driven by rising R&D costs, shortening
of drug patent lives and increasing regulatory scrutiny levels, compounded by the pressure stemming
from external socio-economic and political factors, have brought unprecedented challenges upon the
industry. This conjuncture, in addition to ever present objectives - namely, the desire to minimize the
time-to-market of new drugs, the will to speed up the notoriously slow and expensive process of drug
development through clinical trials and obtaining the required health and safety certificates from the
regulatory entities - has prompted pharmaceutical companies to pursue new standards of operational
excellence.
To this end, pharmaceutical organizations keen on securing present and future competitiveness are
adhering to the paradigm shift spurred on by the extension of the fourth industrial revolution to the
pharmaceutical realm, under the banner of Pharma 4.0. This archetype of Industry 4.0 promises to
introduce a productivity leap across the industry’s key focus areas - drug discovery, development, man-
ufacturing and marketing - sparked by the dissemination of embedded technologies and higher levels of
distributed intelligence, connected and supported by the Internet of Things. Pharma 4.0 can thus be the
catalyst to overcome the challenges facing the industry. The advent of smart manufacturing facilities,
process optimization and digitalization of key information will allow for advanced, data-driven planning
and scheduling tools to be developed. Improving data integrity policies through increased compliance
and transparency levels whilst mitigating the burden of regulatory pressures will help reduce the time to
market of new drugs, a key driving force in the industry.
The pharmaceutical supply chain has developed into a surging research topic, being one of the
main drivers of change in the industry. The current hostile environment of dwindling product pipelines,
established blockbuster drugs nearing their patent expiration date and diminishing R&D productivity
has instigated companies to devote more attention and resources to the modelling and optimization of
supply chain agents, reversing the historical tendency of focusing on both ends of the spectrum – drug
discovery, marketing and sales, respectively [1].
Identifying bottlenecks along the supply chain naturally emerges as one of the first steps in the strive
towards optimization. Until now, the focus has been placed on logistics and manufacturing operations,
with the coupled relationship between production and quality control related activities often being over-
looked, as is evidenced by the contrasting amount of published research papers covering each topic.
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This disparity translates into a great untapped potential for improvement on the quality control front, that
can come to fruition under the context of Pharma 4.0. The development and successful deployment of
continuous and consistent quality monitoring tools across all stages of drug development and manufac-
turing, with special emphasis on the planning and scheduling of analytical work, will allow pharmaceu-
tical companies to capitalize and explore the synergies that a deeper level of quality control integration
can have on the business sector as a whole.
This chapter encloses a brief summary of the pharmaceutical industry. A succinct overview of the
pharmaceutical supply chain is presented, with special emphasis on the role of contract manufacturing
organizations. The topic of quality control in the pharmaceutical industry is introduced, with industry
relevant regulatory agencies and practices being detailed. Particular focus is devoted to the role of
quality control laboratories, the main system this thesis is concerned with. Finally, the challenge at hand
will be detailed, along with the methodologies employed and relevant contributions stemming from this
work.
1.1 Pharmaceutical Industry
The pharmaceutical industry is an intricate network of organizations involved in the practices of
research, development, production, distribution and retail of pharmaceutical preparations, often simply
referred to as drugs.
The complex processes and operations by which the aforementioned practices are performed take
place along a world-wide network of R&D centres, suppliers, factories, warehouses, distribution hubs
and retailers, through which raw materials are acquired, synthesized into drugs and placed at the cus-
tomers’ disposal within a framework akin to that of a modern, integrated Supply Chain (SC), such as the
one introduced in [2].
Large companies used to present high yearly turnovers on a regular basis, relying on the success of
renowned popular products, known as blockbuster drugs, with broad market reach and protected by long
term patent lives. This allowed pharmaceutical companies to effectively secure considerable market
shares for lasting periods of time, through both technological and legal barriers, whilst continuously
reinvesting a sizeable portion of their profits into research and development related activities, culminating
in a rich product pipeline. However, the compound effect of recent disruptive trends has significantly
altered the industry’s status quo. A listing of the most relevant trends, compiled from several sources
([3], [4], [5]), is presented below:
– R&D productivity, measured as the number of approved New Chemical Entities (NCEs) per unit
amount of investment, is declining (as depicted in Figure 1.1);
– Diminishing product pipelines and escalating difficulties in the development blockbuster drugs;
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– Drug patent lives are shortening and providing lower levels of global market exclusivity;
– Diminishing market strength of proprietary products, due to increased competition from generic
manufacturers, globalization and shift in research to meet the needs of developing countries;
– Pressure exerted by healthcare insurance companies, influencing prescribing practices, implies
that new drugs must address new therapeutic areas or present significant cost or health benefits
over existing medicines in order to be successful;
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1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Year
FD
A a
ppro
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NC
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R&D Invesment (Billion US$)
Figure 1.1: Yearly FDA approved NCEs and R&D investment totals (1997-2015)
As the research towards innovative products with high market value makes becomes increasingly
challenging and expensive, companies are hard pressed to replicate the favourable results reported in
previous years. Moreover, the proliferation of generic drug manufacturers eager to capitalize on expiring
patents can imply a sharp decrease in the revenue stream of branded products over a short period
of time. The degree to which companies operating in this sector are exposed to uncertainty should
also be accounted for. Typical risks include (1) demand forecast for the products in their portfolio, (2)
issues related with the sustainable scale-up of chemical processes that might require the chemical
process to be re-engineered during later development stages, and (3) whether or not a drug will achieve
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successful clinical trials. These phenomena have led research-oriented companies striving to shorten
the development cycle of new drugs, and thus their time to market, to strike partnerships with contract
development and manufacturing organizations, promoting a shift in the pharmaceutical SC. As such, the
importance of Contract Development and Manufacturing Organizations (CDMOs) has increased swiftly
in recent years.
1.1.1 Pharmaceutical Supply Chains
As of recent times, increasingly larger importance is being devoted to the supply chain entity, as
focus shifts from the dated requirement of merely having to deliver security of supply at minimum cost,
to the recognition of its ability to generate both value for the customer and the shareholder [3]. Whereas
some of the fundamental concepts of SC management are still applicable to the pharmaceutical industry
framework, this sector presents a set of specific characteristics stemming from the rigid regulations it
must abide by and the technicalities surrounding its core product – the drug – that find no parallel in
other process industries, instigating the need for a more refined modelling approach.
This section covers the topic of supply chains in the pharmaceutical sector, providing a concise
understating of the industry’s key agents and their stance towards the market, followed by the main
drivers of change in the pharmaceutical realm their and, lastly, a selection of operational issues that
hinder the performance of the SC as well as possible measures that can be taken to avert them. The
following notable organizations can be considered:
i. Research and development-oriented companies, with a global presence in branded products, in
both prescription and over-the-counter variants.
ii. Generic manufacturers, who produce out-of-patent prescription and over-the-counter drugs.
iii. Drug discovery and biotechnology companies, often relatively new start-ups with no significant
manufacturing capacity.
iv. Contract Manufacturing Organizations (CMOs) and CDMOs, who do not possess their own prod-
uct portfolio, but provide a plethora of outsourcing services to other companies, that can range
from drug development through manufacturing of active ingredients, key intermediates, and final
products (CDMOs), or have a narrower focus on manufacturing (CMOs).
Organizations from categories i. and ii. (Big Pharma) tend to have several manufacturing sites in dif-
ferent locations, either through direct ownership or by leveraging the services of contract manufacturers,
that cater to the needs of other companies operating in the pharmaceutical industry by providing a wide
range drug development and manufacturing related services. Relinquishing said business practices to
C(D)MOs on a contract basis allows major pharmaceutical companies to focus on discovery and mar-
keting. Oftentimes, these entities coexist as cooperative agents within a given pharmaceutical supply
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chain, connected through a tightly integrated network that handles the material and information flow. A
typical integrated pharmaceutical SC - such as the one depicted in Figure 1.2 - is composed of nodes of
the following types:
• Big Pharma companies
• R&D oriented companies
• CMOs and CDMOs
• Raw materials suppliers
• Warehouses and distribution hubs
• Packagers
• Wholesalers and retailers
• Hospitals, clinics and pharmacies
Information Flow
R&D Companies
Raw Materials Suppliers
Big Pharma Companies
CMOs / CDMOs
Packagers
Retailers & Wholesalers
Distribution Hub
Clinics & Hospitals
Material Flow
Figure 1.2: Overview of the Integrated Pharmaceutical Supply Chain
Typical performance metrics of pharmaceutical SCs, such as those retrieved from [1] and listed
below, flaunt the need to exploit new vectors for improvement:
• Supply chain cycle times (elapsed time between raw materials entering the network and leaving
as a product) are often between 1000 and 8000 hours;
• The value-added time (time during which something happens to the material as a percentage of
the cycle time) is of the order of 0,3 to 5%;
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• Material efficiency (amount of product produced per unit of total material used) ranges from 1 to
10%;
While some of these values emerge as a consequence of the slow dynamics of drug manufacturing
and synthesis methods and are thus beyond the scope of this work, they are further aggravated by
planning and scheduling inefficiencies. The value-added time figure, for instance, can benefit from
increased efficiency in quality control laboratories; if a batch is cleared to proceed to the next production
step as part of an in-process control analysis or is allowed to be shipped from the factory following the
final product quality test at a greater rate, cycle times will decrease as a consequence.
1.1.2 Quality Control in the Pharmaceutical Industry
Given the nature of its core product, the pharmaceutical industry is subjected to heavily regulated
quality guidelines. A comprehensive framework must be in place to ensure the quality assurance
targets are met in a reliable manner, incorporating the mandatory requirements stated in the Good
Manufacturing Practices (GMPs) and other World Health Organization (WHO) associated norms, such
as Good Laboratory Practices (GLPs) ([6]), in addition to market-specific regulatory policies such as
those enforced by the Food and Drug Administration (FDA) (United States) or the European Medicines
Agency (EMA) (European countries).
Most of Quality Control (QC) related work is carried out by analytical chemists in Quality Control
Laboratories (QCLs), key entities that can have a major impact on the overall supply chain service level.
The situation is magnified in the case of CDMOs, that uphold the responsibility for the quality and
efficacy of the drugs they produce under their clients’ brands, ensuring compliance with the required
safety and quality standards across a wide range of of projects.
1.2 Contributions
The work presented in this thesis was developed in close partnership between the Mechanical Engi-
neering Instiute (IDMEC) at Instituto Superior Tecnico and Hovione Farmaciencia, S.A.. In this context, a
data-driven decision support tool was developed in the form of a discrete-event based simulation model,
implemented in Simio. This tool is intended to assist managers in the tasks of laboratory capacity and
resource planning, as well as scheduling of analytical work. Considering a new, state of the art facility
as a case study, crucial workflows were modelled and vectors for improvement pinpointed. A simulation
study was conducted to gather insight into the expected performance of the future laboratory, using the
model as a testing platform to benchmark alternative Governance Models, scheduling heuristics and
resource allocation policies intended to be deployed.
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1.3 Thesis Outline
In chapter 2 the topic of QCL Management is introduced. The importance of adequate planning and
scheduling tools is established, and relevant research work conducted in this field of study is presented,
leading to the proposed solution and expected benefits of the work developed in the context of this
thesis.
In chapter 3 a detailed overview of analytical techniques and sample proprieties are introduced. The
remainder of the chapter is devoted to the topics of workflow & process modelling, along with the data
sources and information systems used in this study.
Chapter 4 provides a brief introduction to systems modelling and simulation, with special emphasis
on Discrete Event Systems. Context is provided on the scope and goals of the simulation study, and the
framework, key parameters and performance metrics of the developed simulation model are introduced.
Model validation and simulation results are presented in Chapter 5. Results are intercalated with
discussion, as to ease the understating of the reader.
Lastly, concluding remarks and future work are presented in Chapter 6.
7
8
Chapter 2
Quality Control Laboratory Management
Large scale contract manufacturers rely on Enterprise Resource Planning (ERP) software solutions
to monitor and manage their resources. In the case of quality control laboratories, implementations of
Laboratory Information Management System (LIMS) packages are often the preferred solution. In addi-
tion to acting as repository that handles analytical work related information, LIMS suites aim to increase
sample throughput, reduce turnaround times and increase output quality by providing mechanisms to
automate and integrate data management tasks, as detailed in the comprehensive platform overview
found in [7].
The assortment of analytical work performed in QCLs is conditioned by the services provided by the
contract manufacturing organization under which they operate. In addition to manufacturing drug prod-
ucts for the various development and commercial stages, these services may extend to the development
and validation of new analytical methods, particle engineering, scale-up of chemical processes and drug
formulation studies. Quality control laboratories are thus a key unit of CDMOs, assisting a wide range of
operational services in the execution of their designated tasks.
Despite its notorious significance, there is a industry-wide tendency to regard QC as a support ser-
vice instead of the primary importance status it arguably deserves. This practice is evidenced as the
majority of management allocated resources are geared towards the optimization of the production pro-
cess, with laboratories being awarded comparatively lower importance. This approach is intrinsically
flawed, given that the timely completion of a production batch is always conditioned by the approval
issued by the QCL. A further manifestation of this trend is found in production capacity planning, such
as the work presented in [8], where the solution space is constrained by the available manufacturing ca-
pacity, but fails to consider whether quality control laboratories are capable of coping with the increase
in demand of analytical work that accepting new projects might entail.
One of the main deterring factors to the seamless integration of drug manufacturing and the ensuing
QC related tasks is the stark contrast between the complexity of the analytical procedures and the
comparatively basic tools currently used to conduct resource planning and scheduling in QCLs. These
tools are predominantly based on the experience of senior laboratory managers and include periodic
scheduling meetings, whiteboard planning and the use of MS Excel worksheets - solutions unfit to handle
such a complex task. Scheduling of QC analysis remains thus a manual, time consuming task, with
ample room for improvement, particularly in CDMOs dealing with increasing diversification of projects.
9
Having established its importance, this chapter addresses the topic of laboratory resource planning
and scheduling, presents a collection of relevant research work conducted in this field of study and
details the proposed solution and expected benefits of the developed work.
2.1 Laboratory Resource Planning and Scheduling
Planning and scheduling are complimentary disciplines, applied to distinct time frames but with the
common purpose of ensuring a faithful imprinting of the long term strategic planning to the daily schedule
of operations, coping with uncertainty and safeguarding that demand for products and services is met.
Planing focuses on long-term decision making, based on expected demand levels, assessing whether
the installed capacity is capable of meeting forecasts and, if necessary, procure the necessary resources
ahead of time. In the short-term, as the planning horizon draws closer to the present date (Figure 2.1),
more detailed information is gradually made available, with aggregated demand forecasts giving way to
actual orders. Scheduling algorithms are employed to allocate specific jobs to machines and personnel,
as well as sequencing their execution list, according a set of predetermined objectives.
Time
Hours Weeks Months
Available Information
Uncertainty
Continuous moving time frame
Days
Figure 2.1: Representation of available information and uncertainty in planning and scheduling with respect to time
(adapted from [9])
The need to improve production plans and schedules in order achieve higher resource utilization
levels and improve response times while reducing manufacturing costs and downtime has long been
identified as a crucial success factor in the pharmaceutical industry. As with other industries whose
manufacturing campaigns rely on the timely execution of strict quality control analysis to monitor product
quality throughout the production process, a holistic approach to increase the overall operational effi-
ciency of a CDMO must award equal importance to the optimization of both production and QC related
tasks. QCLs are also responsible for conducting routine analytical work on raw materials, intermedi-
ates and final products, developing and subsequently validating new analytical methods and conducting
product stability studies. In order to plan and schedule efficiently amidst this level of complexity, a robust
10
computerized solution is required to minimize the time spent by supervisors and provide flexibility to
react to the schedule changes and optimize the overall lab performance [10].
2.2 Related Work
Planning and scheduling of manufacturing systems commanded the attention of Operations Re-
search practitioners throughout the 20th century, as the need to optimize production resources was felt
as factories grew and processes became increasingly complex.
The 1940s saw the introduction of Linear Programming (LP) methods to production planning prob-
lems, that have been continuously refined and remain one of the de facto optimization tools used in
the industry. Throughout the 1950s several heuristics for single-machine scheduling were developed,
many of which are still used today; notable examples include Shortest Processing Time First, focused
on minimizing average flowtime and Earliest Due Date First, optimal if the goal is to minimize maximum
tardiness. The extension to Job Shop Scheduling optimization resulted in a set of NP-hard problems,
whose formulation is unfit to be solved by conventional mathematical programming methods, consid-
ering the computational time needed to compute a solution. During the 1980s and 1990s, the trend
shifted towards the development of nature-inspired evolutionary metaheuristics, such as Genetic Algo-
rithms and Ant Colony Optimization, capable of producing sub-optimal solutions to NP-hard problems in
a comparatively shorter amount of time.
Shorbrys and White [11] compiled a review of standard planning and scheduling methodologies em-
ployed in the process industry and concluded that LP its extensions (Mixed Integer Programming, LP
combined with expert-knowledge) are still the preferred solution, commonly implemented in spread-
sheets that lack integration with information services and need to be manually updated. According to
the authors, automated scheduling tools capable of integrating changes in process status and inventory
levels and thus conduct dynamic rescheduling are deemed as the best practice, but are still a far cry
from today’s implementations.
The first applications of system modelling and simulation to quality control laboratories date back to
the early 1980s. In 1984 Janse and Kateman [12] developed a model of a small water quality moni-
toring laboratory and recognized the use of queueing theory based simulation to emulate QCLs as a
viable approach to investigate organizational features which could increase operational efficiency and
be extended to other analytical domains. Later in the same decade, Klaessens et al. [13] presented a
decision support system that combined historical data and a rule-based framework compiled from ex-
pert knowledge to derive, test and compare laboratory organization structures. Additionally, the authors
identified the five key QCL simulation model components (listed below) and studied the impact of two
key model parameters on the system’s performance: maximum allowed queue size per equipment and
centralized vs. decentralized scheduling of analytical work.
11
• Analytical sample
• Analytical sample generator
• Planner (controls the sample assignment and flow within the laboratory)
• Analyst
• Analytical Equipment
The number of scientific publications covering planning and scheduling of QC laboratories has be-
come increasingly sparse over the years, especially so in the pharmaceutical realm. This trend is un-
derstandable under the light that better QCL management constitutes a competitive advantage and
companies are naturally opposed to publishing internal results on such a sensitive topic. As of recent
years, in lieu of applied research the trend has shifted towards the development of laboratory information
management frameworks.
In [14] Maslaton proposes a generic methodology to oversee data collection and information gather-
ing in the laboratory, most notably time studies to estimate task processing times. The author highlights
the potential issues of conducting a ill-prepared time study might entail that, given the high number of
concurrent activities being performed by the analysts, might not lead to accurate results. To address this
matter, the author devised a series of five steps, presented below, that when followed should shorten
the time needed to collect information and produce results that are more reliable.
i. Develop list of products and raw materials and group them into product families
ii. Identify representative product for each family
iii. Characterize each representative product (i.e. types and number of tests, tests frequency)
iv. Define naming convention for every test
v. Estimate analysis processing time for each test.
In [15] Schafer presents a series of concepts that can be used as a unifying set of definitions to
support a consistent framework for laboratory management. The author addresses all the relevant
components with which the analyst interacts when performing analytical work (i.e samples, instruments,
sensors, results, information systems) and provides a description of a schematic scheduling workflow
that can be applied in quality control laboratories:
12
i. Process description
ii. Information treatment
iii. Generation of working plan elements and relative constraints
iv. Schedule generation
v. Scheduling execution
vi. Instrumental control and data storage
The most comprehensive study in this field was conducted by Costigliola [16]. The author developed
a simulation model of a QCL operating under a pharmaceutical CDMO that represents in detail the
entire analytical work flow. Additionally, a generic framework for information treatment and organization
was proposed, merging data scattered across several databases into a unified repository that allows for
easier access to relevant information and that can be used as the foundation for future planning and
scheduling solutions. This work again reinstated discrete event simulation as a viable means to emulate
the operation of QC laboratories and, through Petri net formalism, provided a graphical representation
of the analytical workflow that can be used as a guideline to implement the model in any simulation
software. Having used Simio, the author created an expandable object library that was adapted and
extended to meet the specifications of the QCL considered in this work.
2.3 Proposed Solution and Expected Benefits
Being tied to other operation areas, the demand for analytical work fluctuates both qualitatively and
quantitatively over time. Due to the multitude of concurrent commercial and R&D projects in CDMOs,
QCL resource planning and scheduling should rely on an advanced, data-driven decision support tool.
This tool should be capable of providing reliable estimates of the required number of analysts and an-
alytical equipment, the two main laboratory resources, and act as a testing platform to benchmark the
performance of alternative scheduling algorithms and heuristics, providing insight into which variant
should be employed in practice.
The laboratory considered in this case study is still in the design phase. It is envisioned as a state
of the art facility and will result of the merger of four presently active laboratories, each providing its
own specialized set of services. Typically, planning and scheduling tasks are approached in hierarchical
fashion, with long-term planning taking precedence over short-term scheduling. However, given that
the system is still under design, the planning and scheduling problems can benefit from being solved
simultaneously in one model [17]. This methodology allows for scheduling constraints dependent on the
planning guidelines (such as the number of analytical equipment and staff members) to be accounted for
in the design stage, easing the task of identifying bottlenecks and addressing them at their root cause.
13
The proposed solution consists of a robust computerized tool, in the form of a discrete-event simu-
lation model of the new QCL being designed. The model acts as a decision support system, assisting
laboratory managers in the tasks of resource planning and scheduling of analytical work, aiming to in-
crease the efficiency of the new facility by seizing the opportunity to capitalize on the synergies that
merging four laboratories entails.
Through the integration of the strategic (planning) and operational (scheduling) tasks into a coupled
problem, the simulation model was used to compare and propose laboratory Governance Models (GMs)
- the set of administrative guidelines according to which the laboratory operates, covering topics such
as analyst staff work schedules, analytical samples’ priority levels and allocation of certain equipments
to specific tasks - based on multi-criteria objectives, such as minimizing the sample time in system while
ensuring that the analysts’ scheduled utilization level remains within specific intervals.
The simulation model was also employed to conduct a future capacity experiment. This is a key topic
in laboratory operations management, given that the process of procuring additional resources to meet
the forecasted demand in the form of increasing volume of analytical samples is cumbersome. Indeed,
to process larger numbers of samples, new analysts have to be hired and undergo trained if needed, new
analytical equipment has to be ordered, shipped, installed and verified. These are very time-consuming
procedures that ought to be foreseen and conducted ahead of time.
14
Chapter 3
Modelling Workflows and Data Processing
Ensuring that the simulation tool under development is capable of accurately emulating the real
system being modelled is of fundamental importance. In order to fulfil this requirement, the design
process must be preceded by an information gathering stage, during which a well-founded conceptual
vision of the system is acquired.
At its core, a QCL can be reduced to the simplistic representation of a black box model (Figure
3.1), that receives inputs in the form of samples to be analysed, conducts the required analytical work
following the protocol of a given analytical method and outputs information, compiled in the form of
detailed reports which are stored in databases for future reference.
Quality Control Laboratoryinput: samples output: report
Figure 3.1: Black box representation of a Quality Control laboratory
As to expand the understanding of this system, its conceptual vision should include a detailed de-
scription of the analytical workflows, as well as the context in which they occur. Doing so will allow for
schedulable tasks to be identified, in addition to uncovering vectors for improvement whose potential is
not presently explored.
A detailed overview of the most relevant analytical techniques practised in the QCL under consid-
eration is presented in this chapter. Common sample proprieties are introduced, and the considered
sample types are listed in detailed fashion. The remainder of the chapter is devoted to the topics of
workflow & process modelling, establishing its importance as a means to model the status quo while
developing a deeper understating of the system and allowing for improvement vectors to be identified in
the the pursue of operational excellence. Lastly, the data sources and information systems used in this
study are presented, along with the required pre-processing routines and methods employed over the
course of this work.
3.1 Analytical Work Overview
Analytical Chemistry (AC) is the science of obtaining, processing, and communicating information
about the composition and structure of matter. It has a broad range of applications, being used exten-
15
sively in healthcare and pharmaceutical sciences within the context of quality control, to ensure that the
purity and potency of drug products is within expected ranges. Analysis serve one of two purposes:
either qualitative (to identify the composing elements of a mixture) or quantitative (to quantify of mass or
concentration of a particular compound in a mixture).
The diversity of analytical techniques employed in the pharmaceutical industry escalates the overall
complexity of QC analysis. For the purpose of this project, the six most frequently performed analytical
techniques were considered. They account for the critical mass of analytical work to be carried out in
the QCL considered in this study, and are listed below:
• Differential Scanning Calorimetry (DSC)
• Gas Cromatography (GC)
• Karl Fischer Titration (KF)
• High Performance Liquid Cromatography
(HPLC)
• Particle Size Analysis (PSA)
• X-Ray Powder Diffraction (XRPD)
Aside from requiring its own specific equipment, each analytical technique, when applied to a given
sample, must follow the procedure stated in the prescribed analytical method. The analytical method
is a document stating the experimental protocol according to which the sample should be analysed,
containing all the relevant info concerning the analytical procedure, such as:
• Safety and handling precautions
• Required equipment, reagents and solvents
• Equipment operating conditions
• Procedure steps
• List of subtests to be performed
• Values to measure and/or compute
The analytical method protocol is thus a valuable document, enclosing valuable information both in
explicit and implicit form. In [16], the author developed a textual information extraction algorithm with
the intent of retrieving the processing times of a comprehensive set of analytical methods, capable of
collecting explicit values when stated and, otherwise, estimating said values based on the combination
of the sequence, number and retention times of the required injections.
Pharmaceutical QC samples compete for the same resources (analysts and equipment) and, de-
pending on the type, have different validity periods and priority degrees. Given the characteristic slow
response times of QCLs, delays in the analytical process increase the storage period and might lead
to the degradation of the sample’s proprieties, impose setbacks on manufacturing batches and post-
pone the release of final products. The number of concurrent projects that large CDMOs typically work
with, both of development and commercial phases, each issuing samples of different types, with their
respective due date and priority levels, further contributes to increase the complexity of QC analysis.
16
The sample types considered in this work are listed below, followed by concise description of the
categories that merit individual discussion.
• Analytical Method Validation
• Raw Material (RM) tests
• Intermediate (IN) Product tests
• Final Product (FP) tests
• In-process Control (IPC) tests
• Change of Line (COL) tests
• Product Stability tests
• Fast Analysis (FA) and Miscellaneous tests
Method Validation: Validation revolves around the approval of newly developed analytical meth-
ods, to be applied as the testing protocol for preclinical, clinical and commercial samples. A method
should be developed with the goal of rapidly testing samples, delivering consistently accurate and ro-
bust results. The purpose of validation is thus to ensure that the method under consideration fulfils
the acceptance criteria for parameters such as specificity, precision, detection and quantitation limits,
while being reproducible under normal but variable laboratory conditions in compliance with regulatory
standards [18].
Raw Materials, Intermediates & Final Products: These three sample types are similar due to
the stable nature of the product at the stages they concern. Raw materials must be tested after being
delivered by the supplier, before being admitted into the manufacturing process. Pharmaceutical inter-
mediates are stable products that must undergo further molecular change or manufacturing steps before
being synthesised into an Active Pharmaceutical Ingredient (API), whose quality must be controlled be-
fore proceeding to subsequent process steps. Final product analysis are the last quality control stage
before manufactured drugs are shipped to clients and, consequently, consumers.
In-process Control: The production of pharmaceutical products is subjected to meticulously con-
trolled conditions. In addition to the continuous monitoring of critical propriety values, made possible by
the highly precise measuring instruments fitted to the production equipment, the Good Manufacturing
Practices, to which all drug manufacturers must abide by, stipulate the need to conduct IPC tests [19].
These tests are of fundamental importance, assuring that pre-determined quality specifications for a
given production batch are met along the whole production process. The ensuing analysis are per-
formed at QCLs, and their significance is underlined by the fact that they effectively hold the power
to halt the progression of their associated production batch until they have been processed and their
results approved. Therefore, IPC tests rank as the highest priority analytical procedures performed at
quality control laboratories, and a structured workflow should be in place to ensure they are handled in
a consistent and timely manner.
17
Change of Line: A sample of this type is created whenever it is necessary to evaluate the sterility
levels of manufacturing equipment between batches of different APIs, to check for residues and ensure
that level of substance carryover between batches is within the specified limits.
Product Stability: Stability tests are devised to monitor how the proprieties of APIs and finished
pharmaceutical products vary with time under the influence of certain environmental factors, such as
exposure to UV light and ill-advised temperature and humidity levels [20]. The scope of stability testing
extends to all degradation inducing phenomena, including interaction with excipients, storage and pack-
aging conditions, with the aim of gathering information on how these factors influence the quality of the
product, defining storage guidelines and devising the testing frequency program for products with long
shelf lives.
Fast Analysis & Miscellaneous Tests: Samples of this nature arise as the laboratory operates.
Fast analysis is a wide-encompassing sample type label, typically assigned to R&D-related tests. The
miscellaneous label is assigned to samples whose type does not match any of the previously listed
categories.
3.2 Process Modelling
As addressed in [15], the development of a useful planning and scheduling platform ought to be
based on a set of consensual ground rules, agreed upon by the project stakeholders, developers and
end users alike, that realistically captures all assumptions and requirements of the modelled processes.
Workflow and process modelling aims to capture and translate the conjunction of ongoing activities
at a given organization, facilitating the understanding of key operational dependencies and levels of
interaction across and within departments. This operational excellence driven practice can act as the
foundation to model and visualize current processes (as-is scope), allowing for vectors of improvement
to be identified in the pursuit of improved, target processes (to-be scope). Process mapping tools are
increasingly regarded as one of the most important components of Knowledge Management ([21]), a
multidisciplinary field concerned with the procurement, consolidation and dissemination of corporate
knowledge, by documenting, analysing and extracting further insight from information on products, tech-
nologies, organizational procedures and individual know-how of employees.
With the aim of mitigating the subjective and imprecise nature of written prose, it is preferable to adopt
the framework set by a standard graphical language, such as Business Process Modelling Notation
(BPMN). BPMN is a flowcharting technique, similar to the Unified Modelling Language activity diagrams,
that further expands its reach by targeting both technical and business users, making use of a technical
yet intuitive notation, capable of representing complex process semantics. This propriety has allowed
for BPMN to be adopted across several industries, including the health and pharmaceutical sectors
18
([22], [23]), becoming one of the business modelling tools of choice when it comes to bridging the
communication gap between process design, implementation and monitoring. The role of BPMN can
extend beyond the traditional applications of process mapping, being used as it was in the context of this
work, to gather specifications of the required information systems and infrastructures that need to be in
place to align the efforts of managers, users and technical support staff.
In addition to the core notation elements depicted in Figure 3.2, a comprehensive overview of BPMN
can be found in [24].
Activities & Swimlanes
Artifacts
InputData
Output Data
Collection Data
Events
Start Event Intermediate Event End Event
Start Start Message Timer Error End End Message
Gateways
Parallel Fork Gateway Parallel Join Gateway XOR Merge Gateway
Connecting Objects
Sequence Flow Conditional Flow Message Flow
Task
Collapsed Subprocess
Poo
l Lan
e 2
Lan
e 1
Figure 3.2: BPMN Core Notation Elements
Each sample type has its own associated workflow. Over the three subsequent subsections, the
cases of IPC (3.2.1), product stability (3.2.2) and analytical validation (3.2.3) are presented in detailed
fashion. These examples were chosen to showcase the contrasting dynamics of QC related tasks per-
formed in QCLs, as well as the intricate network of information and material flow between the operational
and support services found in pharmaceutical CDMOs.
19
3.2.1 In-Process Control
As per the guidelines established by the World Health Organization [6], IPC consists of a series of
checks performed during production, in order to monitor and, if necessary, to adjust the process to en-
sure that the product conforms to its specifications. In compliance to these guidelines, samples intended
for testing are collected from an ongoing production batch at predefined times and stages, identified as
crucial points of the manufacturing procedure at which the product properties should conform to accept-
able tolerance ranges. Following their retrieval and proper packaging, the samples are transported to the
QCL, where they are to be processed. Once the sample arrives at the laboratory, the analyst registers
this event by recording the sample Date Received timestamp under the appropriate database field and
proceeds to prepare the sample and the equipment for the required analytical tests. Once the analysis
has been conducted the result is verified by the analytical chemist and the result is passed on onto the
production overseer.
The IPC workflow modelled in BPMN notation is presented in figure 3.3.
Production Management
Qu
alit
y C
on
tro
lLa
bo
rato
ry
Sample Arrives
Receive SampleRegister Sample
Arrival DataConduct Analysis
Await Conclusion
Validate Results & Notify Production
Overseer
Analysis Veredict
Analysis Parameters
Update LIMS
Sample Retreival Notification
Planned order transitions to ongoing process
Update LIMS
Analytical Method
Figure 3.3: BPMN representation of In-Process Control Workflow
In the case of IPC related tests, samples and the analytical methods according to which they ought to
be analysed are allocated into the existing LIMS when a planned order is assigned the ongoing process
status. At this stage, a communication bridge is established between the production and QCL personnel,
to keep track of the production batch and corresponding IPC samples status.
Presently, such communication bridge is kept over telephone or e-mail. As a vector for improvement,
the events of an order entering the ongoing process status and the collection of samples at the man-
ufacturing line should trigger notifications, delivered to the QC laboratory through an organization-wide
information system, allowing the required preparations to be conducted before the sample arrives and
keep the analytical staff informed of potential delays on the production side.
20
3.2.2 Product Stability
Product stability tests are commissioned by the QC office, that issues the request for a given study
to be carried out following the procedure stated in a given protocol. Upon receiving the product to
be analysed and its test protocol, a sample is retrieved and placed under the specified environmental
conditions for the prescribed exposure time. Once the exposure period has ended, the sample becomes
available to be tested within a certain time frame. Following the analysis, the stability study report is
filled in with the results and sent to the QC office for approval and archiving purposes.
The product stability analysis workflow modelled in BPMN notation is presented in figure 3.4.
Quality Control Office
Qu
alit
y C
on
tro
lLa
bo
rato
ry
Collect Sample Conduct Analysis Share Results with Quality Control
Office
Stability Study
Results
Analysis ParametersUpdate LIMS
Stability Study Request, w/ Template
Receive Stability Study Request, w/ Template
Place Product under Specified
Contidtions
Wait Prescribed Timespan
Analytical Method
Fill in Stability Report
Update LIMS Stability Report
Sample Arrives
Figure 3.4: BPMN representation of Product Stability Analysis Workflow
LIMS’s parameter Target Date registers the end date of the sample’s exposure period, designating
the date from which it becomes ready to be processed. The fact the time frame during which the sample
ought to be processed is relatively large when compared to other samples types, coupled with the low
priority assigned to stability tests often leads to these samples being pushed back in favour of higher
priority work. Since the Target Date is known in advance, a structured scheduling algorithm should take
advantage of downtime opportunities to expedite stability tests, reducing the current average processing
time of this sample type.
21
3.2.3 Method Validation
A single validation can last up to several weeks, and it is common practice to reserve a designated
set of analysts and equipment to tender to a given validation task during its duration. The whole pro-
cess is dependant on several factors, such as experience level of the individual analytical chemists and
the collective experience level of the development and validation department. Method validation work-
sessions are subject to several delay-inducing aspects, including and parameters that prove hard to
validate, issues that may require additional tinkering or even the method to be revised.
The method validation workflow modelled in BPMN notation is presented in figure 3.5.
Qu
alit
y C
on
tro
La
bo
rato
ry
Quality Control Analytical Chesmistry Services
Valid
ation
Offic
e
Equipment Setup
Validate Parameters
Conduct Inspection
Request Final Data Processing &
Written Report
Write ReportReview Report & Compile List of
Incidents
Send Report to client
Notify Analytical Chemistry
Department
Require Protocol Review
Plan Validation Work
Evaluate Protocol
Request Inspection
Receive method to validate
Protocol has errors
Work schedule
Input: Protocol
Notify QC ACS
Output: Validation Report
Major fault detected
Output: inspection results
Report approved
Trasnfer to client?
Yes
No
Link: course of action
Link: course of action
How to Proceed ?
Link: Lab. work
Link: Lab. work
Equipment Parameters
Validation Data
System Suitability Revalidation fails
Full set of Parameters Validated ?
Parameter validation fails
Figure 3.5: BPMN representation of Validation Workflow
22
3.3 Information Sources & Data Processing
The transition to the new QCL will take place over an extended period of time, across several stages.
Nevertheless, project stakeholders expressed the desire to consider the scenario in which the new
facility would receive a volume of samples similar to the total registered across the four laboratories
over the last year, with analogous incidence of sample types, analytical techniques and methods. Under
this request, it is expected that new facility should be able to cope with a workload level akin to that
of the last 12 months, allowing for the remainder capacity to be evaluated. To this end, a data-driven
sample generation framework was developed. Information concerning the number of samples and the
joint distribution of analytical methods and techniques was extracted from LIMS, by merging data from
the four presently active laboratories. LIMS contains valuable information on each sample processed
during the considered time period, stored under the following fields:
• Sample Number: Unique tracking number, awarded to each individual sample
• Analysis: Encoded information on the analytical method and subtest(s) performed on the sample
• Text ID: Encoded information on the sample type and project
• Equipment: The code of the equipment used to perform the analysis
• Received/Completed/Reviewed Date: Timestamps, recorded when the entry the sample was
registered at the QCL / analysis was completed / result was reviewed
• Analyst: The analyst that performed the test
40.68%
32.28%
21.22%
4.35%0.93% 0.32% 0.07% 0.05% 0.04% 0.03% 0.01% 0.01% 0.01%
0%
25%
50%
75%
100%
KF HPLC GC CM CM;KF DSC RX GC;HPLC DSC;RX HPLC;KF GC;KF CM;DSC;RX CM;GC
Analytical Technique Combinations
Rel
ativ
e F
requ
ency
Figure 3.6: Relative Frequency of Occurring Combinations of Analytical Tests on IPC Samples
23
The devised sample generation architecture is modular, in the sense that it is comprised of one mod-
ule per sample type, each type being independently controllable for simulation purposes. The relative
frequency of each occurring combination of analytical tests performed on unique samples was com-
puted as the first step in the development of said framework. Detailed results for IPC and FP samples
are presented as Pareto charts in Figures 3.6 and 3.7, followed by a quantitative summary in Table 3.1.
47.89%
27.57%
9.65%
4% 2.58% 1.96% 1.87% 1.51% 0.89% 0.71% 0.49% 0.49% 0.18% 0.09% 0.09% 0.04%0%
25%
50%
75%
100%
GC;HPLC HPLC CM;KF KF CM;DSC;KF;RX CM CM;KF;RXGC;HPLC;KF GC DSC;KF;RX CM;RX KF;RX CM;DSC;RX HPLC;KF RX CM;HPLC;KF
Analytical Technique Combinations
Rel
ativ
e F
requ
ency
Figure 3.7: Relative Frequency of Occurring Combinations of Analytical Tests on FP Samples
The relative frequency effectively traduces the empirical probability of a given unique sample of type
t being subjected to a specific mix of analytical tests, a, from amongst the set of occurring possible
combinations for that sample type, {At}. This probability can be expressed as:
P (At = a | T = t) (3.1)
Number of Distinct Analytical Tests
Sample Type 1 2 3 4 5 6
Change of Line 99, 76% 0, 24% n.a. n.a. n.a. n.a.
Fast Analysis 92, 44% 6, 02% 0, 97% 0, 41% 0, 11% 0, 04%
Final Product 34, 50% 58, 60% 4, 31% 2, 58% n.a. n.a.
Intermediate 96, 48% 3, 52% n.a. n.a. n.a. n.a.
In-process Control 98, 92% 1, 07% 0, 01% n.a. n.a. n.a.
Miscellaneous 76, 72% 11, 27% 5, 83% 0, 97% 5, 02% 0, 19%
Raw Materials 83, 46% 16, 46% 0, 08% n.a. n.a. n.a.
Stability 22, 81% 44, 64% 19, 75% 10, 39% 2, 18% 0, 23%
Table 3.1: Quantitative Analysis of the Number of Analytical Tests Performed on Unique Samples, per Sample Type
24
With the exception of final product and stability samples, most types are subjected to a single ana-
lytical test.
Having created sets of analytical tests to be performed on samples based on the underlying empir-
ical distribution of each type, the second step of the sample generation engine covers the assignment
of methods to each technique. A similar approach to that of the first step was followed: the relative
frequency of each recorded method (m ∈ M ) per sample type (t) ↔ analytical test (a) pairings was
computed, resulting in several lookup tables for the probabilities:
P (M = m | {t, a}) (3.2)
Further details on the sample generation framework, such as the modelling of arrival processes and
its implementation in Simio, is presented in section 4.3.1.
25
26
Chapter 4
Quality Control Laboratory Simulation Model
To cope with time-varying demand for the services provided by QCs, facility managers are faced with
the challenges of assembling a team composed of the appropriate number of analysts - working under
adequate schedules - and ensuring that the available equipment pool is sufficient to process pending
orders in a timely manner. These are classical examples of Operations Research problems, a field of
study that addresses topics such as forecasting demand, estimating capacity, deploying resources and
optimal management of service levels.
Simulation is one of the most widely used Operations Research techniques, if not the most. This
claim is backed up by several surveys conducted in the recent past ([25], [26]), where simulation consis-
tently ranks amongst the top methodologies, being surpassed only by ”math programming”, a catch-all
term that includes many individual tools, such as linear programming [27]. Simulations are frequently
used to assist in the design and operation monitoring of complex systems, enabling the modelling en-
gineer to assess both the performance of new systems and the effect of changes to existing systems.
This is made possible through the development of simulation models, that allow for the behaviour of
the system to be explored under various configurations and circumstances, whilst avoiding the practical
considerations of performing experiments on real systems, such as feasibility, cost and down-time [28].
The review of related work conducted in the context of this study (section 2.2) divulged Discrete
Event Systems (DES) as the state of the art paradigm for modelling and simulation of QC laboratories.
This methodology was thus adopted, due to it being suitable to emulate the underlying dynamics and
processing logic of the laboratory considered in this work.
This chapter provides a summary overview of systems modelling and simulation, with special em-
phasis on DES. Subsequently, context is provided on the scope and goals of the simulation study, and
the framework, key parameters and performance metrics of the developed model are introduced.
4.1 Discrete Event Systems
A system can be broadly defined a as combination of components that act together towards the
accomplishment of a purposeful goal, with its state at a particular time being defined by a collection
of variables that describe the system under the objectives of a particular study. Systems can be of
two types, depending on the regime according to which the variables change state: either discrete, if
changes occur instantaneously at isolated points in time, or continuous, when variables change contin-
27
uously with respect to time.
Due to the disruptive nature of alternative configurations and prohibitive constraints imposed by cost
and downtime, it is rarely feasible to perform experiments on the actual system. To this end, models are
developed to emulate the system’s behaviour through mathematical and logical relationships, that can
be adjusted to estimate how the system would react under particular scenarios. If a model has a closed-
form analytical solution that can be computed in a computationally efficient manner, this is usually the
preferred approach to solve the problem. However, some analytical solutions can be extremely complex
or even unattainable, in which case simulation emerges as the methodology of choice to run the model,
assessing how a set of varying inputs affect the devised output measures.
Similarly to the contrast between discrete and continuous systems, simulation models are also sub-
ject to the same distinction. Continuous simulation is applied to systems whose state variables change
continuously with respect to time; differential equations are employed to translate dynamic relationships
between variables and their rates of change over time. Conversely, the variables in discrete models
change due to events - instantaneous occurrences that might prompt a change in the overall state of
the system. Lastly, simulation models can be distinguished by the random nature of their components.
If there are no probabilistic factors, the model is said to be deterministic; most systems, however, fea-
ture random parameters such as entity arrival rates and processing times, and are thus referred to
as stochastic. The output of stochastic models is itself random, and must therefore be treated as an
estimate of the true characteristics of the model [27].
Given the dynamic nature of discrete event simulation models, simulation clocks are used to keep
track of the present value of simulated time and advance the simulation along the sequence of events,
be it deterministic or stochastic. The typical notation used in DES is presented below, and illustrated in
Figure 4.1 for the case of single-server queueing system.
ei: time of occurrence of the ith event
ti: time of arrival of the ith entity (t0 = 0)
Di: delay in queue of the ith entity
Ai = ti−ti−1: arrival time between entities {i−1, i}
Si: service time of the ith entity, excluding delay
in queue
ci = ti+Di+Si: time of departure of the ith entity
𝑇𝑖𝑚𝑒
𝑆1 𝑆2
𝐴1 𝐴2 𝐴3
0 𝑡1 𝑡2 𝑐1 𝑡3 𝑐2
𝑒0 𝑒1 𝑒2 𝑒3 𝑒4 𝑒5
Figure 4.1: DES Time Advancement in Single Server Queueing Systems
(source: [27])
28
General events (ei) are marked on the time axis and might spark a change of state of the system.
In the case of stochastic systems, the occurrence of events and the length of service times are random
variables, bound to underlying probability distributions whose parameters need to be estimated.
4.2 Simulation Study Scope
Complexity in pharmaceutical QCLs operating under CDMOs stems from two major factors: (1)
variety of analytical tests, compounded by the wide range of specific methods, and (2) the diversity
amongst concurrent projects. Moreover, constrains imposed by management policies, such as contrived
organizational guidelines, further contribute to hamper the responsiveness of the QC department.
Quality Control services at the CDMO considered in this study are arranged in branches, following
an organizational structure that mimics the segmentation between three key operational areas. In the
interest of preserving the identity of each branch, they are referred to as branches A, B, and C in the
context of this work. Additionally, due to its relatively slow dynamics and priority level, project stake-
holders are considering the possibility of treating stability work as a separate service, which led to this
distinction being considered in the simulation study.
Undeterred by the fact that the pool of resources (namely, the analyst staff and the equipment at their
disposal) could theoretically be shared between branches, they operate contiguously under proprietary
resource allocation policies. This structured self-governing regime fails to capitalize on possible fruitful
benefits that a free-for-all approach, built upon an improved organization-wide integration of services,
could entail.
Seizing the opportunity presented during the design and planning stage of the new facility, project
stakeholders expressed the desire to exploit shortcomings that currently hinder the QC services at labo-
ratory level by comparing the performance of two governance models - structured vs. free-for-all. Based
on these two governance models and a through scenario-based approach, the impact of (1) breakdown
by branches, (2) varying analyst schedule configurations (2) and (3) high-level sample allocation and
scheduling policies can be measured and compared.
The spatial arrangement of laboratory benches, equipment groups and data processing workstations
was based on the rolling blueprint of new QCL. Since every object was rendered to scale, the 3D model
of the laboratory in itself was used as a tool for validating the required bench space and conduct visual
inspection of the basic laboratory layout.
29
4.3 Model Parameters
The discrete event simulation paradigm implemented in software packages such as Simio revolves
around the definition of entities, that flow through the system along steps of an underlying logic frame-
work, that aims to robustly replicate the actual system. Typically, entities are treated as objects that seize
the capacity of resources for given periods of time, as they undergo some process.
Under this object-oriented architecture, and in the context of QC laboratories, samples are modelled
as entities, with equipment and analysts being treated as resources. The three subsequent sections
introduce further details on fundamental parameters of the model: section 4.3.1 addresses the arrival
of entities, concluding the detailed explanation of the sample generation framework introduced in sec-
tion 3.3; sections 4.3.2 and 4.3.3 cover the two main laboratory resources, analyst staff and analytical
equipment, respectively.
4.3.1 Demand Forecasting and Sample Arrival Rate
In the context of quality control laboratories operating in pharmaceutical CDMOs, the demand for an-
alytical work can be quantified as the time-varying volume of incoming samples in need to be processed.
This demand is subject to seasonality effects and, depending on the sample type, it might also fluctuate
with the time of day and day of the week.
The LIMS’ field Date Received consists of a timestamp, manually inserted by the analysts as they
register the arrival of samples at the laboratory by logging this event in the database. As not to disrupt
their workflow, analysts tend to postpone the registration on newly received samples until after they
have completed the task they are working on. This results in imprecise time-keeping records, with
multiple samples being registered at once and given the same arrival time, when in fact they arrived
over the course of an undetermined period of time. Aware of this limitation, the data enclosed in the
Date Received propriety was used as the foundation to derive a model that accurately emulates the
arrival of samples at the laboratory, considering important factors such as the effect of seasonality, the
actual inter-arrival times between consecutive samples and whether the samples arrive one at the time
or grouped in a batch.
Historical data from the previous year, retrieved from LIMS, was used to estimate the amount and
arrival rate of incoming samples. Detailed analysis of the arrival patterns revealed comprehensive dif-
ferences between sample types across three fundamental proprieties:
i. Period of the day during which samples of a certain type arrive at the laboratory
ii. Days of the week during which samples of a certain type arrive at the laboratory
iii. Arrival of samples either one at the time or as part of a batch
30
Depending on the nature of the sample type, some arrive at the QCL in continuous fashion (e.g.,
in-process control and change of line samples, due to ties with ongoing drug manufacturing), whereas
others are only admitted during certain periods of the day (such as raw materials, typically between
08:00h-17:00h). For similar reasons, based on the sample type’s priority and urgency levels, some types
are delivered at the laboratory seven days a week while others conform to only five. Lastly, samples can
arrive either one by one or grouped in a batch of several entities.
Clustering analysis was conducted to assess the impact of seasonality on the arrival rate of samples.
The K-means algorithm was employed to group months of the year into sets of similar workload level,
quantified by the number of samples received over the course of each period of days. This analysis
was performed for each sample type, considering up three workload classes - low, moderate and high.
Detailed results for IPC samples are presented in Figure 4.2; the number of samples was normalized by
the monthly average value, and axis labels wilfully removed as to mask the data. The remaining plots
can be found in Appendix A.
Month-1 Month-2 Month-3 Month-4 Month-5 Month-6 Month-7 Month-8 Month-9 Month-10 Month-11 Month-12Month
No
rmal
ized
Nu
mb
er o
f R
ecei
ved
Sam
ple
s
Monthly Workload Below average Average Above average
Figure 4.2: Monthly Workload Levels - IPC Samples
The effect of seasonality on the volume of samples received per month was found be prevalent
in the remaining sample types (Figure 4.3), implying that reducing the arrival rate of each type to a
yearly summary measure would be overly simplistic, neglecting important system dynamics. However,
increasing the granularity to an hourly level is ill-advised, given the previously mentioned imprecise time-
keeping limitation, that restrains the use of regression and time series based models to represent the
variation of demand over time. A statistical inference based approach was deemed better suited for the
31
available data and was thus employed.
CL
FA
FP
IN
IP
MS
RM
TE
Month-1 Month-2 Month-3 Month-4 Month-5 Month-6 Month-7 Month-8 Month-9 Month-10 Month-11Month-12Month
Sam
ple
Typ
e
Monthly Workload Low Moderate High
Figure 4.3: Monthly Workload Levels, per Sample Type
The results presented in Figure 4.3 conform with expected patterns: Months 1 and 2 are a ramp-up
period for the workload peak observable towards the end of the fiscal year (Month 4-Month 5), whereas
there is noticeable decrease in Month 8, due to holidays. For the particular set of laboratories considered
in this study, the volume of incoming intermediate samples is constant throughout the year, with no data
being registered in Month 8. A high volume of change of line samples is received in the months leading
up to and on the aftermath of high IPC workload, as changes occur in production lines to accommodate
different projects.
Table 4.1 presents a summary of the sample arrival process properties, per sample type.
Arrival ProcessSample Type Grouping Weekday Pattern Hourly Pattern Workload Levels
Change of Line Batch 7 days/week 24 hours/day 3
Fast Analysis Single Mon. − Fri. 24 hours/day 3
Final Product Batch Mon. − Fri. 08:00h - 17:00h 2
Intermediate Single 7 days/week 24 hours/day 1
In-process Control Single 7 days/week 24 hours/day 3
Miscellaneous Batch Mon. − Fri. 08:00h - 17:00h 3
Raw Materials Batch Mon. − Fri. 08:00h - 17:00h 3
Stability Batch 1 day/week 08:00h - 17:00h 2
Table 4.1: Arrival Process Properties per Sample Type
32
In Discrete Event Systems, the arrival of entities (in this context, samples) is mapped onto a sequence
of points in time 0 = t0 ≤ t1 ≤ t2 ≤ ..., such that the ith event occurs at time ti (i = 1, 2, ...), with time in-
stants {ti} following an underlying distribution. This formulation typically denotes N(t) = max{i : ti ≤ t}
as the number of events to occur at or before time t and Ai = ti − ti−1 as the inter-arrival time between
entities {i − 1, i} of the stochastic process {N(t), t ≥ 0}. Being the most commonly used model for
the arrival process of entities to a queueing system [27], the Poisson process and its variants naturally
emerged as one of the first alternatives to be considered. The Poisson process is suitable for cases
where the Ai ’s are independent and identically distributed (IID) exponential random variables, with its
application to a given stochastic arrival process depending on the following requisites:
i. Entities arrive one at the time
ii. N(t+s)−N(t), the number of arrivals in the time interval [t, t+s], is independent of {N(u), 0 ≤ u ≤ t}
iii. The distribution of N(t+ s)−N(t) is independent of t for all t, s ≥ 0
Property i. is verified by sample types that arrive one at the time, but needs to be adapted to fit the
case of types whose arrival occurs in batches.
Property ii. requires the number of arrivals in a given time interval [t, t+ s] to be independent of the
number of arrivals in the earlier time intervals [0, t], which holds true for the QCL under consideration.
Precondition iii., however, requires the samples’ arrival rate to be independent of the time of day,
day of the week and other time-related factors. Due to the imprecise time-keeping limitation, the integrity
of this property could not be checked at hourly level and was thus evaluated at day of the week level.
This analysis was conducted for each sample type, over each specific arrival window (see Table 4.1),
per monthly workload level; summary statistics for the number of samples received per week day were
computed and the mean values found to be approximately equal, suggesting that the arrival rate is fairly
constant over each 24-hour period and thus not dependent on the day of the week. Detailed results for
IPC samples are presented in Figure 4.4.
Given that the three requisites were met, sample types arriving as singular entities were modelled as
a Poisson process, implying that the number of arrivals k in any positive interval of length s is a Poisson
variable, with parameter λs.The probability of k samples arriving over the course of a time interval of
duration s can be computed as:
P [N(t+ s)−N(t) = k] =e−λs(λs)k
k!, for k = 0, 1, 2, ...and t, s ≥ 0 (4.1)
The expected number of arrivals in any interval of length 1, λ, is referred to as the the rate of the pro-
cess. It follows that the corresponding inter-arrival times A1, A2, ... are IID exponential random variables,
with mean 1/λ.
33
Hig
h W
orklo
adM
od
erate Wo
rkload
Lo
w W
orklo
ad
Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7
0
20
40
60
80
0
20
40
60
80
0
20
40
60
80
Weekday
Rec
eive
d S
amp
les
mean
Figure 4.4: Summary Statistics: IPC Samples Received per Weekday
Some of the considered sample types arrive at the QCL grouped in batches, violating requisite i. of
Poisson process applicability. Nonetheless, a simple modification can be introduced to the formulation,
allowing an extension of this model to be suited for modelling the arrival of batches. Defining N(t) as
the number of batches of individual entities to have arrived by time t and provided that the inter-arrival
times of successive batches are IID exponential random variables, then a given batch arrival process
{X(t), t ≥ 0} can be modelled as a compound Poisson process by fitting a discrete distribution to the
sizes of the batches. In this case, the total number of samples X(t) to have arrived by time t, with Bi
denoting the batch size of the ith batch (assumed to be IID random variables), is given by
X(t) =
N(t)∑i=1
Bi for t ≥ 0 (4.2)
34
Batches are not explicitly declared in LIMS, so a special purpose routine was developed to group
samples, while also estimating the underlying empirical cumulative density function associated with the
batch sizes Bi of each type. Batch sizes were assumed to be dependent on the monthly workload,
resulting in one empirical distribution function per sample type ↔ level of workload pairing. The high-
level implementation of the batch grouping algorithm is presented below; parameter batch timer was
used as the admissible time-window for group entities, with samples arriving within a period shorter than
the specified being considered as part of the same batch.
Algorithm 4.1: Sample Batch Grouping Algorithmbegin
% initialize counters & set batch grouping time-window,:batch number ←− 1batch size[batch number]←− 1batch timer ←− batch grouping timeframe
for sample i in samples doif difftime(samplei+1.arrival time, samplei−batch size+1.arrival time) < batch timerthen
% increment batch size:batch size[batch number]←− batch size[batch number] + 1
else% store batch size:batch number.size←− batch size[batch number]% extract batch arrival timestamp, from the first sample of the batch:batch number.arrival time←− samplei−batch size+1.arrival time% proceed to next batch:batch number ←− batch number + 1% re-initialize counter:batch size[batch number]←− 1
Having hypothesized on theoretical and empirical grounds that the arrival of samples (both singular
entities and grouped in batches) follows a Poisson process with exponentially distributed inter-arrival
times, the rate λ of each process (per sample type ↔ monthly workload level pairing) was estimated
using the maximum likelihood estimator, as described in [27]. The ”quality” of the fitted parameters was
evaluated by means of two heuristic procedures: Density-Histogram and Q−Q & P −P probability plots,
again following the methodology presented in [27]. Detailed results for in-process control (single arrival)
and change of line (batch arrival) samples are presented in Figures 4.5-4.7 and 4.8-4.13, respectively.
The remaining plots can be found in Appendix A.
35
Histogram and theoretical densities
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ies
Figure 4.5: IPC Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots
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030
Fitted Distribution
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Theoretical probabilities
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Figure 4.6: IPC Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots
36
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
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●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure 4.7: IPC Samples, High Monthly Workload: Density Histogram, Q−Q & P − P plots
37
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 20000 40000 60000 80000 100000 120000 140000
0.0e
+00
1.0e
−05
2.0e
−05
Fitted Distribution
●●●●●●●●●●●●●●
●●●●●●●●
●●●●●●●●●●
●●●●●●●●
●●●●●
●●●●●
●●●●●●
●●●●●●
●●●●●●●●●●●●●
●●●
●●
●
● ●
●
● ●●
●
● ● ●●
●
●
0 50000 100000 150000
040
000
8000
012
0000
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●
●●●●●●●●
●●●●●
●●●●●
●●●●● ●●
●●●●
●●●●●●
●●● ●●● ● ●●● ●●
●● ●●●● ● ●
0 20000 40000 60000 80000 100000 120000 140000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●
● ● ●●●●●● ●●
●●● ●● ● ●●●●●●
● ●● ●●●● ● ●●
● ●●● ●● ●●
● ● ● ●●●●●●● ● ●●●
●●● ● ●● ●●
●●●●●
●●●● ●● ●●● ● ●●
●●●●●
●●●●
● ●
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure 4.8: COL Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
●
●
● ●● ● ●
●
●
●
●
●
● ●● ●
25%
50%
75%
100%
1 2 3 4 5 6 7 8 14 15Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure 4.9: COL Samples, Low Monthly Workload: Batch Size Empirical Cumulative Distribution
38
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 20000 40000 60000 80000 100000 120000 140000
0e+
001e
−05
2e−
053e
−05
Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●
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●●●●●●●●●●●● ●
●
● ● ●● ●
● ●●
●
●
0 50000 100000 150000
040
000
8000
012
0000
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●● ● ●●●●● ●● ● ● ●
0 20000 40000 60000 80000 100000 120000 140000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●●●●
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●●●●●●●●●●●●●●●●●●●●●●●
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●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure 4.10: COL Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
●
●
●
●● ● ● ● ● ● ● ● ●
●
●
●
●
●
●
●● ● ● ● ● ● ● ●
0%
25%
50%
75%
100%
1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 21Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure 4.11: COL Samples, Moderate Monthly Workload: Batch Size Empirical Cumulative Distribution
39
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 20000 40000 60000 80000 100000 120000 140000
0e+
001e
−05
2e−
053e
−05
4e−
05 Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
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●●●●
●●●●
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●●●●●●●●●
●●
● ●●
●
● ● ●
●
●
●
●
0 50000 100000 150000
040
000
8000
012
0000
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●
●●●●●●●●● ●●●●●● ●●●●●●●●● ●●● ●●●● ● ●●● ● ● ● ●
0 20000 40000 60000 80000 100000 120000 140000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●
●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●
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●●●●●●●● ●●●●●
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●●●●●●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure 4.12: COL Samples,High Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
●
●
●
●●
●● ● ● ● ● ● ● ● ●
●
●
●
●
●
●
●●
●● ● ● ● ● ● ● ●
25%
50%
75%
100%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 19 21Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure 4.13: COL Samples,High Monthly Workload: Batch Size Empirical Cumulative Distribution
40
For simulation purposes, the agglutination of the arrival process properties i. and ii. - the arrival
window - was modelled as the activation period for the entity sources of each sample type. Having
covered all the building blocks of the sample generator framework, an illustration of its underlying logic
process is presented in Figure 4.14. Under this representation, λk{l,m, h} denotes the arrival rate of
sample type k for months of low, moderate or high workload. This notation is extensible to the batch size
Bk. For illustrative purposes, under Figure 4.14, sample types {1, n} arrive as single entities, whereas
samples of type i arrive grouped in batches.
Simulation Clock
𝜆1
Source
Sample Type 1
𝜆𝑛
Source
Sample Type n
𝜆𝑖
Source
Sample Type i
⁞
⁞
Arrival Triggered
Look-up Analytical Tests
Look-up Analytical Methods
Assign Sample
Properties
Look-up Batch size
Arrival Triggered
Look-up Analytical Tests
Look-up Analytical Methods
Assign Sample
Properties
Arrival Triggered
Look-up Analytical Tests
Look-up Analytical Methods
Assign Sample
Properties
Look-up Tables Type 1
𝜆1{l,m,h}
Tests Methods
Look-up Tables Type i
𝜆𝑖 {l,m,h}
Tests Methods
𝐵𝑖 {l,m,h}
Look-up Tables Type n
𝜆𝑛{l,m,h}
Tests Methods
Figure 4.14: High-level Sample Generator Framework Representation
The sample generator framework is modular, allowing sample types to be added on ad hoc basis,
depending on the scope of the simulation study. Moreover, simulation runs can be configured to follow
the natural sequence of months of the year or hypothetical scenarios; this allows for specific responses of
the laboratory to particular sequences of workload to be simulated, such as the system’s step response,
that can be simulated by following a pattern of low−high−high workload levels across all sample types.
41
4.3.2 Analyst Staff
Analysts are one of the key resources in QC laboratories. They are accountable for several of tasks,
including but not limited to:
• Sample Preparation
• Equipment Setup & Verification
• Data Processing of Analytical Results
• Equipment Cleaning and Calibration
• Disposal of Samples
• Stock Management (Standards, Reagents,...)
Ensuring that the right number of analysts is allocated to meet the time-varying amount of incoming
samples is of paramount importance. In practice, the basic demand forecasting techniques employed by
laboratory managers to estimate the arrival of samples over a period of time tend to be inaccurate, re-
sulting in either under or overstaffed analyst teams. Both scenarios lead to negative repercussions, such
as contributing to longer sample time-in-system (analyst understaffing) or lower scheduled utilisation of
human resources (analyst overstaffing). The work conducted by analytical chemists is taxing, requiring
high levels of focus to ensure that no detail is overlooked. Understaffing can increase the compliance
risk, given that analysts subjected to workload levels above a reasonable threshold are more prone to
committing errors.
At the CDMO considered in this study, three analyst work-shift variants are presently employed. A
summary of this information is presented in Table 4.2.
Work-shift Weekdays Hours Rotating Teams
#1 7 days/week08:00h - 20:00h
20:00h - 08:00h4
#2 Mon. − Fri.08:00h - 17:00h
17:00h - 24:00h2
#3 Mon. − Fri. 08:00h - 17:00h n.a.
Table 4.2: Analyst Work-shifts Variants
The field Rotating Teams refers to the number of distinct analyst teams operating under each
regime, that alternate to comply with the mandatory resting periods between extended shifts. Project
stakeholders expressed the desire to simulate and compare shift-heavy scenarios (by predominantly
assigning analysts to work-shifts #1 and #2) with a regular work schedule (work-shift #3), as well as
exploring different breakdowns between shifts.
42
4.3.3 Analytical Equipment & Generic Analysis Workflow
Alongside the analyst staff, analytical equipment plays a key role as one of the fundamental re-
sources in QC laboratories. Drawing a parallel between classic manufacturing systems theory and QCL
operations, a strong duality is discernible amidst job shop machines [29] and analytical equipment: each
device serves its own designated purpose, in the form of the analytical test it was designed to perform;
additionally, similar equipment tend to be grouped according to the specific analysis they execute.
Only a fraction of the analytical procedure makes use of the actual equipment. Samples are usually
subjected to bench work, where they are prepared and furbished before being ready to be processed.
Apart from the sample, supplementary products required to carry out the analysis - such as standard
solutions and solvents - also need to be prepared in advance. Before conducting the analysis, the
equipment must be configured; this requires the analyst to calibrate the required parameters according
to information specified in the analytical method and, in the case of equipment requiring their suitability
to be validated, to allocate the solutions used for this purpose. Ensuring that a given system is suitable
to run a specific method consists on injecting a series of standard solutions with known responses that,
when replicated, certify that the equipment is properly calibrated to run the analysis. This step, confined
to GCs and HPLCs, can be rather time-consuming, but does not require the analyst to be present during
its execution. Once the system’s suitability has been checked by the analyst, the equipment is deemed
available to analyse samples according to the ratified method. After the analysis has finished, the analyst
must disassemble the equipment, collect the sample and process the results. This task is carried out at
data processing workstations, and may involve hand and computer-assisted calculations.
Despite the notorious differences between the analytical tests considered in the context of this work,
it is possible to identify six common procedural steps between techniques. This information is presented
in concise manner in Table 4.3, followed by a representation of the generic analytical workflow in BPMN
notation in Figure 4.15.
Analysis Process Step Work Environment Analyst Required
System Preparation BenchWork Y es
Sample Preparation BenchWork Y es
Equipment Setup Equipment Y es
System Suitability Equipment No
Analysis Equipment No
Data Processing Workstation Y es
Table 4.3: Common Core Analysis Process Steps - Work Environment & Required Resources
43
The field Analyst Required denotes whether the presence of the analyst is mandatory, either to
perform or oversee the bulk of a task. Process steps system suitability and analysis are predominantly
executed without an analyst being present; however these steps still required limited levels of interaction
with the equipment, such as checking the conformity of the system suitability status and removing the
sample after the analysis has finished.
Quality Control Laboratory Scheduling Platform
Qu
alit
y C
on
trol La
bo
rato
ry
Scheduled Sample for Analysis
Input:Analytical Method Parameters
Sample arrives at the Laboratory
System Preparation
Suitability Required?
Wait for Sample
System Suitability
Yes
Check System Suitability
Output:Suitability Checklist
Sample Preparation
Analysis
Input:Analytical Method Parameters
Data Processig
Output:Analytical Report
Equipment Setup
Await Suitability / Sample Preparation
Schedule Report Review
UpdateLIMS
UpdateLIMS
Figure 4.15: BPMN representation of the Generic Analysis Workflow
Data concerning the processing times of sample preparation, equipment setup, analysis runtime and
data processing activities gathered by Costigliola in [16] was retrieved and used in this work. Table
4.4 is presented for reference; fields listed as Deterministic were obtained by the information extraction
algorithm alluded in section 3.1, whereas the probability density functions where the result of a time
study conducted by the author.
Test Sample Preparation Equipment Setup Analysis Data Processing
DSC Tr(5, 10, 30) Tr(1, 3, 12) U(12, 180) Tr(4, 9, 16)
KF Tr(1, 6, 25) Tr(4, 8, 16) Tr(2, 5, 56) Tr(10, 20, 30)
GC Tr(5, 10, 35) Tr(2, 5, 30) Deterministic Tr(2, 5, 10)
HPLC Tr(5, 40, 100) Tr(25, 50, 65) Deterministic Tr(10, 20, 45)
PSA Tr(5, 7.5, 21) U(1, 32) Tr(5, 10, 30) Tr(2, 6, 10)
XRPD Tr(5, 10, 20) Tr(1, 5, 20) Tr(11, 25, 203) Tr(2, 7, 30)
Table 4.4: Processing times’ distributions (Tr(a, b, c): Triangular pdf; U(a, b): Uniform pdf); time in arbitrary units
Information on the pool size of each equipment variant to be deployed in the new laboratory was
obtained from the rolling blueprint of the new facility. Project stakeholders expressed the desire to use
this variable as a simulation parameter, as to make a better-informed decision on the equipment capacity
to install, based on data-driven device performance metrics.
44
4.4 Model Framework Overview
The QCL simulation model framework developed by Costigliola, presented in [16], was adapted and
expanded to fulfil the requirements of this work. Namely, the hierarchical model library, originally com-
prised by the generic sample and generic equipment archetypes, was complemented with the addition
of the generic sample source, part of the sample generator framework. Changes were also made to
the generic sample and equipment objects, to meet the desired expressed by project stakeholders of
including additional properties and tracking a greater number of performance metrics.
Under the proposed process-oriented architecture, samples are treated as model entities and imple-
mented as objects, whose key properties - such as the prescribed analytical method and preparation
times - are assigned by the sample generator framework. Furthermore, a generic equipment model
was implemented by mapping the stages of the generic analysis workflow presented in Figure 4.15
onto a series of logic process steps, with associated task processing times and resource dependency
specifications. The implementation of the devised equipment model in Simio is presented in Figure 4.16.
Input Buffer System Preparation
Sample Preparation
System Suitability
Analysis Data Processing
Figure 4.16: Simio Implementation of the Generic Equipment Model
Multiple generic equipment objects were grouped into device pools of the same variant, and assigned
class-related and sample-independent properties, such as equipment setup time. By referencing the
incoming samples’ properties, the generic equipment model is suitable to emulate the six analytical
techniques considered in this study, resulting in a general process sequence that can be applied to
simulate every analytical test.
The scope of the model covers the entire sample flow within the laboratory, across 3 relevant stages:
(1) moment of arrival (event triggered by the sample generator framework, that operates as described in
section 4.3.1), (2) allocation to an equipment of the appropriate variant required to perform the analytical
test, according to the scheduling policy implemented at equipment group level and (3) the actual analyt-
ical workflow, consisting of the steps detailed in Figure 4.15. The high-level model flowchart is depicted
in Figure 4.17, and two snapshots of the 3D visualization are presented in Figure 4.18.
The QCL simulation model in Simio contemplates two assumptions:
i. The couple sample ↔ analytical test(s) was treated as a single entity. In practice, this translates
into each sample being separated into as many instances as the total number of analytical tests it
must undergo, and each instance being processed by an equipment of the respective kind.
45
Analytical Test?
Sample Generator Framework
COL FA FP IN IPC Misc. RM Stability
Buffer DSC
Buffer KF
Buffer GC
Buffer HPLC
Buffer PSA
Buffer XRPD
HPLC_1 HPLC_n
⁞
KF_1 KF_n
⁞
XRPD_1 XRPD_n
⁞
DSC_1 DSC_n
⁞
PSA_1 PSA_n
⁞
GC_1 GC_n
⁞
Group Scheduling
Node
Group Scheduling
Node
Group Scheduling
Node
Group Scheduling
Node
Group Scheduling
Node
Group Scheduling
Node
Analyst Staff
Allocation Policy
⁞
Analyst_1 Analyst_n
Figure 4.17: High-level QCL Simulation Model Flowchart
ii. System suitability is valid for 24 hours; during this period, a given equipment remains suitable to
process samples according to the validated method. Once it expires, or a sample with a different
method is scheduled to the processed that particular equipment, the suitability run must be carried-
out beforehand.
Assumption i. is justifiable on the basis that it is common practice for analysts to do the same in
practice. As for assumption ii., the value of 24 hours was agreed with project stakeholders and was
deemed as a reasonable, albeit conservative, duration for the equipment suitability time-frame.
Figure 4.18: 3D Renders of the QCL Simulation Model Implemented in Simio
46
Sample sequencing and scheduling policies were enforced at two distinct levels: global equipment
group and individual equipment queue. At global group level, an heuristic allocation rule that aims to
reduce the impact of system suitability on the sample’s time in system was implemented. This rule
consists on scanning the equipment pool for devices whose last validated method matches that of the
sample to be scheduled and, provided that such equipment exists and its queue contains less samples
than the maximum number allowed, the sample is allocated to that equipment; if no match is found, the
scope of the search algorithm is widened to available but invalidated equipment. If yet again no such
equipment is found, the incoming sample is retained at the equipment group buffer, awaiting a change
of state that enables it to be assigned. At individual equipment level, the maximum queue size (Qmax)
was regarded as a tunable simulation parameter.
Two sample priority levels were considered: high, awarded exclusively to IPC samples, and regular,
attributed to the remaining sample types; this binary decision variable was used as the primary entity
sequencing rule. For the purpose of ordering samples of the same priority level competing for resources
(both at group and individual equipment levels), the performance of three scheduling heuristics was
compared: First In First Out (FIFO), Shortest Processing Time First (SPTF) and Longest Processing
Time First (LPTF). FIFO is self-explanatory: entities are processed according to the order or their
arrival; under SPTF (LPTF), whenever an event prompts the selection of an entity from a buffer holding
several candidates, the entity with the shortest (longest) estimated processing time is given priority over
the rest. SPTF tends to minimize the minimize the average amount of time each sample has to wait until
its analysis starts [30], but can result in long waiting times for samples which take long time analyse.
LPTF tries to place the shorter analysis towards the end of the schedule, where they can be used for
balancing the equipment loads [31]. It should be noted that, since sample priority was used as the first
decision factor, an IPC sample has precedence over other sample types - even it arrived at a later time
or has a shorter (higher) processing time.
As for the allocation of analysts to specific samples, the two alternative governance model frame-
works introduced in section 4.2 - structure and free-for-all - were compared. Under the structured
organizational policy, the breakdown of sample types per QC branch, suggested by project stakeholders
and presented in Table 4.5, was followed. Under the the free-for-all paradigm, the entire analyst staff
available at the laboratory at a given time is allowed to process every sample, regardless of its type.
QC Branch Allocated Sample typesBranch A Change of Line, IPC, IntermediatesBranch B Raw Materials, Final Product, Fast Analysis, Misc.
Branch C Raw Materials, Final Product, Fast Analysis, Misc.
Branch S Stability
Table 4.5: QC Branches and their allocated Sample Types
47
4.5 Model Performance Metrics
To assess the behaviour of the model and estimate the real-world performance of the new laboratory
under varying governance models, a set of key QCL performance metrics was gathered and compared
between simulation runs. These metrics concern the throughput of samples and utilization of resources
- both analyst staff and analytical equipment; they are listed in the diagram of listed in Figure 4.19,
followed by a summary description of each parameter.
QCL Performance Metrics
Sample Throughput Resource Utilization
Time in System Throughput Rate Analyst Staff
Scheduled Utilization
Equipment
Usage Rate
Figure 4.19: QCL Performance Metrics
Time in System: Translates the total time that takes to process a given sample, form the moment of
its arrival at the QCL until the analysis and subsequent data processing has finished.
Throughput rate: A measure of the capacity of the QCL to process the incoming volume of samples;
it is computed by diving the number of processed samples by the total number of incoming samples.
Equipment usage rate: A measure of the fraction of time a given equipment spent performing active
work; in this context, active work includes all the stages of the analytical workflow that make use of the
equipment: Equipment Setup, System Suitability and Analysis. To keep in trend with the way this
performance metric is calculated at the CDMO under consideration, the value is computed over 24 hours
a day, 7 days per week. While useful for comparison with past results, this metric does not represent
an accurate overview of equipment utilization, given that the analysis process cannot be carried out in
complete autonomous fashion, with the presence of the analyst being required to place the sample on
the equipment, validate the suitability check and start the analysis.
Eusage is computed according to expression 4.3, where EPT represents the active work equipment
processing time, and TRT the total simulation runtime.
Eusage% =EPT
TRT(4.3)
Analyst scheduled utilization: A measure of the fraction of time that the analysts spend working,
calculated over the corresponding total shift-time for each employee.
48
Chapter 5
Simulation Study
To ensure that the developed model provides a robust representation of the actual system, verification
was conducted across three fronts: (1) validation of the input parameters, (2) visual inspection of the
3D laboratory environment during simulation runs and (3) analysis of output data, expressed in the
designated performance metrics. Topics (1) and (2) are addressed in section 5.1, with simulation results
being presented and discussed separately in section 5.2.
5.1 Model Validation Data
Validation of input parameters was performed by comparing the number of incoming samples created
by the sample generator framework with the historical data referent to the last 12 months, collected from
LIMS. To achieve this goal, the number of generated samples was logged over 20 year-long simulation
runs, where each monthly workload level per sample type was set as the same recorded over the last
year. Results are presented in Figure 5.1; to conceal the real number of received samples, the axis tick
marks were wilfully removed. The upper and lower bounds of one standard deviation of the mean (µ±σ)
are also presented, to convey the extent of variability between simulation runs.
Change of Line
Fast Analysis
Final Product
Intermediates
In-process Control
Raw Materials
Stability
Sam
ple
Typ
e
Actual Data Simulation Input Data
Figure 5.1: Sample Generator Framework - Number of Incoming Samples: Simulation Input Data Validation
From the data presented in Figure 5.1, coupled with the goodness-of-fit tests presented in section
4.3.1, that attest the modelling decision of representing the arrival of samples as Poisson processes, it
is possible to conclude that the devised sample generator framework is capable of consistently creating
accurate volumes of incoming samples, providing a solid foundation for simulation input data.
49
Visual inspection of the 3D laboratory environment was carried out with the intent of validating the
flow of samples and analysts within the system, as well as providing insight into the spatial organization
of workbenches, equipment groups and data processing stations. Project stakeholders expressed the
desire of exploring the Virtual Reality rendering feature available in Simio to navigate throughout the
laboratory, recognizing the potential of the simulation model to assist in layout planning decisions.
5.2 Simulation Results
In the context of this work, the primary application of the simulation model is to compare Governance
Models to be instilled at the new laboratory. To this end, a scenario-based approach was devised by
assembling and comparing a set of alternative GMs, each resulting from different configurations of the
model parameters introduced in previous sections and summarised below:
i. Overall governance policy: structured vs. free-for-all (described in sections 4.2 and 4.4)
ii. Total number of analysts and their breakdown per work-shifts (depicted in Table 4.2)
iii. Total number of devices per equipment variant (refer to section 4.3.3)
iv. The scheduling policy at equipment group level (detailed in 4.4)
v. The maximum equipment queue size, Qmax (introduced in section 4.4)
Considerations on alternative GMs were derived by comparing their performance based on the output
metrics detailed in section 4.5. The results here presented stem from simulation runs spanning a period
of 92 days, modelled as an hypothetical three month sequence of low-high-high workload levels, across
all sample types (with the exception of intermediates and final product, where the highest workload
level registered in the previous year - moderate - was used instead). Having two successive months of
high workload, the simulation results translate the performance of the laboratory under high demand for
analytical services, as requested by project stakeholders.
Sample Time in System & Analyst Scheduled Utilization
For the purpose of assigning analysts to the existing work-shifts (Table 4.2), information concerning
the arrival regime of each sample type (Table 4.1) was considered in tandem with the sample types
processed by each QC branch (Table 4.5). Given that the sample types allocated to branch A arrive
continuously over 24 hours, analysts assigned to this branch should operate under work-shift #1. The
type of work done by branchesB and C does not require constant presence of analysts at the laboratory;
therefore, analytical staff of these two branches was predominantly assigned to work-shift #2. Lastly,
given its relatively lower priority, analysts performing stability work were appointed to work-shift #3.
50
A benchmark of the average Time in System (TiS) registered under six alternative GMs is presented
in Figure 5.3; for this comparison, three structured and three free-for-all GMs were considered. This
metric was computed as the weighted average TiS off all analytical samples processed per type of work.
To allow for the effect of the governance policy to be considered independently of other parameters,
the equipment group scheduling rule was set as FIFO for all six scenarios; moreover, the maximum
equipment queue size was limited to two samples (Qmax = 2), and number of equipment available kept
the same as currently planned in the rolling blueprint of the laboratory (Table 5.4). Additionally, the
impact of scaling the number of analysts was assessed by comparing three tiers of employed staff.
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
Change of Line
0.0 2.5 5.0 7.5 10.0
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
Fast Analysis
0.0 2.5 5.0 7.5 10.0
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
Final Product
0 3 6 9
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
Intermediates
0.0 2.5 5.0 7.5 10.0
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
In-process Control
0.0 2.5 5.0 7.5 10.0
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
Misc.
0.0 2.5 5.0 7.5 10.0
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
Raw Materials
0.0 2.5 5.0 7.5 10.0
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
Stability
0 20 40
44
52
60
Time in System [arbitrary units]
Num
ber
of A
naly
sts
Governance Policy Free-for-all Structured
Figure 5.2: Comparison of Governance Model’s Mean Time in System, per Sample Type
From the analysis of Figure 5.3 it is discernible that, for the same number of analysts, TiS is consis-
tently and considerably smaller under free-for-all governance polices. The mean relative time-savings
achieved under free-for-all are presented in Table 5.1. The allocation of analysts to work-shifts under
each GM, along with the average scheduled utilization of employees, is detailed in Tables 5.2 (struc-
tured GMs) and 5.3 (free-for-all GMs). The field Σ Analysts results from the rotating teams discussed
in section 4.3.2. A set of summary conclusions are listed following the data tables.
51
Sample Type
Σ Analysts CoL FA FP Inter. IPC Misc. RM Stability
44 +3, 83% −28, 74% −20, 49% −37, 9% −27, 56% −29, 44% −34, 04% −74, 63%
52 −9, 53% −18, 99% −12, 65% −36, 19% −36, 89% −33, 42% −28, 37% −77, 50%
60 −12, 64% −22, 93% −15, 41% −36, 26% −40, 28% −35, 47% −28, 54% −79, 81%
Table 5.1: Mean relative difference in TiS between free-for-all and structured GMs
QC Branch
Gov. Model Work-Shift A B C S Σ Analysts
#1 6 (67.36%) 1 (74.68%) 1 (65.47%) n.a.
#2 n.a. 2 (79.72%) 2 (65.02%) n.a.1
#3 n.a. n.a. n.a. 4 (56.95%)
44
#1 6 (66.41%) 2 (57.96%) 2 (38.58%) n.a.
#2 n.a. 2 (69.23%) 2 (44.52%) n.a.2
#3 n.a. n.a. n.a. 4 (56.96%)
52
#1 6 (66.05%) 2 (44.98%) 2 (23.28%) n.a.
#2 n.a. 4 (57.37%) 4 (19.07%) n.a.3
#3 n.a. n.a. n.a. 4 (58.96%)
60
Table 5.2: Structured Governance Models - Analyst Breakdown per Branch/Work-shift (Scheduled Utilization %)
Gov. Model Work-Shift Free-for-All Σ Analysts
#1 8 (65.23%)
#2 n.a.4
#3 12 (68.84%)
44
#1 10 (53.48%)
#2 n.a.5
#3 12 (63.57%)
52
#1 12 (45.31%)
#2 n.a.6
#3 12 (62.36%)
60
Table 5.3: Free-for-All Governance Models - Analyst Breakdown per Branch/Work-shift (Scheduled Utilization %)
52
• The two-tier sample priority policy results in In-process Control having the shortest TiS of all sam-
ple types; this imperative requisite, given the importance of IPC due to ties with ongoing manufac-
turing, was thus met. Under free-for-all guidelines all available analysts prioritize this type of work,
reducing the overall time it takes to complete a production batch.
• The biggest reduction in TiS occurs in stability samples. Given the low priority of this type of work,
it does not warrant a high number of dedicated analysts when a structured policy is considered.
However, under free-for-all, provided that no higher priority samples are pending, analysts will
leverage the opportunity to process stability samples, reducing the TiS of this sample type in
around 70% and thus fulfilling another requisite expressed by project stakeholders.
• With the exception of GM #1, all five other GMs considered in this study result in scheduled utiliza-
tion of the analyst staff under 70%, a requirement stated by project stakeholders. Progressively
increasing the number of analysts allows for lower TiS to be achieved, but reduces the scheduled
utilization of human resources. This is understandable under the light that not all stages of the
analysis workflow require the presence of the analyst (refer to Table 4.3); partial automation of the
tasks that do require an analyst should be considered.
• Crucially, for the same number of analysts and available equipment, nearly every sample type is
processed faster under free-for-all ; The potential time-savings that can be achieved by transitioning
to a free-for-all policy demonstrate that the performance of the laboratory can be improved through
an organizational rearrangement, without the need to procure additional resources.
EquipmentDSC GC HPLC KF PSA XRPD
3 50 100 4 12 1
Table 5.4: Planned Equipment Pool Size per Device Variant
The results portrayed in Figure 5.3 can be interpreted as macro-level laboratory performance metrics.
However, they fail to convene detailed insight into the TiS of each analytical test, a metric that warrants
scrutiny as it can help to identify bottlenecks in the form of shortage of equipment of a given kind.
Detailed results for analytical tests conducted on IPC samples are presented in Figure 5.3, where the
upper and lower bounds of one standard deviation from the the mean Time in System (TiS±σ) are also
presented, to convey the extent of variability between tests on different samples.
53
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
PSA
0.0 2.5 5.0 7.5
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
DSC
0.0 2.5 5.0 7.5
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
GC
0.0 2.5 5.0 7.5
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
HPLC
0.0 2.5 5.0 7.5
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
KF
0.0 2.5 5.0 7.5
44
52
60
GM# 1
GM# 4
GM# 2
GM# 5
GM# 3
GM# 6
RX
0 5 10 15 20
44
52
60
Time in System [arbitrary units]
Num
ber
of A
naly
sts
Governance Policy Free-for-all Structured
Figure 5.3: Comparison of Mean Time in System for IPC samples, per Analytical Test
The following conclusions can be drawn from the data presented in Figure 5.3:
• Equipment pools consisting of smaller number of equipment (PSA, DSC, KF, XRPD) benefit the
most from operating under free-for-all. Since every analyst can process any sample, regardless of
its type, a given equipment is less likely to be left idling while waiting for a designated analyst. If the
laboratory managers decide to implement a structured governance policy, the planned equipment
pool-sizes of PSA, DSC and KF should be increased.
• GC and HPLC tests are heavily conditioned by the need to perform system suitability runs before
the analysis. This factor, combined with the large equipment pool-size of this two device variants,
results in smaller benefits under a free-for-all governance policy. This is underlined by the fact
that increasing the number of analysts results in small reductions of TiS; the bottleneck introduced
by the system suitability procedure should be tackled by relying on the communication bridge
between manufacturing and QC services alluded in section 3.2.1, so that when a sample arrives
at the laboratory the equipment has already been validated and is ready to process the sample.
54
Equipment Usage Rate
Detailed equipment usage rate statistics for the six considered GMs are presented in Table 5.5, along
with the maximum registered number of concurrent equipment in use during one simulation run.
Equipment
Gov. Model DSC GC HPLC KF PSA XRPD1 38.67% (3) 38.58% (34) 46.84% (57) 40.70% (4) 32.36% (12) 11.25% (1)2 37.30% (3) 37.96% (35) 46.50% (56) 37.62% (4) 32.49% (12) 9.95% (1)3 39.64% (3) 38.04% (34) 46.23% (57) 37.40% (4) 32.85% (12) 10.34% (1)4 34.76% (3) 38.12% (35) 45.87% (54) 24.09% (4) 31.60% (12) 11.25% (1)5 33.92% (3) 37.38% (35) 45.41% (53) 19.54% (4) 31.25% (12) 9.95% (1)6 33.60% (3) 37.35% (35) 45.90% (51) 17.99% (4) 31.07% (12) 11.45% (1)
Table 5.5: Equipment Usage Rate % (maximum number of concurrent equipments in use)
• HPLCs: At most, only 57 out of the total 100 HPLCs were used simultaneously, with this num-
ber dropping to 51 under GM #6. This value suggests that the initially planned capacity of 100
HPLCs was overestimated; average utilization is approximately 46%, a value that rises to 58,48%
if only the 10 most used devices are considered. The low equipment usage rates for HPLCs can
be explained by the model assumption of considering a system suitability validity time window
of 24 hours. During this time the equipment is ready to process samples according to the vali-
dated method, and remains in low flux mode until the suitable period expires, waiting the arrival of
samples.
• GCs: Similar conclusions can be drawn for GCs as those stated for HPLC: out of the 50 devices
planned to be installed, at most 35 were used concurrently. In the case of GCs, the 10 most used
devices registered an utilization rate of 45,75%.
• DSCs, KFs and PSAs: A similar pattern occurs for these three equipment variants: transitioning
to a free-for-all governance policy reduces the equipment usage rate. This behaviour highlights
what was stated when the utilization rate metric was introduced; since the analyst must interact
with the equipment to start the analysis and collect the sample after it is finished, having a greater
pool of analysts who can process a given sample reduces the time an equipment spends in idle
state waiting to be tended by an analyst, increasing the time it is available for use.
• XRPD: The single X-Ray device is deemed sufficient to cope with the volume of samples requiring
this type of analytical test.
55
Sample Throughput
All six GMs variants considered in the initial analysis achieved a throughput rate in excess of 98%;
in practice, this implies that the laboratory was able to cope with the sequence of low-high-high monthly
workloads without accumulating work-in-process at the end of the simulation run. The residual corre-
sponds to the samples that were being processed / waiting in queue when the simulation was halted.
Equipment Queue Size
The impact of the maximum allowed equipment queue size, Qmax, on system performance was
evaluated by comparing the average TiS between two GMs variants that employ the same number of
analysts: GM #2 (structured) and GM #5 (free-for-all).
GM# 2
GM# 5
GM# 2
GM# 5
GM# 2
GM# 5
Change of Line
0.0 2.5 5.0 7.5 10.0
2
5
10
GM# 2
GM# 5
GM# 2
GM# 5
GM# 2
GM# 5
Fast Analysis
0.0 2.5 5.0 7.5 10.0
2
5
10
GM# 2
GM# 5
GM# 2
GM# 5
GM# 2
GM# 5
Final Product
0 5 10 15
2
5
10
GM# 2
GM# 5
GM# 2
GM# 5
GM# 2
GM# 5
Intermediates
0.0 2.5 5.0 7.5 10.0
2
5
10
GM# 2
GM# 5
GM# 2
GM# 5
GM# 2
GM# 5
In-process Control
0.0 2.5 5.0 7.5 10.0
2
5
10
GM# 2
GM# 5
GM# 2
GM# 5
GM# 2
GM# 5
Misc.
0.0 2.5 5.0 7.5 10.0
2
5
10
GM# 2
GM# 5
GM# 2
GM# 5
GM# 2
GM# 5
Raw Materials
0.0 2.5 5.0 7.5 10.0 12.5
2
5
10
GM# 2
GM# 5
GM# 2
GM# 5
GM# 2
GM# 5
Stability
0 10 20 30 40 50
2
5
10
Time in System [Hours]
Equ
ipm
ent Q
max
Governance Policy Free-for-all Structured
Figure 5.4: Effect of Qmax on Mean Time in System, per Sample Type
56
Detailed analysis of the data presented in Figure 5.4 yields the following conclusions:
• Increasing Qmax from 2 (the value considered up to this point) to 5 reduces the overall mean
TiS across all sample types. The relative difference is more pronounced under the structured
governance policy, which suggests that for GM #6 the TiS was already near its lower bound.
• Increasing Qmax from 5 to 10 however, results in longer sample TiS; this trend is more noticeable
for sample types that arrive grouped in batches (Change of Line, Final Product, Misc., Raw Ma-
terials and Stability, as per Table 4.1), given that samples of the same batch are to be processed
according to the same analytical method. In practice, it is more likely that the system suitability
time window will expire before all samples placed in the queue of equipment with larger values
of Qmax can be processed; TiS will thus be higher for samples that have to wait for a second
suitability run to be performed.
The trend pinpointed in the second concluding remark presented above suggests that an analysis
to estimate the optimal Qmax per analytical method should be conducted, resulting in individual queue
sizes fit to process the maximum conceivable number of samples before the equipment’s suitability
status expires.
Equipment Group Scheduling Policy
The effect of the group scheduling policy on system performance was assessed, again by comparing
its effect on two GMs, alternatives #2 and #5. For this analysis, a value of Qmax = 5 was adopted, as
it proved to produce better results under the previous experiment. The three scheduling policies listed
in section 4.4 - FIFO, SPTF and LPTF were considered. Since the processing times are stochastic, the
sample sequencing resulting from applying SPTF and LPTF was based on the estimated processing
time of each analysis, computed as the sum of randomly sampled times from the distributions listed in
Table 4.4, for each corresponding stage of the work-flow of each analytical test.
Results are presented in Table 5.6, in the form of the relative difference between the mean TiS
achieved under SPTF / LPTF and FIFO (base value for comparison, omitted from the table).
Gov.Model CoL FA FP Inter. IPC Misc. RM Stability
#2 SPTF +3.57% −6.93% −2.73% −1.41% +1.06% −5.04% −1.14% +1.99%
#2 LPTF +4.99% +1.71% +7.70% −2.23% +4.94% −1.80% +0.61% +8.02%
#5 SPTF −5.51% −2.81% +1.03% −0.19% −0.24% −0.87% +2.99% −0.89%
#5 LPTF +1.54% −1.49% +1.50% −2.03% +0.23% −3.75% +2.73% +3.40%
Table 5.6: Relative difference in mean TiS between SPTF, LPTF and FIFO heuristics
Under a structured governance policy (GM #2), five out the eight sample types register lower mean
TiS when the SPTF heuristic is employed. In the case of free-for-all, this number ascends to six out
57
of eight. The reverse occurs when group scheduling policy follows LPTF: six sample types see their
TiS rise in the case of GM #2, with the same being true for five work types under GM #5. However,
the relative differences resulting from changing the group scheduling policy are not remarkable, and the
effect of this model parameter may be partially attributed to the variability between simulation runs.
Given the limitations imposed by the academic version of the simulation software used in this work -
that restrain the number of logic processes and objects that can be defined - the intent of implementing
a re-scheduling architecture could not be a realised. Therefore, samples are sequenced only at the two
stages: the arrival at the laboratory and before being assigned to an equipment.
58
Chapter 6
Conclusion
The core goal of this project − developing a data-driven decision support system to assist Quality
Control Laboratory managers in the tasks of resource planning and scheduling − was achieved through
the implementation of a discrete-event simulation model. Said model was employed in the context of a
real-world application, with a future state of the art facility currently under design posing as a case study.
To ensure that the model provides a robust representation of the system under consideration, its
behaviour was discussed with project stakeholders after each landmark development stage. Crucial
workflows were modelled, ensuing vectors for improvement proposed, and a comprehensive simulation
study was conducted to assess the impact of alternative Governance Models, scheduling heuristics and
resource allocation policies on laboratory performance.
A modular sample generator framework was devised for simulation purposes. The arrival of samples
was modelled as Poisson process variants, resulting in a configurable source of simulation input data,
capable of capturing the effect of seasonality on the fluctuating demand for analytical services and
allowing for hypothetical scenarios to be considered.
Through the approach of integrating strategic (planning) and operational (scheduling) constraints into
the design stage of the laboratory, detailed considerations on the effect of model parameters on system
performance were drawn and presented in Chapter 5. As an overview, the factor with the highest impact
on the considered performance metrics was found to be the high-level organizational policy; crucially, for
the same allocated resources, free-for-all Governance Models resulted in lower values of sample Time
in System. The time-savings when compared to a structure policy are substantial, amounting to 40% in
the case of IPC samples, and 80% for stability work.
Concerning the planned number of equipment to be installed at the new laboratory, the predicted
capacity of HPLCs and GCs was found to be overestimated for the considered sample volume, but would
provide ample room for increasing demand in the future; The overall low values of equipment usage rate
are partially explainable by the way this metric is computed. Moreover, tasks such as equipment cleaning
and scheduled maintenance were not factored into this analysis, so the real value should be higher in
practice. Since the volume of samples was estimated from the raw data extracted from LIMS, analysis
not registered in this database (non-GMP and validation work) were not accounted for.
Increasing the size of the analyst staff contributed to lower sample Time in System, but the effect
was not as pronounced as the shift resulting from changing the organizational policy.
The effect of the maximum equipment queue size was found to be non-linear, with the Time in System
59
increasing beyond a certain threshold.
In summary, the laboratory was found to be more responsive under a free-for-all framework, employ-
ing moderately sized equipment queues. An analyst staff in the range of 50 to 60 employees should
be allocated to cope with short term demand for analytical work, resulting in analyst utilization levels in
the interval of 50% to 70%, as requested by project stakeholders. It was also demonstrated that the
performance of the laboratory can improve through an organizational shift to free-for-all governance,
without the need to procure additional resources.
6.1 Future Work
Future vectors of improvement, such as those resulting from modelling the IPC, validation and stabil-
ity samples’ workflows, will require sophisticated communication and cooperation between all branches
of the CDMO considered in this study. The integration of planning and scheduling activities, leveraging
tools such as the platform developed over the course of this work, holds great potential. Introducing
the third vertex of operations management, control, will allow for more advanced solutions do be im-
plemented, such as reactive scheduling and dynamic priority queues. An organization-wide effort is
required in order to implement information retrieval protocols, capable of storing all relevant data in a
unified database. Otherwise, mismanaged and fragmented information, scattered across several and
disjointed repositories, will hinder the power of knowledge discovery and other data-driven application,
whose full potential – dependent on the quality of the available data – cannot be fully realised.
The model can be improved by expanding the extent of considered tasks to maintenance and clean-
ing of equipment, by conducting a time study to acquire this missing data.
The influence of the maximum equipment queue size should be addressed per analytical method
and, within the conceivable limits of analytical chemistry, newly developed methods should pursue longer
validity periods.
It would be interesting to explore the option of assigning analysts to specific stages of the analysis
workflow, such as sample preparation and data processing. This way, the effect of the experience
curve on execution times could be evaluated. The composition of work-shifts could be customized with
analysts better suited to perform a given type of analysis, for instance by using a Genetic Algorithm to
pick a set of analysts from a competency matrix of those better suited to perform a task.
Should a more complete version of the software be available, allowing for the extra entities required
to model solvents and reagents to be implemented, the model could be used as an auxiliary mechanism
to already existing stock management solutions.
60
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64
Appendix A
Arrival of Samples: Clusters & Distributions
Month-1 Month-2 Month-3 Month-4 Month-5 Month-6 Month-7 Month-8 Month-9 Month-10 Month-11 Month-12Month
No
rmal
ized
Nu
mb
er o
f R
ecei
ved
Sam
ple
s
Monthly Workload Low Moderate High
Figure A.1: Monthly Workload Levels - FA Samples
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 10000 20000 30000 40000
0e+
002e
−05
4e−
056e
−05
8e−
05 Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●
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0 10000 20000 30000 40000 50000 60000 70000
010
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Q−Q plot
Theoretical quantiles
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piric
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Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.2: FA Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots
65
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 10000 20000 30000 40000
0e+
002e
−05
4e−
056e
−05
8e−
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Fitted Distribution
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●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.3: FA Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 10000 20000 30000 40000
0e+
004e
−05
8e−
05
Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●
●●●●●●●●
●●●●●●●
●●●●●●●
●●●●●
●●●●●
●●●
●●●●●●●●
●●●●●●● ●
●
● ● ● ●●
●● ● ●
●
0 10000 20000 30000 40000 50000 60000
010
000
2000
030
000
4000
0
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●● ●●●●●●●●●●●●●●●●●●● ●●●●● ● ●●● ●●●●●●●●● ●●●●●● ● ●●●●● ● ●●● ●
0 10000 20000 30000 40000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●● ●●● ●●●●●● ●●●●●
●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●
●● ●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●
●●●● ●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●
●●●●●●
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.4: FA Samples, High Monthly Workload: Density Histogram, Q−Q & P − P plots
66
Month-1 Month-2 Month-3 Month-4 Month-5 Month-6 Month-7 Month-8 Month-9 Month-10 Month-11 Month-12Month
No
rmal
ized
Nu
mb
er o
f R
ecei
ved
Sam
ple
s
Monthly Workload Low Moderate
Figure A.5: Monthly Workload Levels - FP Samples
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 10000 20000 30000 40000
0e+
002e
−05
4e−
056e
−05
8e−
05 Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●●●
●●●●●●●●●●
●●●●●●●
●●●●●●●●
●●●●●●●●
●●●●●●●
●●●●●●
●●●●●●●●●●●●●●
●●
●● ●
●
●
●●
● ●●
●● ●
● ●
0 10000 20000 30000 40000 50000 60000
010
000
2000
030
000
4000
0Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●● ●●●●●●●
●●●●●●●●●
●●●●●●●●
●●●●●● ●●●
●●●●●●●
●●●●●●●●●
●●●●●●●●
●●●●● ●●● ● ● ● ● ●● ● ●●● ●●
0 10000 20000 30000 40000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●●●●●
●●●●●
●●●●●●●●●●●● ●●
●●●●●
●●●●●●
●●●●
● ●●●●
●●●●
●●●●●
●●●● ●●
●●●●
●●●●●●
●●●●●●●●●●
●●●● ● ● ●●
●●●● ●●
●●●●●
●●● ●● ●●●●
●●●● ●●
●● ●●●●●
●●●●●
●●●●●●●●●●●●●
●●●●●●
●●●●●●
●● ●●●● ● ●●
●●●●●
●●●
0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.6: FP Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
● ●● ● ●
● ●
●
●
●
● ●● ● ●
●
60%
80%
100%
1 2 3 4 5 6 7 8 9 10Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure A.7: FP Samples, Low Monthly Workload: Batch Size Empirical Cumulative Distribution
67
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 10000 20000 30000 40000
0e+
002e
−05
4e−
056e
−05
Fitted Distribution
●●●●●●●●●●●●●●
●●●●●●●●●
●●●●●●●●●●
●●●●●●
●●●●●
●●●●●●●●
●●●●●
●●●●●
●●●
●●●●●●●
●●●●●●●●●
●
●● ● ● ●
● ●
●
●●
●
● ●
●
● ●
●
0 10000 20000 30000 40000 50000 60000
010
000
2000
030
000
4000
0
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●
●●●●●●●●
●●●●●
●●● ●● ● ●●
●●●●
●●●●
●●●●●● ● ●●●●
● ●●●●●
●●●● ● ● ●●
●●●●● ●● ● ●● ● ●● ●
0 10000 20000 30000 40000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●
●●●●
●●● ●●
●● ●●● ●●●●● ●●
●●●● ●●
●● ●●●● ●●
● ● ●●●● ●●
● ● ● ●●●●●● ●●
●●●● ● ●● ● ● ●●●●
● ●●●●●
●●●● ● ●●●
●●●●
● ●●●●●
●●●●
0.2 0.4 0.6 0.8
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.8: FP Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
●
● ●●
●
●
●
●
● ●
40%
60%
80%
100%
1 2 3 4 5 6 8Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure A.9: FP Samples, Moderate Monthly Workload: Batch Size Empirical Cumulative Distribution
68
Month-1 Month-2 Month-3 Month-4 Month-5 Month-6 Month-7 Month-8 Month-9 Month-10 Month-11 Month-12Month
No
rmal
ized
Nu
mb
er o
f R
ecei
ved
Sam
ple
s
Monthly Workload Moderate
Figure A.10: Monthly Workload Levels - IN Samples
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0e+00 2e+04 4e+04 6e+04 8e+04 1e+05
0.0e
+00
1.0e
−05
2.0e
−05
Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●
●●●●●●●
●●●●●●●●●
●●●●●●●●●●
●●●●●●●●
●●●●●●●●●
●●●●●●●●●●● ● ● ● ● ● ● ● ● ● ● ● ●
0 50000 100000 150000 200000 250000
0e+
004e
+04
8e+
04
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
0e+00 2e+04 4e+04 6e+04 8e+04 1e+05
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●● ●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●● ●●●●●●
●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
0.0 0.2 0.4 0.6 0.8
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.11: IN Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots
69
Month-1 Month-2 Month-3 Month-4 Month-5 Month-6 Month-7 Month-8 Month-9 Month-10 Month-11 Month-12Month
No
rmal
ized
Nu
mb
er o
f R
ecei
ved
Sam
ple
s
Monthly Workload Low Moderate High
Figure A.12: Monthly Workload Levels - MS Samples
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 10000 20000 30000 40000
0e+
002e
−05
4e−
056e
−05
8e−
05
Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●
●●●●●●●●●●
●●●●●●
●●●●●●●●●
●●●●●●●●●●
●●●●●●●
●●●●●●●
●●●●●●●
●
●●●
●●●●●
●●●●●
●●●
●● ●●
● ● ● ●
● ●
●● ● ● ●
●
0 10000 20000 30000 40000 50000 60000
010
000
2000
030
000
4000
0
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●
●●●●●●●
●●●●●●
●●●● ●●●
●●●●●●●
●●●● ● ●●● ●●●● ●●●●
●● ●●● ●●●● ●●●● ●● ●●●●● ●
0 10000 20000 30000 40000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●●●●●●●●●●●
●●● ●●
●●●●●●●●
●●●●● ●●
● ●●●●●●●●●●
●●●●●● ● ●● ●●●
●●● ●●
●●●●
● ●●●●
● ● ●●●●● ●●●●● ●●
●●●●●
●●● ● ● ●●● ●●●
●●●●
●●●●●●
●●●●●
●● ●●●●
●●●●●●●●
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.13: MS Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
●●
●●
●
●
●
●
●●
●●
80%
90%
100%
1 2 3 4 5 6 7 8Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure A.14: MS Samples, Low Monthly Workload: Batch Size Empirical Cumulative Distribution
70
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 10000 20000 30000 40000
0e+
002e
−05
4e−
056e
−05
8e−
05
Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●●●●●
●●●●●●●●
●●●●●●●●
●●●●●●
●●●●●●●●
●●●●
●●●●●●
●●●●●
●●●
●●
●●●●●●●●
●● ● ● ●●
●● ● ●
●
●
● ●●
0 10000 20000 30000 40000 50000 60000
010
000
2000
030
000
4000
0
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●
●●●●●●●●●●●●●
●●●●●●●●●● ●●●●●
●●●●●●●●●●●● ●●●●●
● ●●●●● ●●●●● ●●●●●●●● ●●●●●● ● ●●● ● ● ●● ●
0 10000 20000 30000 40000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●● ●●●
●●●●●●●●
●●●●●●●
●●●●●●● ●●●● ●●●
●●●●●●
●●●●●●●●●●●●●●●●●
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●●●●●●●●●●●●
● ●●●●● ●●●●●●
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●●●●●●●●●●●●
●●●●●●●● ●●●
●●●●●●●●●●●
●●●●●●
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●●●●●●●●
●●●● ●●●
●●●●●●
●●●●●●●●
●●●●●●
●●●●●●●●
●● ●●●●●●●●●●●●●●●
●●●● ●●●
●
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.15: MS Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
●
●● ●
● ●●
●
●
●
●
●● ●
● ●
70%
80%
90%
100%
1 2 3 4 5 6 7 8 9 12Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure A.16: MS Samples, Moderate Monthly Workload: Batch Size Empirical Cumulative Distribution
71
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 5000 10000 15000 20000 25000 30000 35000
0.00
000
0.00
004
0.00
008
0.00
012
Fitted Distribution
●●●●●●●●●●
●●●●●●●●●●●●●
●●●●●●●
●●●
●●
● ●
● ●● ● ●
●● ●
● ● ●
●
●
●
0 10000 20000 30000
050
0015
000
2500
035
000
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●
●●●●●●●●●●●●
●●●●●
●●●●●●
●●●
●●
●●●
●●
●●●
●●●
●●●
●●
●
0 5000 10000 15000 20000 25000 30000 35000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●
●●●●
●●
●●
●●
●●
●●●●
●●
●●
●●●●
●●●
●●
●●
●●
●●
●●
●●
●●
●●
●●●
●●
●
0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.17: MS Samples,High Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
60%
70%
80%
90%
100%
1 2 3 4 5 6 7 9 10Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure A.18: MS Samples,High Monthly Workload: Batch Size Empirical Cumulative Distribution
72
Month-1 Month-2 Month-3 Month-4 Month-5 Month-6 Month-7 Month-8 Month-9 Month-10 Month-11 Month-12Month
No
rmal
ized
Nu
mb
er o
f R
ecei
ved
Sam
ple
s
Monthly Workload Low Moderate High
Figure A.19: Monthly Workload Levels - RM Samples
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 5000 10000 15000 20000 25000
0.00
000
0.00
004
0.00
008
0.00
012 Fitted Distribution
●●●●●●●●●●●●●●●●●●●●
●●●●●●●●
●●●●●●●●●●●●●●
●
●●
●●
●●●●
●
●
●●
●
●
●
●●
●●
● ●●
●
●
●
0 5000 10000 15000 20000 25000 30000
050
0015
000
2500
0
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●● ●●
● ● ●●●● ● ● ●● ● ● ● ● ●●● ●●
● ● ● ●
0 5000 10000 15000 20000 25000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●●●●●●●●●●●●
●●●
●●
●●
●●
●●
●●●●●●●
●●●
●●
●●
●●
●●
●●
●●●●
●●
●●
●●
●●●●●●●●●●●
0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.20: RM Samples, Low Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
●●
●●
●
●
●
●
●●
●●
80%
90%
100%
1 2 3 4 5 6 7 8Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure A.21: RM Samples, Low Monthly Workload: Batch Size Empirical Cumulative Distribution
73
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 5000 10000 15000 20000 25000 30000
0e+
004e
−05
8e−
05
Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●
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●●●●●●●●●●●●●
●●●●●●
●●●●
●●●●
●●●
●●●●
●●●
●●●●
●●●● ●
● ● ● ●
● ● ●● ● ●
● ●
0 10000 20000 30000 40000 50000
050
0015
000
2500
0
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
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●●●●●●●●
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●●●●●●●●●●●
●●●●●●●●
●●●●●●●●● ●●●●
●●● ●●● ●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●● ●● ●●● ●●●● ●●● ●●● ●●
0 5000 10000 15000 20000 25000 30000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●●●●●●●●●●●●●
●●●●●●●● ●●●
●●●●●●●●●●●● ●●●
●●●●●●●
●●●● ●●●
●●●●●●●
● ● ●● ●●●●●●●●●●●●●
● ●●●●● ●●●●●●●●
● ● ●●●●●●●
●●●●● ●●●●●●●●●●●
●●●●●●●●●●
● ●●● ●●●●● ●● ●●● ●●●●●●●●●●●●●●
● ●●●●●●
●●● ●●●●●●
●●●●●●●●●●
●●●●●●●●
0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.22: RM Samples, Moderate Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
● ●●
●● ●
● ● ● ● ● ● ●
●
●
●
● ●●
●● ●
● ● ● ● ● ●
60%
70%
80%
90%
100%
1 2 3 4 5 6 7 8 9 10 13 15 16 17 26 29Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure A.23: RM Samples, Moderate Monthly Workload: Batch Size Empirical Cumulative Distribution
74
Histogram and theoretical densities
Inter−arrival Times [time units]
Den
sity
0 5000 10000 15000 20000 25000 30000
0e+
004e
−05
8e−
05
Fitted Distribution
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●
●●●●●●●●●
●●●●●●
●●●●●●●
●●●●●●
●●●●
●●●
●●●●●●
●●●●●
●●●●
●
●●
●●
●●
●●●
● ● ● ● ● ●
●● ●
● ● ● ● ●
●
0 10000 20000 30000 40000
050
0015
000
2500
0
Q−Q plot
Theoretical quantiles
Em
piric
al q
uant
iles
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●
●●●●●●●●●●●●●●●
●●●●●●●●●●●●
●●●●●● ●●●
●●●●●●
●●●●● ●●●●●● ●● ●● ● ●● ●●●● ● ●● ● ● ●● ●●● ●●●●●● ●●● ●●●
●● ●
0 5000 10000 15000 20000 25000 30000
0.0
0.2
0.4
0.6
0.8
1.0
Empirical and theoretical CDFs
Inter−arrival Times [time units]
CD
F
Fitted Distribution●●●●●●●●●●●●●●●●
●●●●●●
●●●●●●
●● ●●●●●●●●●● ●● ●●
●●●●
●●●●●
●●●●
●●●●●
● ● ●●●●●
●●● ●●
●●● ●●
●●●●●●●● ●●
● ●● ●●● ●●●
●●● ●●
●●● ●●
●●●●
● ●●●●●●
●●●●●●●●●●●
●●●●●●●
0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
P−P plot
Theoretical probabilities
Em
piric
al p
roba
bilit
ies
Figure A.24: RM Samples,High Monthly Workload: Density Histogram, Q−Q & P − P plots
●
●
●
●●
●●
●●
● ● ● ● ● ● ● ●
●
●
●
●●
●●
●●
● ● ● ● ● ● ●
60%
70%
80%
90%
100%
1 2 3 4 5 6 7 8 9 10111213 17 24 30 60Batch Size
Cum
ulat
ive
Pro
babi
lity
Figure A.25: RM Samples,High Monthly Workload: Batch Size Empirical Cumulative Distribution
75
76
