Analytical Observations of Work Breakdown
Structure Parameters
Brendan Robinson
University of New South Wales
brendan.robinson@student.adfa.edu.au
Michael Ryan
Alireza Abbasi
University of New South Wales
University of New South Wales
M.Ryan@adfa.edu.au
A.Abbasi@adfa.edu.au
ABSTRACT
The work breakdown structure (WBS) is the foundation to develop robust and resilient resource, time
and cost plans and estimates. Despite the WBS being a practised mechanism for project planning and
estimating, what is not understood is how, in particular, the width and depth parameters of the WBS
affect project schedule duration. This paper investigates the influence of depth and width of the WBS
on project schedule duration by leveraging graph theory which represents the relationships between each
work package using an adjacency matrix (AM). Initial analytical observations show that increasing the
depth or the width of the WBS increases the likelihood of a reduced project schedule duration. However,
these improvements to the project schedule duration reduce with progressive decomposition and appear
to diminish after level 6.
INTRODUCTION
The WBS is a fundamental technique in project planning. The concept was initially suggested by
Malcolm, Roseboom, Clark and Fazar (1959) and standardised by the United States Department of
Defense (1968). Since its inception, the WBS has become a prevalent tool for deriving the project
deliverables, defining scope, and providing a framework for identifying all associated work. This is
achieved through the hierarchical sub-division of the project deliverables into progressively smaller and
increasingly defined scope elements terminating with the work packages (WPs). WPs encompass a set
of activities, which is not included in the WBS but is a foundation for determining the schedule and
budget.
The hierarchical organisation of the WBS is homogenous with a tree which is simply a collection of
vertices and edges forming a connected acyclic graph. Sedgewick and Wayne (2011) defined the level
within a tree to be the number of vertices between any given vertex and the root vertex. The depth of a
tree is the maximum number of levels within the tree. Accordingly, the depth of a WBS represents the
maximum direct number of elements within the WBS between the WP and the root element. The width
of the WBS is the total number of WPs, i.e., total number of leaves of the tree.
Determining a definitive level of detail within a WBS is not conclusive. Guidance provided by Haugan
(2008) indicates WPs should be established at a level that allows reasonable definition and estimation
of the underlying activities and can be assigned unequivocally to a responsible organisational unit.
Lavold (1988) and Globerson (1994) indicated between four and six levels is suitable for WBS’
developed for major projects; with the implication the desired number of levels is associated with
effective management. Kerzner (2009) also mentioned the most common WBS consists of five levels
with the WPs situated at level five. However, Kerzner (2009) further clarifies WPs can exist at any level
within the WBS below the first level.
Whilst the WBS is a practised mechanism for project planning and estimating, its importance has not
been afforded analytical investigation or examination. What is not understood is how the characteristics
of the WBS influence project planning and estimation and, in particular, how the width and depth
parameters of the WBS affect schedule duration.
Increasing the depth or width of the WBS is expected to reduce the duration of the project schedule. As
the WBS increases in width or depth, the quantity of WPs increases, which reduces the duration of each
WP and increases the number of combinations in which the WPs can be sequenced.
In order to undertake analytical examination of the WBS depth and width parameters, a set of schedules
is produced at each level of the WBS. Simulating each schedule within the set produces a distribution
of schedule durations. Observing the variation with the durations at each level of the WBS demonstrates
the relationship between the WBS and schedule duration. Decomposing the WBS to emphasise depth
or width parameters enables measuring the effect each parameter has on project schedule duration.
METHOD
A model of the WBS and schedule was developed to simulate the effect the WBS width and depth have
on schedule duration. The depth and width of the WBS are the independent variables and the duration
of the project schedule is the dependent variable. The model was developed and simulated using
MATLAB (MATLAB 2015b).
Simulation of the WBS model was approached by defining the initial WP level and progressing toward
the root level of the WBS—bottom-up. A set of project schedules was derived for the set of WPs
associated with each defined WP level. Each WP was assumed to contain a single activity to simplify
the translation between the WBS and project schedule—WP and activity are identical.
A project schedule is interchangeable with a directed acyclic graph (DAG) which was represented using
an adjacency matrix (AM). The creation of adjacency matrices was the foundation for collecting the
data set, which was achieved by producing and mapping a binary vector into the form of a matrix.
Enumerating all possible valid matrix combinations was achievable for small adjacency matrices.
However, as the dimensions of the matrix increased, enumerating all possible valid combinations
became impossible. Overcoming this limitation was achieved by randomly sampling the population of
possible valid matrix combinations. The random samples were collected by using the Single Instruction
Multiple Data oriented Fast Mersenne Twister Pseudorandom Number Generator (Saito and Matsumoto
2008) to produce the binary vector. The number of samples that was collected was determined by the
time period in which the algorithm was permitted to execute.
There was a chance with each randomly produced AM that the same AM had been previously produced.
To avoid duplication, the data set was searched using a binary search algorithm. If the AM was detected
within the data set, it was excluded and if not the final search position within the data set was saved to
support storing the current AM once the algorithm completes.
Not all adjacency matrices produce valid DAGs. Only matrix combinations that represent minimum
equivalent DAGs, those that do not include redundant edges, are valid. All AMs were tested and those
that did not represent a minimum equivalent DAG were excluded from the data set.
The AM associated with the next level, progressing toward the root element of the WBS was created
from the AM associated with the current level. The AM associated with the current level of the WBS
is compressed by a constant factor to create the AM for the next level.
Activities within a proper project schedule have at least one predecessor and at least one successor. The
exception is the ‘start’ and ‘finish’ milestones, which do not have a predecessor and a successor
respectively. This was simulated by adding two null vertices; one at the start and one at the end of the
AM. An edge was created between the newly created front null vertex and all vertices that did not have
a predecessor—vertices with an in-degree equal to zero. Similarly, an edge was created between all
vertices that did not have a successor and the newly created end null vertex —vertices with an outdegree equal to zero. The null vertices ensure all vertices are connected and all paths through the DAG
commence and complete with a null vertex.
Each vertex has an associated duration collectively defined in a vector. The exception is the null start
and finish vertices which do not have a duration and accordingly the duration in the vector is zero. The
duration vector and the AM are required to determine the longest path through the DAG when the
duration of each vertex is considered. The longest path, alternatively the critical path when referencing
a project schedule, sets the minimum duration of the project schedule.
Adjacency Matrix and Binary Vector
The fundamental requirement of a DAG is each edge has an orientation and there are no cycles. The
orientation of the edge establishes the precedent relationship between the two vertices and mirrors the
finish-start relationship in a precedent project schedule. A cycle exists when a vertex is directly or
indirectly both a predecessor and a successor of itself—this is impossible in a project schedule.
The relationships between vertices are captured in the AM by either a one or a zero. If vertex vn precedes
vertex vn+1, then a one will exist in the AM at the intersection of the row representing vertex vn and the
column representing vertex vn+1; this relationship is portrayed in Figure 1. Conversely, if the relationship
were to be reversed, then a one will exist in the AM at the intersection of the row representing vertex
vn+1 and the column representing vertex vn.
vn
vn+1
v1 v2
vn vn+1
v1
v2
0 0
0 0
0 0
0 0
vn
vn+1
0 0
0 0
0 1
0 0
Figure 1. Vertex Relationship Represented in the AM
To avoid cycles, a consistent approach to labelling the vertices is applied —topological ordering. A set
of vertices labelled {v1, v2, ... , vn, vn+1} follow the constraint vn+1 cannot precede vn and vn cannot precede
vn. This constraint, depicted in Figure 2, is captured in the AM through prohibiting a one on the diagonal
or below the diagonal of the AM.
v1 v2
vn vn+1
v1
v2
0 e
0 0
e e
e e
vn
0 0
0 0
0 e
0 0
vn+1
Figure 2. Topological Ordering Implemented in the AM
Limiting the relationships in the AM to matrix elements above the diagonal supports a reduced binary
vector required to produce the AM. An n×n AM, where n is the number of vertices, requires a binary
vector length of n2. Limiting the binary vector to satisfy the matrix elements above the diagonal reduces
the binary vector length to Equation (Eq.) 1. The Pseudorandom Number Generator was used to
randomly select a one or a zero for each element of the binary vector.
Binary Vector Length =
n(n - 1)
2
(1)
The binary vector was mapped to the AM commencing with the first element in the binary vector and
completing with the last. The binary vector is mapped to the AM columns commencing with the second
column and completing with column n. Only the first element from the binary vector is mapped to the
second column of the AM. The number of elements from the binary vector mapped to the AM
increments by one for each successive column; concluding with n−1 elements mapped to column n.
The diagonal elements of the AM and the elements of the AM below the diagonal are set to zero.
Adjacency Matrix Reduction
Simulation of WBS decomposition is implemented in reverse. The initial WP level contains the
maximum number of WPs which is reflected in an AM with the maximum number of vertices. The
maximum number of vertices is determined in Eq. 2 where f (f > 1) is the factor and l (l > 0) is the
number of levels in the WBS.
Maximum Vertices =f(l - 1)
(2)
The factor controls the size of the decomposition between levels of the WBS. The first level of the WBS
will always be a single element f0. The second level of the WBS will be f1; simulating the decomposition
of the root element into f WPs and an f×f AM. The third level of the WBS will include f2 WPs simulating
the decomposition of each element of the second level of the WBS by the factor. The third level of the
WBS produces an f 2×f 2 AM.
Transitioning the AM from one level of the WBS to the next expands a single element of the AM into
an f×f sub-matrix. How a single zero or one translates into an f×f sub-matrix of ones and zeros is a
challenge and is simple to achieve in reverse —AM reduction.
Reversing the decomposition of the WBS applies the same principle. An f×f sub-matrix within the AM
is reduced to a single matrix element in the AM associated with the next level of the WBS—depicted in
Figure 3. A single or multiple one in an f×f sub-matrix element will translate to a one in the
corresponding matrix element on the reduced AM; otherwise the corresponding matrix element in the
reduced AM will be zero.
v1
v2
v3
v4
v5
v6
v7
v8
v1
0
0
0
0
0
0
0
0
v2
0
0
0
0
0
0
0
0
v3
0
0
0
0
0
0
0
0
v4
0
0
0
0
0
0
0
0
v5
0
0
0
0
0
0
0
0
v6
0
0
0
0
0
0
0
0
v7
0
0
0
0
0
0
0
0
v8
0
0
0
0
0
0
0
0
v1
v1 0
v2 0
v3 0
v4 0
v2
0
0
0
0
v3
0
0
0
0
v4
0
0
0
0
v1 v2
v1 0 0
v2 0 0
Figure 3. AM Reduction Visualisation
The upper diagonal constraint applies to the reduced AM. The reduced AM is not valid if a matrix
element on the diagonal or below the diagonal is set to one. To avoid this, a test was completed during
the reduction and if an element on the diagonal or below the diagonal was set to one, then it would be
reset to zero. This applies to further reductions of the AM.
Furthermore, each reduced AM must represent a minimum equivalent DAG. If a reduced AM is not a
minimum equivalent DAG, it is discarded and all derivatives are discarded.
Each level of the WBS must produce a valid AM to be included in the data set.
Minimum Equivalent Directed Acyclic Graph
Producing all possible AM combinations will include AMs that produce a DAG that includes redundant
edges. In a set of vertices {v1, v2, v3} an edge connects v2 and v3 and two edges connect v1 and v2 and v1
and v3—depicted in Figure 4. In this circumstance, the edge connecting v1 and v3 is redundant. In the
context of a project schedule, the dependency exhibited between v3 and v2 naturally includes a
dependency on v1 because v3 is reachable from v1 through v2. The same outcome is achieved if v3 is
simply connected to v2 which is simply connected to v1—depicted in Figure 4. The latter representation
is considered the minimum equivalent graph which represents the minimum set of edges without
affecting the reachability properties of the DAG. To achieve this, the algorithm initially developed by
Moyles and Thompson (1969) and later revised by Hsu (1975) is used to identify minimum equivalent
graphs. To test if a graph is a minimum equivalent, the algorithm refines the AM to represent the
minimum equivalent graph. The refined AM is then compared to the initial AM and if there is a
difference the AM is discarded.
v1
=
v2
v1
v2
v3
v3
Figure 4. Minimum Equivalent DAG Visualisation
Dummy Vertices (Start and Finish Milestones)
To enable the correct calculation of the DAG, vertices in the directed graph require at least one
predecessor and at least one successor vertex. The exception to this is the start milestone which does
not have a predecessor and the finish milestone which does not have a successor. Milestones are zero
duration activities. Both start and finish milestones are added to the AM as a null vertex with a zero
duration value in the duration vector. The start milestone provides a predecessor to all vertices that lack
a predecessor and similarly the finish milestone provides a successor for all vertices that lack a successor.
Two additional rows and columns are added to the AM to represent the start and finish milestones.
Vertices that lack a predecessor will have nil entries in the corresponding column of the AM representing
the vertex. Similarly, vertices that lack a successor will have nil entries in the corresponding column of
the AM representing the vertex.
Iteratively summing each column of the AM and identifying those columns that return a sum of zero
indicates no predecessor relationship for that vertex. Adding an entry in the corresponding position in
the first row will create a relationship between the start milestone and that particular vertex. Reversing
the operation and iteratively summing each row of the AM and identifying those rows that return a sum
of zero indicates no successor relationship for that vertex. Adding an entry in the corresponding position
in the last column will create a relationship between the finish milestone and the particular vertex.
Duration Vector
The duration of each vertex is defined in the duration vector d. The length of the duration vector is
determined by Eq. 3 and is equivalent to the number of vertices determined for each level of the WBS
plus two null vertices.
Duration Vector Length = f(l - 1) + 2
(3)
The sum of all vertex durations is normalised to 100 units. The maximum duration that can be associated
with the DAG is fixed and will be 100 units. The minimum duration that can be associated with the
DAG is variable and will be the represented by the vertex with the longest duration.
The duration of each null vertex is always zero. The duration of each vertex is set by a ratio r vector
which is used to divide the vertices in the DAG to form the new set of vertices. The simulation algorithm
applies reverse decomposition which requires the duration vector to be determined in advance for each
level of the WBS.
Longest Path
The longest path through the DAG is determined using the shortest path algorithm developed
independently by Ford (1956), Bellman (1958), and Moore (1959) modified to determine the longest
path. The modification includes two changes. The initialisation process in the original shortest path
algorithm sets the distance for each vertex to equal infinity. The change to the longest path algorithm
sets the distance for each vertex to equal zero. The inequality within the original shortest path algorithm
tests if the path to vertex is less than previous paths. Changing to the longest path algorithm, the
inequality is changed to test if the path to the vertex is greater than the previous paths. The longest path
through the vertex is identified as the vertex with the greatest duration.
Data Collection and Analysis
The AM and the longest path duration is collected and stored in the data set for each valid DAG. The
difference between the longest path of the DAG and the longest path of the DAG of the root element is
also captured and stored in the data set—difference duration.
Simple statistical analysis of the data set is limited to the difference duration and includes determining
the maximum, minimum, mean, and mode and standard deviation measures.
RESULTS
Two simulations were completed using the method described. The first simulation sought to understand
how the depth (i.e., independent variable) parameter of the WBS affects project schedule duration (i.e.,
dependent variable). The second simulation sought to understand how the width (independent variable)
parameter of the WBS affects schedule duration (dependent variable).
The binary vector length required to produce a 32 vertex DAG, in both depth and width simulations, is
496 elements and creates a sample space with 2496 different possible DAGs. The time required to
calculate all valid DAGs from the sample space was impossible to achieve. Subsequently, samples were
collected from the sample space for a period of 720 hours (30 days).
The sample space for a DAG with two vertices is 21 outcomes, the sample space for a DAG with four
vertices is 26 outcomes and for eight vertices is 228 outcomes. In these instances, sampling the sample
space over the designated time period achieved every possible outcome within the sample space. There
are no sampling errors associated with the data collected for these vertices.
DAGs with 16 and 32 vertices have sample spaces with 2120 and 2496 outcomes respectively. In these
instances, collecting enough samples to achieve every possible outcome within the sample space was
difficult within the sampling time period. Consequently, there were potential sampling errors within the
data collected for these vertices.
Five separate duration vectors were calculated and applied to each valid sample collected during the
simulation time period. The duration vectors were calculated using 5:5, 4:6, 3:7, 2:8, and 1:9 ratios.
The duration of each DAG produced at each level of the WBS was compared to the duration of the
single DAG associated with the root element. The difference between the two directed graph durations
was stored in the data set—difference duration.
Basic statistical analysis was completed for the data sets produced during each simulation. Charts
depicting the mode, mean and standard deviation for each simulation have been provided below.
The vertical axis in each figure presents the duration difference ranging between 0 and -100 time units;
the negative vertical axis values represent a reduction in the schedule duration. A result of 0 time units
indicates no difference between the durations of the DAG at the root element and at each level of the
WBS. Conversely, a result of -100 time units indicates a total difference between durations of the DAG
at the root element and at each level of the WBS.
The horizontal axis in each figure presents the WBS level described by the number of vertices associated
with the DAG associated with the level. A logarithmic base 2 scale was used for the horizontal access.
Depth Simulation
The depth parameter is isolated by limiting the division between each level of the WBS to a minimum
of two. The simulation commenced with the WPs situated on level six of the WBS which associates
with a DAG with 32 vertices.
The mode, mean and standard deviation for the depth simulations is presented in Figure 5, Figure 6 and
Figure 7 respectively:
Mode Duration
0.00
-10.00
-20.00
-30.00
-40.00
-50.00
-60.00
-70.00
-80.00
-90.00
-100.00
1
2
4
8
16
32
Vertices
Ratio 5:5
Ratio 4:6
Ratio 3:7
Ratio 2:8
Ratio 1:9
Mean Duration
Figure 5. Comparison of Schedule Mode Durations between Successive Levels and the First
Level of a WBS for WBS Depth Simulations
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
1
2
4
8
16
32
Vertices
Ratio 5:5
Ratio 4:6
Ratio 3:7
Ratio 2:8
Ratio 1:9
Figure 6. Comparison of Schedule Mean Durations between Successive Levels and the First
Level of a WBS for WBS Depth Simulations
Duration Standard Deviation
40
35
30
25
20
15
10
5
0
1
2
4
8
16
32
Vertices
Ratio 5:5
Ratio 4:6
Ratio 3:7
Ratio 2:8
Ratio 1:9
Figure 7. Comparison of Schedule Duration Standard Deviation between Successive Levels and
the First Level of a WBS for WBS Depth Simulations
Figure 5 and Figure 6 both demonstrate a reduction in the mode and mean durations of the DAGs as the
vertices increase. Figure 7 demonstrates that the standard deviation also reduces as the number of
vertices in the DAG increases.
Width Simulation
The width parameter is isolated by limiting to level two of the WBS and increasing the number of WPs
at level two. The simulation commenced with a set of two WPs and then increased to sets of four, eight,
16, and 32 WPs. The WPs directly correlated to the number of vertices in the DAG.
Mode Duration
The mode, mean and standard deviation for the width simulations are presented in Figure 8, Figure 9,
and Figure 10 respectively:
0.00
-10.00
-20.00
-30.00
-40.00
-50.00
-60.00
-70.00
-80.00
-90.00
-100.00
1
2
4
8
16
32
Vertices
Ratio 5:5
Ratio 4:6
Ratio 3:7
Ratio 2:8
Ratio 1:9
Figure 8. Comparison of Schedule Mode Durations between Successive Levels and the First
Level of a WBS for WBS Width Simulations
Mean Duration
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
1
2
4
8
16
32
Vertices
Ratio 5:5
Ratio 4:6
Ratio 3:7
Ratio 2:8
Ratio 1:9
Figure 9. Comparison of Schedule Mean Durations between Successive Levels and the First
Level of a WBS for WBS Width Simulations
Duration Standard Deviation
40
35
30
25
20
15
10
5
0
1
2
4
8
16
32
Vertices
Ratio 5:5
Ratio 4:6
Ratio 3:7
Ratio 2:8
Ratio 1:9
Figure 10. Comparison of Schedule Duration Standard Deviation between Successive Levels
and the First Level of a WBS for WBS Width Simulations
The results presented in Figure 8, Figure 9, and Figure 10 are similar to the results presented in the
figures connected to the depth simulations. Figure 8 and Figure 9 both demonstrate a reduction in the
mode and mean durations of the DAGs as the vertices increase. Figure 7 demonstrates the standard
deviation also reduces as the number of vertices in the DAG increases.
DISCUSSION
Notwithstanding the potential sampling errors associated with the larger vertex count, both depth and
width simulations demonstrate a reducing trend in the mode, mean and standard deviation measures,
exhibiting minor variation despite existing at different levels of the WBS.
The exception is the modal trend for both width and depth simulations which shows that the mode
associated with two and four vertices is the same. Two vertices produce a bimodal data set —21 possible
DAGs. The MATLAB mode function selects the smallest value in a multimodal situation. The
difference duration mode for each two vertex data sets will be zero when both vertices are in series and
will be the negative of the difference between 100 and the vertex with the longest duration when both
vertices are in parallel. The MATLAB mode function selects the latter because it is the smaller value.
Additionally, two vertices are the most common path length through the four vertex DAG, which
influences the longest duration mode through the DAG and subsequently the difference duration mode.
The longest duration through the DAG is formed by the two vertices with the longest durations when
the path length is two vertices in length. The two vertices with the longest durations are derived from
the vertex with the longest duration in the preceding two vertex simulation. The outcome is the
difference duration mode for two vertices and four vertices is the same.
This observation of the depth or width of the WBS does not directly influence the duration of the project
schedule duration. More precisely, the total number of vertices representing WPs does directly influence
the project schedule duration irrespective of the location of the WPs within the WBS.
The trends in Figure 5 to Figure 10 demonstrate the reduction of durations in a linear manner as the
number of vertices increase. However, once the logarithmic horizontal axis in each figure is considered,
the trend presents an exponential trend approaching a limit. It is pragmatic to appreciate that project
duration cannot reduce to or less than zero with progressive decomposition of the WBS. Consequently,
a reduction in project duration associated with the decomposition of the WBS must diminish and
approach a limit. The limit becomes recognisable within the range of 16 to 32 vertices. In relation to
the depth simulations, 16 and 32 vertices correspond to a WBS depth of five and six. Whilst not
conclusive, this observation correlates with the recommended number of WBS levels, i.e. six as
suggested by Lavold (1988) and Globerson (1994). This is apparent in Figure 5, Figure 6, Figure 8, and
Figure 9 and is consistent with changing WP durations.
The trend is consistent with variations to WP durations; although the quantum of the reduction
diminishes with increasing difference between WP durations. The greatest reduction was observed
when WPs have consistent —uniform— durations. Accordingly, the least reduction was observed when
WPs had significantly different durations. This result is due to the increasing probability that the longer
WP durations appear on the longest path and due to the nature of the WP length extending the longest
path.
The outcomes of the simulations need to be considered amidst limitations that potentially influence the
outcomes. The limitations are considered in two high level categories. The first category considers the
limitations of technology to complete simulations. The second category considers the limitations of the
model.
The Pseudorandom Number Generator is fundamental to producing a uniform distribution of AM, which
is a transformation of a randomly generated binary vector. Any statistical bias toward one or zero will
influence the number of relationships between vertices in the AM.
Large numbers of vertices are associated with significantly large sample space. The largest sample
space produced in the simulations was 2496 associated with 32 vertices. Further decomposition of the
WBS or decomposition of the WBS using a factor greater than two will further increase the sample
space. Increasing the sample space increases the time period to obtain a set of samples that represents
the sample space. Moreover, the demands on computer hardware in particular computer processing and
memory capacity is strained with large sample spaces.
The AM used in the simulation model represents precedent relationships between vertices; specifically
finish-start relationships. The finish-start relationship is the most common. The simulation model does
not consider start-finish, finish-finish, or start-start relationships or offsets. The inclusion of these
relationships increases the size of the sample space and varies the possible outcomes.
The simulation model implemented through the binary vector and the AM does not assume that any
particular vertex combination is more likely than another. Assuming a particular WP sequence is more
common will influence the outcome, for example the assumption that WPs are more likely to be linear
than parallel.
The simulation model does not consider resource constraints. Associating WPs with a limited number
of resources will limit the number of WPs that can be completed in parallel by a particular resource.
Future simulation models designed to explore the relationship between the WBS and project duration
will consider the limitations identified.
CONCLUSION
The relationship between the WBS and project schedule duration was examined using simulation. In
particular, the investigation focused on the effect the WBS depth and width parameters have upon
project schedule duration. The analysis of the data collected indicates that the difference between the
depth and the width parameters is negligible. Both parameters with the same number of WPs affect the
project schedule duration in a similar manner. Decomposing the WBS increases the number of WPs
which has an increasing likelihood of reducing the project schedule duration. However, the magnitude
of the reduction progressively diminishes as the number of the WPs increases.
ACKNOWLEDGEMENTS
Support has been provided through an Australian Government Research Training Program Scholarship.
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BIOGRAPHIES
Brendan Robinson
Brendan Robinson is a Project Manager within the Australian Defence industry and is a Doctor of
Philosophy candidate studying at the University of New South Wales (UNSW), Canberra. He holds a
Bachelor degree in Engineering and a Master’s degree in Project Management. He has been awarded
Chartered Professional Engineer (CPEng) status by Engineers Australia (EA) in electrical, information,
telecommunication and electronic engineering (ITEE), and leadership and management colleges.
Additionally, he has been established as a Certified Professional Project Manager (CPPM) by the
Australian Institute of Project Managers (AIPM). He has over 10 years’ experience in engineering and
project management supporting acquisition and sustainment projects.
A/Prof Michael Ryan
Associate Professor Mike Ryan is the Director of the Capability Systems Centre, University of New
South Wales, Canberra. He holds Bachelor, Masters and Doctor of Philosophy degrees in engineering.
In addition, he has completed two years formal engineering management training in the United
Kingdom. He has over 35 years of experience in communications engineering, systems engineering,
project management, and management. Since joining UNSW, he has lectured in a range of subjects
including communications and information systems, systems engineering, requirements engineering and
project management and he regularly consults in those fields. He is the author or co-author of 12 books,
three book chapters, and over 200 papers. He is a Fellow of Engineers Australia, a Chartered
Professional Engineer (CPEng) in electrical and ITEE colleges, a Senior Member of IEEE, a Fellow of
the International Council on Systems Engineering, and a Fellow of the Institute of Managers and
Leaders.
Dr Alireza Abbasi
Dr Alireza Abbasi is a lecturer with the School of Engineering and Information Technology, the
University of New South Wales (UNSW Australia), Canberra. He obtained his Doctor of Philosophy
from the University of Sydney in 2012, Master of Science at Seoul National University in 2008 and a
Bachelor of Science in Software Engineering at Isfahan University of Technology in 2002. Dr Abbasi
has written 1 book, 3 book chapters and over 45 technical journal and conference papers. His research
interest covers a wide range of topics in Management Science, Organisation and Network Science and
Information Systems Management.