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Управління проектами
©
A. Oganov, V. Gogunsky, O. Sherstyuk
13
УДК 005.8
Andrey Oganov
Master of project management, certified project management professional (PMP PMI & IPMA C),
Deputy Chief of service on operational management major ammonia pipeline, ORCID: 0000-0002-2492-2654
Ukrainian state company ”Ukrkhimtransamiak”, Kiev
Viktor Gogunsky
Doctor of Technical Sciences, Professor, Head of Department of Vitality protection systems management,
ORCID: 0000-0002-9115-2346
Odessa national polytechnic university, Odessa
Olga Sherstyuk
Graduate student, ORCID: 0000-0002-0482-2656
Odessa national polytechnic university, Odessa
ANALYSIS OF WORK-LOAD RATE OF PORTFOLIO MANAGER
BY MEANS OF MARKOVIAN MODEL OF STATES
Abstract. Current conditions of most project-oriented businesses based activities are related to the
implementation of projects requires the management of these companies develop and apply appropriate
procedures, methods and management techniques. The complexity of using classical approaches arises
from the fact that the activities of design organizations is in many ways a unique non-recurring process.
The practice of these companies shows that much attention from their owners paid not only to the global
strategic objectives, but the current results of operations. In real situations, work portfolio management
takes place in a high degree of uncertainty: the time of admission of projects, time and costs of their
implementation, as well as other factors are random variables with specified or unknown distribution laws.
On the basis of the standard portfolio management Project Management Institute USA (PMI) analyzed the
portfolio management process using Markov chains for discrete states of the system. Identified processes
(state) in which the portfolio manager is busy most of the time. Markov model state changes to determine
the loading of a portfolio manager at various stages of portfolio management, which makes it possible to
use these data in determining the KPI project managers when evaluating their work.
Keywords: project; portfolio management; team; project management office; Markov’s chain;
transition probabilities
Problem statement
Year by year С-level managers at the enterprises
pay more attention to the quality of portfolio selection
and management. In the situation of scarcity of
resources it is vital for the entities not only to do
projects "right" so to timely achieve the results, but also
to launch the "right" projects at the proper time. For this
purpose, entities are recommended to create the Project
Management Office (PMO) [1].
Whether those PMO – whose responsibility is to
bring projects to success – have been introduced at the
enterprise or not, or better portfolio management is
achieved through appointment of certain managers, the
success of a portfolio depends on the level of expertise
of the portfolio managers as well as of the level of
maturity of the organization in project management.
The size of portfolios depends on the size of the
organization itself, be that the general number of
projects and works or their value. Therefore when the
size of a portfolio is insignificant, the portfolio manager
should not be appointed from among designated
managers, but someone from among middle rank
managers to combine his regular duties with portfolio
managing activities. In this circumstance the CEO or
CIO of the entity wants to be sure that his portfolio
manager has a full work-load and effectively fulfills the
duties, to justify receiving "good" salary.
Modern companies have been long using key
performance indicators (KPI) for the purpose of
motivation for their employees, and for determining the
size of bonuses at successful performance of work.
To define KPI for portfolio managers it does
necessary to have the idea of approach to portfolio
management as such, the knowledge of necessary
processes of portfolio management; understand what
they deal with, why and for how long they are engaged
in certain processes.
Analysis of the recent publications
In order to develop successfully the companies
need not only to render high quality services or make
high quality production, but also to improve and
modernize them, to create new services and products,
Управління розвитком складних систем (22 – 2015) ISSN 2219-5300
14
gaining competitive advantage through innovations. For
this purpose it is necessary to launch programs and
projects which will yield expected results. This in turn
requires having the staff of managers at hand who are
capable to manage programs and projects well. Besides,
a set of conditions is to be created in the organizations
and proper environment attained for successful
implementation of projects, seeking to bring the
company project management into maturity [2].
The recent study has shown [3-6] that the majority
of companies owe their success to all-round
implementation of PMO which are reporting directly to
C-level managers and “communication-up” is sustained
by project managers and resource managers.
Community of Practitioners of PMI together with PMO
Subject Matter Experts (SME) have distinguished 5
kinds of PMO structures as follows:
1. Organizational Unit PMO/ Business Unit PMO/
Divisional PMO/ Departmental PMO; 2. Project-
Specific PMO/ Project Office/ Program Office;
3. Project Support/ Services/ Controls Office or
PMO; 4. Enterprise/ Organization-wide/ Strategic/
Corporate/ Global PMO; 5. Center of Excellence/
Center of Competency [7]. The PMO highest level that
returns the highest dividends to the enterprises is
Strategic PMO.
Of course, implementation of Strategic PMO can
run into opposition from heads of divisions, project
managers, and the staff of existing structures motivated
by personal, mercantile interests of certain employees
[8]. But there are ways of mitigation of Strategic PMO
implementation at the enterprise with use of tools of the
theory of constraints [9, 10].
At the enterprise where Strategic PMO is being
introduced, all processes of preparation, definitions,
prioritization of portfolios of the enterprise are
employees’ concern and responsibility. Otherwise
portfolio manager should be appointed, who will be
responsible for that. In both cases the success of a
portfolio depends on the correct application of portfolio
management processes which are recommended in the
form of good practices by professionals from all over
the world being the attachments to PMI portfolio
management standards [11]. Under the auspices of
International Organization of Standardization (ISO),
special committee ISO/TC 258 is established to create
international standards Project and Programme Portfolio
Management (ISO/DIS 21502) and Guidance on
governance of projects, programmes and portfolios
(ISO/WD 21503). Most probably, in likelihood with
standard for project management ISO 21500 the above
mentioned standards will become adaptation of the
version of ANSI standards of PMI to the international
ISO standard.
PMI standards being the basis for training and
certifying experts in 170 countries of the world, ISO
standards represent the adapted version of PMI
standards.
Therefore it would be relevant to study the
measure of portfolio manager with a view to application
in practice of portfolio management processes as per
PMI standard [11] which is given in table 1.
Research objective
The purpose of this research is to create a model of
portfolio manager work-load at different stages of
portfolio management processes according to the
standard [11] with application of Markovian chains for
further use with KPI. At the same time the obligatory
requirement is the compliance with the specialty passport
according to the recommended directions listed in [12].
Table 1 – Portfolio Management Process Groups and Knowledge Areas Mapping
Knowledge Areas Process Groups
Defining Process Group Aligning Process Group Authorizing and
controlling Process Group
Portfolio Strategic
Management 4.1 Develop Portfolio
Strategic Plan
4.2 Develop Portfolio Charter
4.3 Define Portfolio Roadmap
4.4 Manage Strategic
Change
Portfolio Governance
Management 5.1 Develop Portfolio
Management
5.2 Define Portfolio
5.3 Optimize portfolio 5.4 Authorize Portfolio
5.5 Provide Portfolio
Oversight
Portfolio Performance
Management 6.1 Develop Portfolio
Performance Management
Plan
6.2 Manage Supply and
Demand
6.3 Manage Portfolio Value
Portfolio
Communication
Management
7.1 Develop Portfolio
Communication
Management Plan
7.2 Manage Portfolio
Information
Portfolio Risk
Management 8.1 Develop Portfolio Risk
Management Plan 8.2 Manage Portfolio Risks
Управління проектами
15
Discussion
Markovian chains for definition of probabilities of
conditions in various systems were described by different
researchers in their articles [13-17]. Prior to begin our
research we will display in fig. 1 the diagram of portfolio
management in the form of transitions during interaction
of the processes described in the standard [11].
We will consider system S in fig. 1 which can be
with some probability of P(k) in one of conditions of S
i
{i=1, 2, …, 17} and in certain (discrete) time points of
t
k
{i=1, 2, …, k} to pass from a condition of S
i
into
condition of S
k
with probability of P
ik
*P
i
.
Casual process which proceeds in system S is
called Markovian if it possesses the following property:
for each time point of t
0
probability of any condition of
system in the future (at t > t
0
) depends only on its state
in the present (at t = t
0
) and doesn't depend on when and
how the system came to this state (i.e. how the process
developed in the past). The process that take place in the
system can be presented as a sequence (chain) of events
called Markovian chain where for each step the
probability of transition from any condition of S
i
to any
condition of S
j
does not depend on when and how the
system came to a condition of S
i
.
We will display the system from fig. 1 by means of
the directed graph in fig. 2, where S
i
is vertices of the graph
corresponding to certain conditions (processes) of the
system: {(4.1) → S
4
; (4.2) → S
6
; (4.3) →S
5
;
(4.4) → S
6
;
(5.1) → S
8
; (5.2) → S
10
;
(5.3) → S
9
;
(5.4) →S
13
; (5.5)
→ S
11
; (6.1) → S
7
; (6.2) → S
12
; (6.3)→ S
3
; (7.1) → S
14
;
(7.2) → S
15
; (8.1) → S
16
; (8.2) → S
17
;}.
Figure 1 – Diagram of portfolio management
The vertices are connected between themselves by
focused arches (edges of the graph), representing the
directions of transitions between conditions of the
system (processes). Thus for transformation scheme of
states in a Markovian chain from fig. 1 we need to add
possibility of system’s "delay" in each of conditions of
Si {i=1, 2, …, 17} in the form of additional
communications πi.i.
The outward arrows proceeding from vertices of
graph mean probability of transition from current state
of S
i
, and inward arrows represent probability of
transition to this condition of S
i
.
Figure 2 – Directed graph of a Markov's chain
Управління розвитком складних систем (22 – 2015) ISSN 2219-5300
16
The outward arrows proceeding from vertices of
graph mean probability of transition from current state
of S
i
, and inward arrows represent probability of
transition to this condition of S
i
.
Direct graph of the system with 17 vertices can be
presented in the form of a matrix 17×17 which elements
are probabilities of transitions of π
ij
between vertices of
the graph. This kind of matrix is called a matrix of
transitional probabilities. Elements of the matrix have to
meet the following conditions:
10
ij
≤
π
≤
(1)
1
1
=
∑
=
n
j
ij
π
(2)
Condition (1) – usual property of probabilities and
condition (2) means that the system S certainly either
passes from any condition of S
i
into other state, or
remains S
i
. The π
ij
elements of a matrix of |π
ij
| represent
probabilities of transitions in system during one step.
In Markovian chain with time change (k step)
distribution of probabilities of states {p1(k), p2(k)...
p
m
(k)} varies. The distribution of probabilities on any
following (k+1) step is calculated with the well- known
formula of a total probability. The common decision of
Markovian chain with 17 states looks as follows:
,
...
...
.......
.......
.......
...
...
T
)(
)(
.
.
.
)(
)(
T
)1(
)1(
.
.
)1(
)1(
17.1716.172.171.17
17.1616.162.161.16
17.216.22.21.2
17.116.12.11.1
17
16
2
1
17
16
2
1
ππππ ππππ
ππππ ππππ
⋅=
+
+
⋅+
+
kp
kp
kp
kp
kp
kp
kp
kp
where T is a transposing symbol.
Each raw of a matrix ||πij|| is to satisfy the
following condition:
},17,,2,1{,1
17
1
L==
∑
=
i
j
ij
π
(3)
where m = 17 is a number of possible conditions of
system.
The sum of probabilities of conditions of p
i
(k) on
each step of k is equal to:
,1)(
1
=
∑
=
m
i
i
kp
(4)
where p
i
(k) – probability of i state on k step.
For a transition matrix we will determine values of
conditional probabilities through expert method, by
obtaining data from portfolio managers who apply
processes of the standard [11] in their work. As a result
we will receive a matrix in fig. 3.
Matrix of transitions allows developing a model of
Markovian chain with which to carry out the forecast of
a condition of the system for some steps onward. The
results of the modeling a portfolio management system
is given in fig. 4 where it is possible to determine a
work-load of portfolio manager at different stages of
portfolio management per each process.
At the initial stages of management of a portfolio
(up to 3-rd step on model) most part of portfolio
manager’s time is spent on developing strategic
portfolio plan р4 (k), defining portfolio road map р5(k)
and developing portfolio charter р6(k).
At later stages (from the 10th step on model) most part
of time is consumed by the following processes on
decrease: р10(k) – define portfolio; р13(k) – authorize
portfolio; р9(k) – optimize portfolio; р15(k) – manage
portfolio information; р11(k) – provide portfolio
oversight; р12(k) – manage supply and demand; р17(k)
– manage portfolio risks.
Figure 3 – Matrix of transition probabilities with estimates of expert
Управління проектами
17
Figure 4 – Change of probabilities of conditions
of portfolio management system
As is known, the transition probability matrix shows
the level of technological maturity of the organization
[18, 19]. In relation to the portfolio team – is its potential
characteristic or property to perform the work of the
portfolio of projects in accordance with existing
environmental conditions and the level of competence of
team players [20]. In other words, different portfolio
teams will have different transition matrices for the same
portfolio of projects. This is a consequence of the known
law S.D. Bushuev's [14]. Therefore, if the transition
matrix |π
ij
| defined during the portfolio, long before its
closure can be assessed by the portfolio activity.
Conclusions
The presented Markovian model of change of
states allows defining the measure of time portfolio
manager spends on different steps of portfolio
management. This will give the chance to use those data
when determining KPI of project managers at an
assessment of their work.
____________________________________________________________________________________________
References
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Article received editorial board 07.04.2015
Reviewer: Doctor of Engineering, Professor Rudenko S.V., Odessa National Maritime University, Odessa.
Управління розвитком складних систем (22 – 2015) ISSN 2219-5300
18
Оганов Андрій Валерійович
Магістр, сертифікований проектний менеджер PMP PMI USA та IPMA Level C UPMA,
Заступник начальника служби оперативного управління магістрального аміакопроводу, ORCID: 0000-0002-2492-2654
Державне підприємство «Укрхімтрансаміак», Київ
Гогунський Віктор Дмитрович
Доктор технічних наук, професор, завідувач кафедри управління системами безпеки життєдіяльності, ORCID: 0000-
0002-9115-2346
Одеський національний політехнічний університет, Одеса
Шерстюк Ольга Ігорівна
Аспірант кафедри управління системами безпеки життєдіяльності, ORCID: 0000-0002-0482-2656
Одеський національний політехнічний університет, Одеса
АНАЛІЗ НАВАНТАЖЕННЯ МЕНЕДЖЕРА ПОРТФЕЛЯ ПРОЕКТІВ
ЗА ДОПОМОГОЮ МАРКОВСЬКОЇ МОДЕЛІ СТАНІВ
Аннотація. Як правило робота портфельного менеджменту відбувається в умовах високого ступеня
невизначеності: моменти надходження проектів, час і витрати їх виконання, а також інші фактори є випадковими
величинами із заданими або невідомими законами розподілу. Дана стаття присвячена розвитку методів сценарного
управління для поточного управління проектно-орієнтованим підприємством шляхом використання марковських
моделей. На основі стандарту з управління портфелями інституту проектного менеджменту США (PMI) виконано
аналіз процесів управління портфелями за допомогою марковських ланцюгів для дискретних станів системи. Виявлено
процеси (стани), в яких керівник портфеля проектів зайнятий більший період часу.
Ключові слова: проект; управління портфелем; команда; офіс управління проектами; ланцюг Маркова;
перехідні ймовірності
Оганов Андрей Валерьевич
Магистр, сертифицированный проектный менеджер PMP PMI USA и IPMA Level C UPMA,
Заместитель начальника службы по оперативному управлению магистрального аммиакопровода, ORCID: 0000-0002-
2492-2654
Государственное предприятие «Укрхимтрансаммиак», Киев
Гогунский Виктор Дмитриевич
Доктор технических наук, профессор, заведующий кафедрой управления системами безопасности жизнедеятельности, ORCID:
0000-0002-9115-2346
Одесский национальный политехнический университет, Одесса
Шерстюк Ольга Игоревна
Аспирант кафедры управления системами безопасности жизнедеятельности, ORCID: 0000-0002-0482-2656,
Одесский национальный политехнический университет, Одесса
АНАЛИЗ ЗАГРУЗКИ МЕНЕДЖЕРА ПОРТФЕЛЯ ПРОЕКТОВ
С ПОМОЩЬЮ МАРКОВСКОЙ МОДЕЛИ СОСТОЯНИЙ
Аннотация. В реальных ситуациях работа портфельного менеджмента протекает в условиях высокой степени
неопределенности: моменты поступления проектов, время и затраты их выполнения, а также прочие факторы
являются случайными величинами с заданными или неизвестными законами распределения. На основании стандарта по
управлению портфелями института проектного менеджмента США (PMI) выполнен анализ процессов управления
портфелями с помощью марковских цепей для дискретных состояний системы. Выявлены процессы (состояния), в
которых руководитель портфеля проектов занят большую часть времени.
Ключевые слова: проект; управление портфелем; команда; офис управления проектами; цепь Маркова;
переходные вероятности
______________________________________________________________________________________________________
Link to publication
APA Oganov, A.V., Gogunsky, V.D., & Sherstyuk, O.I. (2015). Analysis of work-load rate of portfolio manager by means
of markovian model of states. Management of Development of Complex Systems, 22 (1), 13 – 18.
ГОСТ Оганов, А.В. Аналіз навантаження менеджера портфеля проектів за допомогою
марківської моделі станів
[Teкст] / А.В. Оганов, В.Д. Гогунський, О.І. Шерстюк // Управління розвитком складних систем. – 2015.
– № 22 (1). – С. 13 – 18.
