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A Multi-Objective Optimization Model for Designing
Business Portfolio in the Oil Industry
Amir Kamran Kiamehr
Faculty of Management and Economics,
Department of Industrial Management,
Tarbiat Modares University, Tehran, Iran
Adel Azar
Faculty of Management and Economics,
Department of Industrial Management,
Tarbiat Modares University, Tehran, Iran
azara@modares.ac.ir
Mahmoud Dehghan Nayeri
Faculty of Management and Economics,
Department of Industrial Management,
Tarbiat Modares University, Tehran, Iran
Abstract—Designing a business portfolio is one of the key
decisions in developing corporate strategy. Most of the previous
models are either non-quantitative or financial with an emphasis
on optimizing a portfolio of investments or projects. This
research represents a multi-objective optimization model that
firstly, employs quantitative methods in strategic decision-
making, and secondly, quantifies and considers non-financial,
strategic variables in problem modeling. In this regard, links
between businesses within a portfolio have been classified into
four groups of market synergy, capabilities synergy, parenting
costs, and sharing benefits, and have been structured as a
conceptual model. Although the conceptual model can be applied
to various industries, it is formulated for designing the portfolio
of multi-business companies in Iran oil industry. The model has
been solved for three cases by NSGA-II algorithm and strategic
insights have been explored for different corporate types.
Keywords-corporate strategy; business portfolio; multi-objective
optimization; oil industry
I. INTRODUCTION
The historical trend about how business portfolios form
represents the tendency of companies to engage in diverse
businesses during the 50's to 80's and the emergence of large
multi-purpose companies; then, the trend reversed from the 80's
to now by focusing on a major and specialized business, or
ultimately a portfolio of “related” businesses [1]. Over the past
decades, how to define a business portfolio has been one of the
key issues in strategic planning for businesses. Studies in this
regard have been developed in areas such as diversification,
vertical integration, outsourcing, M&A, partnerships, and
allocation of resources among businesses [2]. The studies and
models in this area can be divided into two main groups. The
first group includes famous models such as GE/McKinsey
matrix and Boston Consulting Group growth/share matrix [3,
4]. They consider entering or not entering into a business with
limited and conceptual criteria such as industry attractiveness
and competitive status. On the contrary, the second group of
financially-focused studies are seeking to maximize profit or
minimize risk of investment portfolios, like numerous studies
based on Markowitz's famous model for portfolio optimization
[5]. However, it seems that the studies and the developed
models in this area are faced with weaknesses in terms of
efficiency for strategic decision-making because the first group
of models is conceptual and high level and they cannot provide
the necessary analysis to support management decisions.
Meanwhile, the second group is suitable for optimizing stock
and investments portfolios while the components in design of a
business portfolio cannot be described only in the context of
financial indicators. In order to meet this need, this research is
an attempt to develop a quantitative model that can support
strategic decision-making at the corporate level for designing a
business portfolio.
II. LITERATURE REVIEW
Over the past decades, two key levels of strategy have been
defined for organizations. First, “corporate strategy” that
defines the territory of the corporation and shows businesses
which corporates should enter into. Secondly, “business
strategy” that deals with how corporations compete within an
industry or market [2, 6]. Authors in [7] structured approaches
related to corporate strategy in four groups including portfolio
management, restructuring, transferring skills, and sharing
activities. Each approach is based on a different mechanism for
value adding by the corporation. Portfolio management is
based on diversification, mainly through the acquisition of
attractive businesses, providing capital, goal setting, and
monitoring of business outcomes. In restructuring approach,
the focus is on potentials of business units that are prone to
change. In skills transfer approach, focus is on synergy and the
transfer of skills and knowledge among the value chain of
businesses. In sharing activities approach, the value is created
through shared operations in value chain such as the use of a
shared distribution system or creation of competitive advantage
through cost reduction. In the above structure, the first two
approaches are based on the creation of value through the
association of the parent company with each of the independent
businesses, while the other two concepts are focused on
extracting value through the link between businesses and their
synergy. In a general view, corporate strategy can be
considered as a decision on product range and vertical range,
which is discussed in the literature in terms of diversification
and vertical integration, respectively. Evidence suggests that in
the 1950s and 1980s, companies began to design diverse and
unrelated business portfolios, they set up multifunctional
companies and diversified businesses that ultimately led to the
formation of so-called “conglomerates”. Based on the
Engineering, Technology & Applied Science Research Vol. 8, No. 6, 2018, 3657-3667 3658
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experience, the above process was reversed from 1980, and in
that period unprofitable businesses were left aside. Then, re-
focusing has once again been highlighted on major and
specialized businesses or the formation of a portfolio of related
businesses [2]. In some studies, it has been shown that the
focus strategy has a positive impact on the corporate's value for
shareholders, but some argue that corporate devaluation after
diversification is due to the ownership of new businesses at
lower prices during the diversification process [8]. Despite
decades of debate in this area, portfolio design and issues like
the amount of diversification and vertical integration are still at
the heart of the attention of businesses and researchers [9-11].
The persistence of these questions is because of the fact that
although there are evidence of failure of many diversification
strategies in the age of diversification, there are still undeniable
advantages for diversity including the possibility of growth (in
the sense of going beyond the current industry's boundaries),
risk reduction due to its distribution in a portfolio of
businesses, savings by globalization, benefit of the parent
company, and reaching an internal market [2, 12, 13]. It can be
concluded that the effectiveness of diversification is subject to
conditions [14, 15].
Moreover, importance and complexity of decision making
on the business portfolio in various industries varies according
to the volume of the required investment, the variety of
components in the value chain, and the existing risks. In this
regard, the oil industry can be ranked high. For example, in the
field of exploration and production, decisions are very complex
and risky due to the uncertainty and large number of factors
involved. The selection of the optimal portfolio of projects in
this section is influenced by diverse topics including corporate
strategies and constraints, reservoir geology assessment,
engineering data, economic forecasts, financial model, and
regulatory aspects [16]. In this regard, mathematical
optimization models have been widely developed for the oil
industry by researchers. Author in [17] used genetic algorithm
for optimizing portfolio in the oil and gas industry. In his
model, the portfolio is composed of projects, not businesses. In
other words, it is the investment portfolio of the oil company.
He also argues the advantages of the portfolio theory for this
purpose. It enables decision makers to consider set of available
opportunities beyond merely examining the independent
economic indicators of each project and approving or rejecting
investment in it. It also gives them the opportunity to reach a
portfolio of projects with maximum returns at a certain level of
risk.
In general, mathematical optimization models offered for
the oil industry can be classified into three strategic areas of
portfolio selection, tactical planning such as production
planning, and operation such as well optimization [18]. In this
framework and given the complexity of decision making in the
oil industry, portfolio design models have always been
considered, used and developed [19, 20]. New tools such as the
theory of real options have also been used for this purpose [21].
However, in previous researches on portfolio optimization,
financial approaches based on Markowitz's foundation have
been applied. In the oil industry, the use of portfolio concept
and portfolio theory has focused primarily on portfolio
selection methods for projects and assets. Hence, quantitative
models for designing a business portfolio that consider strategic
concepts have not developed in this industry.
III. DESIGNING MODEL
A. Conceptual Model
In order to develop a model that provides the optimal
business portfolio, we first need to determine the goals we are
seeking for optimization. According to the existing literature
and workshops organized by a focus group of experts, four
main objectives were identified, namely maximum
profitability, minimum investment, maximum growth and
maximum profit robustness (minimum profitability risk). The
first two objectives can be integrated as the economic value
added (EVA) concept. Economic value added, one of the most
widely used criteria in economic profitability models [22], is a
good indicator of differentiation between portfolio with higher
returns than lower returns [23]. Despite fundamental
similarities, EVA provides better strategic and management
illustration of economic returns for a company compared to
NPV which is basically developed to model the profitability of
a project [24]:
P
EVA WACC C
C
= −
(1)
In this equation, P is net operating profit after tax, C is
invested capital, and WACC is weighted average cost of
capital. Accordingly, it can be said that each of the businesses
in the portfolio at each period creates an economic value added
independently and this trend of value adding during the periods
leads to growth and robustness. Based on existing literature, we
formulate this cross-business impact as follows:
1. Capability synergy: A business in a portfolio can affect the
level of capability in another business by different ways,
such as sharing activities or utilizing existing knowledge
and expertise.
2. Market share synergy: Participating in a business can
change the market of another business. For example,
creating a market for another business or prevent its
presence in a market, because of legal constraints.
3. Parenting costs: Having a portfolio of businesses instead of
an individual business can create costs such as overheads,
management costs or so-called holding costs, which are
called “parenting costs” in this research.
4. Sharing benefits: Engaging in a business can save money in
the cost structure of another business, which is called
“sharing benefits”. These benefits can be realized in a
variety of ways such as using shared resources or services,
or increasing bargaining power with suppliers.
Therefore, we can present a high-level, conceptual model
(Figure 1) in which the value creation of any business is a
function of the revenue, cost, and profitability mechanisms of
the business. These factors are independently influenced by the
internal variables (capabilities) and the external variables
(market) of each business, while being systematically affected
by the link between the businesses in the fourfold form above.
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Fig. 1. Conceptual model
Now, if x represents the presence or absence in a business,
the above model can be formulated for business i in the period t
in the form of the following mathematical relations:
( )1 , i tMax Z f EVA= (2)
,
2
i t
dE
Max Z f
dt
=
(3)
)
,
2
3
(
i tP
Min Z f = (4)
( ), , ,,i t i t i tEVA f P I= (5)
( ), , ,,i t i t i tP f E C= (6)
( ), , ,and , , , ,i t i t i tE C f I S CB PC SB= (7)
), , , (S CB PC SB f G= (8)
)( jG f x= (9)
B. Structuring Industry Businesses
According to existing literature [25-27], industry evidence,
and expert opinions, a structure for oil industry businesses is
presented at three levels in Figure 2.
Fig. 2. Three-level structure for value chain of oil industry businesses
C. Modeling Level-1 Businesses
For modeling development and production business, a
simplified model of Iran's new oil contracts, known as IPC, is
considered. In this model, the contract period for a field is 20
years, during which the development of the field will take place
over a period of 5 years, after which there will be three 5-year
periods equal to 15 years of production. Capital expenditures
related to the development period will be repaid by the
National Oil Company during the operation period (with a
delay of 5 years) including financial costs. Operating costs are
repaid on an annual basis, and the oil company will receive a
certain amount of remuneration (reward) per barrel of
production. In refining business, we consider five years as
construction (or acquisition) period as well, while having 25
years (5 periods) of operation. We assume that there is no
competition to obtain the license for investment in these two
businesses of level-1. Since this research seeks to model a
business and not a project, we consider another type of costs as
indirect costs of a business in the model. It includes non-project
costs such as costs for administration or key personnel of the
headquarters.
TABLE I. MODEL VARIABLES FOR LEVEL-1 BUSINESSES
Variable Description
𝑪𝑿𝒊,𝒕 Investment in business i in period t
𝒖𝒕 Increase in oil production capacity in period t
𝑼𝒕 Oil production in period t
𝒒𝒕 Increase in refining capacity in period t
𝑸𝒕 Production of refining products in period t
𝑹𝒕 Rewards of oil production (remuneration) in period t
𝑶𝑿𝒕 Direct costs of refinery operation in period t
𝑬𝒊,𝒕 Income from business i in period t
𝑰𝑪𝒊,𝒕 Indirect business costs i
𝑷𝒊,𝒕 Profit by business i in period t
𝑷𝒊
𝒇
Future potential benefits from investment in business i
𝑬𝑽𝑨𝒊,𝒕 Economic value added from business i in period t
In development and production, if cx dollars is needed to
increase production capacity for a barrel per day, with CB1 as
the capabilities level of the company in this business (which is
defined in the range of 0 to 1 and its average is the normal
capability in the industry), we will have:
1 1,
( .5).
t
t
CB CX
u
cx
+
= (10)
The power relationship is used to estimate the amount of
investment required to build a refinery. It is widely applied to
estimate initial investment costs for a refinery based on
investment and capacity of a reference refinery [28]. According
to this equation, if C0 is regarded as the amount of investment
to build a sample refinery with an annual capacity of Q0 while
we have company's capability (CB2), then:
2,
0.6
2 0
0
( .5). .
t
t
CX
q CB Q
C
= + (11)
The production capacity added in each period will be
achieved not in that period but in future periods. Therefore, the
amount of oil produced and refined product in each period is:
1
t 3 0
t
t i
i
U u
−
= −
= (12)
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1
5 0
t
t i
i t
Q q
−
= −
= (13)
In the contracts described for development and production,
the corporate's profits in each period are equivalent to f dollars
reward per barrel of oil production:
( )5*365 . . t tR f U= (14)
In refining business, income is equal to the sales of refined
products. If p is the weighted average price of the corporate’s
refined products, by assuming 330 days of operation annually,
we have:
2,
(5*330) .
o
t t t
E Q p= (15)
In development and production, the investment and the
operating costs are both reimbursed by the National Iranian Oil
Company, therefore, they are eliminated from the model
calculations. In the refining business, the operating costs,
which mainly include cost of feed, fuel, catalysts, etc. are
directly related to the amount of refined products produced per
period. Therefore, if we assume that the production of a barrel
of petroleum products costs ox dollars, operation cost in each
period can be calculated considering the level of corporate's
capability in refining business:
2,
2
(5 * 330) .
( .5)
t
t
ox Q
OX
CB
=
+
(16)
Meanwhile, indirect costs are affected by both
production/operation and development of fields or new
refineries. Therefore, they could be considered as a function of
income or profits in each period (ai dollar per barrel), the
volume of investments in development (bi dollars per
investment dollar), and fixed costs of the business (ci).
1
1, 1 1 1, 1
1
( )
( .5)
t t t
x
IC a R b CX c
CB
= + +
+
(17)
2
2, 2 2, 2 2, 2
2
( )
( .5)
t t t
x
IC a E b CX c
CB
= + +
+
(18)
In these equations, ci represents the costs involved in
having an operating business, regardless of contracts and
projects such as cost of key personnel, buildings, etc. Now we
can calculate the business profits of development and
production in each period:
1
1, 1 1 1, 1
1
( )
( .5)
t t t
x
IC a R b CX c
CB
= + +
+
(19)
2, 2, 2,
t t t t
P E OX IC= − − (20)
Therefore, the economic value added is:
, , ,
.
i t i t t i t
EVA P WACC CX= − (21)
In addition, it should be noted that a part of investments in
the 20-year period of the model, leads to future production in
years after the problem period. Hence, at the end of the 20th
year, potential future profits have been generated in addition to
the profits received. If the average profitability per production
over the 20 years is calculated and called pi, we assume that
profitability for production in future periods will continue
according to such average. By discounting future profits with
the rate of WACCt, we will have:
4
1,1
1 4
1
tt
tt
P
p
U
=
=
=
(22)
4
2,1
2 4
1
tt
tt
P
p
Q
=
=
=
(23)
( )
7
1
1
5
.
1
f t
t
t t
p U
P
WACC=
=
+
(24)
( )
9
2
2
5
.
1
f t
t
t t
p Q
P
WACC=
=
+
(25)
D. Modeling Level-2 and Level-3 Businesses
While investment is a key function in level-1 businesses, in
level-2 and level-3 businesses that are contracting and service
businesses, investment is not essential. In these businesses, the
cash flow depends on the company’s contracts and invoices.
Nevertheless, drilling services (k=2) and construction and
installation (k=4) are “equipment-based”. Therefore, investing
in machines and equipment is required in mentioned
businesses. The variables for each business in level-2 (j=1-3)
and level-3 (k=1-5) are defined in Table II.
TABLE II. MODEL VARIABLES FOR LEVEL-2 AND LEVEL-3 BUSINESSES
Variable
Description
Level-3 Level-2
𝑲𝒌,𝒕
′′
- Investment in period t
𝑬𝒌,𝒕
′′
𝑬𝒋,𝒕
′
Income in period t
𝑰𝑪𝒌,𝒕
′′
𝑰𝑪𝒋,𝒕
′
Direct costs in period t
𝑫𝑪𝒌,𝒕
′′
𝑫𝑪𝒋,𝒕
′
Indirect costs in period t
𝑷𝒊,𝒕 𝑷𝒊,𝒕 Profit in period t
𝑬𝑽𝑨𝒊,𝒕 𝑬𝑽𝑨𝒊,𝒕 Economic value added in period t
If we show the total market value of business j in period t as
M'j,t and the total market value of business k in period t as M''j,t
, we will have:
' ' ' '
, ,
( .5)
j t j j t j j
E y M S CB= + (26)
'' '' '' ''
, ,
( .5)
k t k k t k k
E z M S CB= + (27)
where S'j and S''j represent the corporate’s potential market
share (percentages) in business j and k, which is affected by the
market conditions, the number of competitors and the intensity
of the competition. Since service contracts are often awarded
competitively through tenders, all this potential market share is
not actualized. Indeed, the corporate's capability in a business
(CB'k and CB''j) is a determinant factor in this regard.
Therefore, in the above relation, S'j and S''k indicate the effect
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of external factors outside the control of the company. CB'j and
CB''k represent the effects of internal factors such as bid prices
on tenders, capabilities, competitive advantage, and so on. We
also assume that each business has a specific profit margin (m'j
and m''k), which is the remainder of the contract after deducting
direct costs. Thus, we have the direct costs:
( )'
' '
, ,'
1
( .5)
j
j t j t
j
m
DC E
CB
−
=
+
(28)
( )''
'' ''
, ,''
1
( .5)
k
k t k t
k
m
DC E
CB
−
=
+
(29)
Indirect costs of a business are a function of the amount of
contracts in hand (a' and a'' dollars per each dollar of contract
value) as an indicator of current workload of the corporate. In
case of equipment-based businesses, it is also a function of in-
hand equipment (b'' dollars per each dollar of investment in
equipment) as an indicator of business size and related
maintenance costs:
' ' ' '
j, ,'
( )
( .5)
j
t j t
j
y
IC a E c
CB
= +
+
(30)
'' '' '' '' '' ''
k, k, k,''
( )
( .5)
k
t t t
k
z
IC a E b K c
CB
= + +
+
(31)
where c' and c'' indicate the fixed costs that occur regardless of
having a contract during a period only because of the presence
of that business, such as the cost of key personnel and staff.
Based on the above, the profit could be calculated as:
' ' ' '
, , , ,j t j t j t j t
P E DC IC= − − (32)
'' '' '' ''
, , , ,k t k t k t k t
P E DC IC= − − (33)
and for economic value added:
' '
, ,j t j t
EVA P= (34)
'' '' ''
, , ,
.
k t k t t k t
EVA P WACC K= − (35)
E. Synergy of Businesses
So far, the model has been developed by considering
businesses independent. However, the link and synergy
between them is a decisive factor in portfolio design. In other
words, adopting a systematic look at the portfolio of businesses
suggests that being or not being in a business can affect
parameters of another business. If cbi, cb'j and cb''k are
independent capability parameters in each business of level 1, 2
and 3, adopting a system approach means that being in an
business can lead to an increase or decrease in the capability
level of another business. If CBi, CB'j and CB''k are respectively
the variables relating to the corporate's capabilities in each
three level businesses, we define: [-1,1]
Cb
m, p ,n,q
as the
capability impact factor of business m from level p on business
n from level q. Now, the effect of all other businesses on
business n of the level q could be shown by the “capability
synergy function” for business n of level q which is defined as:
2 3 5
,1, , , 2, , ,3, ,1 1 1
, 3 3 5
1 1 1
. . .
Cb Cb Cb
i i n q j j n q k k n qi j kCb
n q
i j ki j k
x y z
G
x y z
= = =
= = =
+ +
=
+ +
(36)
Therefore, we will have:
),1.(1
Cb
i i i
CB cb G= + (37)
)' ' ,2.(1
Cb
j j j
CB cb G= + (38)
)'' '' ,3.(1
Cb
k k k
CB cb G= + (39)
Having the above mentioned function, corporate's
capability level in a business that was considered as an
independent parameter is now modified by considering the
synergistic effect of other businesses in the portfolio. In the
same way, if the parameters si, s'j and s''k are the potential
market share in each business of level 1, 2 and 3, adopting a
system approach and considering the presence in other
businesses can lead to an increase or decrease in this share and
a change in the market position. If Si, S'j, and S''k are
respectively the variables indicating potential market share in
each of the level 1, 2 and 3 businesses, by considering the link
between businesses in a portfolio, we define: [-1,1]
S
m, p ,n,q
as the market impact factor of business m from the level p on
business n from level q. Meanwhile, we can define the “market
synergy function” for business n from level q as:
2 3 5
,1, , , 2, , ,3, ,1 1 1
, 3 3 5
1 1 1
. . .
S S S
i i n q j j n q k k n qi j kS
n q
i j ki j k
x y z
G
x y z
= = =
= = =
+ +
=
+ +
(40)
,1
)1.(
i
S
i i
S s G= + (41)
' '
,2
.(1 )
S
j j j
S s G= + (42)
'' ''
,3
.(1 )
S
k k k
S s G= + (43)
F. Parenting Cost and Sharing Benefits
By establishing a portfolio of businesses, new overhead
costs, called “parenting costs”, are generated. Since these costs
have a direct relation to size of the corporate and its operation,
we can estimate them as a percentage (h) of the total income:
2 3 5
' ''
, , ,
1 1 1
.
t i t j t k t
i j k
PC h E E E
= = =
= + +
(44)
Moreover, given that these costs are mainly spent on
strategic management, financial management, audits and
controls, etc., we distribute it equally among active businesses:
, 3 3 5
1 1 1
.
i t
i t
i j ki j k
x PC
PC
x y z
= = =
=
+ +
(45)
'
, 3 3 5
1 1 1
.
j t
j t
i j ki j k
y PC
PC
x y z
= = =
=
+ +
(46)
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''
, 3 3 5
1 1 1
.
k t
k t
i j ki j k
z PC
PC
x y z
= = =
=
+ +
(47)
Conversely, by forming a business portfolio, it is possible
to share costs among some businesses. For this purpose, we
define [-1,1]
Sb
m, p ,n,q
as the sharing impact factor between
business m at level p with business n at level q. Now, we define
the “sharing benefit function” for business n from level q as:
2 3 5
,1, , , 2, , ,3, ,1 1 1
, 3 3 5
1 1 1
. . .
Sb Sb Sb
i i n q j j n q k k n qi j kSB
n q
i j ki j k
x y z
G
x y z
= = =
= = =
+ +
=
+ +
(48)
To apply the benefits of cost sharing into the model, we
assume that the cost-sharing function decreases the indirect
costs of each business in each period. Since this cost sharing
cannot be unlimited and must include a part of indirect costs,
we restrict it to a θ percentage of indirect costs. Therefore, we
will have:
, ,1 ,
( , ).
Sb
i t i i t
SB Min G IC= (49)
' '
, ,2 ,
( , ).
Sb
j t j j t
SB Min G IC= (50)
'' ''
, ,3 ,
( , ).
Sb
k t k i k
SB Min G IC= (51)
By considering parenting costs and cost sharing benefits,
business profits should be modified as follows:
1, 1, 1, 1,
t t t t t
P R IC SB PC= − + − (52)
2, 2, 2, 2, 2, 2,
t t t t t t
P E OX IC SB PC= − − + − (53)
' ' ' ' ' '
, , , , , ,j t j t j t j t j t j t
P E DC IC SB PC= − − + − (54)
'' '' '' '' '' ''
, , , , , ,k t k t k t k t k t k t
P E DC IC SB PC= − − + − (55)
G. Objective Function
According to the conceptual model, the objective function
is:
( )
4 2 3 5
' ''
1 , , ,
1 1 1 1
1 2
1
1
i t j t k tt
t i j kt
f f
Max Z EVA EVA EVA
WACC
P P
= = = =
= + + +
+ +
(56)
( ) ( ) ( )
4 2 3 5
' ' '' ''
2 , 1 , , 1 , , 1 ,
2 1 1 1
i t i t j t j t k t k t
t i j k
Max Z E E E E E E
+ + +
= = = =
= − + − + −
(57)
2
4 2 3 5
' ''
3 , , ,
1 1 1 1
i t j t k t
t i j k
Min Z P P P P
= = = =
= + + −
(58)
H. Constraints
The first constraint is the limitation of resources for
investment. If the total capital available for the period t is Ct,
then we have:
'' ''
1, 2, 2, 4,
t t t t t
CX CX K K C+ + + (59)
Moreover, minimum required investment for level-1 and
equipment-based businesses in level-3 can be defined as:
,
( )
i t i
CX C min (60)
'' ''
,
( )
j t j
K K min (61)
In equipment-based businesses (k=2,4), we consider that
reinvestment in each period should be at least equal to the rate
of depreciation in that business (τk):
''
, 1
''
,
k t
k
k t
K
K
+
(62)
Although size, the potential contribution of the market and
capabilities are still decisive for equipment-based businesses
(“drilling” and “construction and installation”), available
equipment is also a limiting factor because the services
provided by these businesses are depended on their equipment
and machinery. Hence, we apply the following limitation in the
model for these businesses (k=2,4):
'' ''
, ,
1
5
t
k t k k k i
i
E z K
=
(63)
Where ηk is the “revenue generating ratio” which is defined
for each equipment-based business (k=2,4) as the maximum
amount of annual revenue that could be generated per unit of
investment in equipment and machinery. Meanwhile, investing
in a business is subject to the presence in it. So:
( ) ,1 0i i tx CX− = (64)
( ) '' ,1 0k k tz K− = (65)
Finally:
, 0,1
i j
x y = (66)
Other variables 0 (67)
IV. SOLVING THE MODEL AND RESULTS
To solve the model, three companies in the Iranian oil and
gas industry were studied (Cases 1-3). Each of these companies
represents a type of corporate that has the competitive
advantage and capability mainly in level 1, 2 and 3 of the
hierarchy presented in Figure 2 respectively. In order to
analyze the results better, the model is solved in two modes:
• System Inter-Relationship mode (SI-mode): In this case, the
links among businesses in the forms of market synergy,
capabilities synergy, parenting costs and sharing benefits
are included in the model.
• Elements Independency mode (EI-mode): In this case, the
relationships between businesses and their impact on each
other are removed from the model. Hence, all variables and
parameters are considered independent of other existing
businesses in the portfolio. To solve in the EI approach, the
values of
Cb
m, p ,n,q
,
S
m, p ,n,q
, h ,and θ are considered equal to
zero.
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Fuzzy Delphi method has been used to determine the
parameters of synergy, sharing benefits and capability level of
case studies (Tables IV-VI). The linguistic variables used for
this purpose are the seven-point scale presented in Table III
[29]. Defuzzification of values is done by center of gravity
(COG) method [30]. Other parameters used to solve the model
are presented in Tables VII and VIII.
TABLE III. LINGUISTIC VARIABLES USED IN THE RESEARCH
Fuzzy number Linguistic variables
(0.9,1, 1) Very high (VH)
(0.7, 0.9, 1) High (H)
(0.5, 0.7, 1) Medium high (MH)
(0.3, 0.5, 0.7) Medium (M)
(0.1, 03, 05) Medium low (ML)
(0, 0.1, 0.3) Low (L)
(0, 0, 0.1) Very low (VL)
TABLE IV. MARKET IMPACT FACTOR (
S
m ,p ,n ,q
)
q=1 q=2 q=3
Total n=1 n=2 n=1 n=2 n=3 n=1 n=2 n=3 n=4 n=5
p=1
m=1 0.000 0.190 0.430 0.430 0.033 0.550 0.430 0.550 0.367 0.033 3.013
m=2 0.240 0.000 0.033 0.033 0.430 0.033 0.033 0.033 0.367 0.550 1.752
p=2
m=1 0.097 0.033 0.000 0.240 0.033 0.430 0.430 0.097 0.033 0.033 1.426
m=2 0.097 0.033 0.240 0.000 0.033 0.097 0.033 0.430 0.367 0.033 1.363
m=3 0.033 0.097 0.033 0.190 0.000 0.033 0.033 0.097 0.367 0.430 1.313
p=3
m=1 0.097 0.033 0.240 0.097 0.033 0.000 0.190 0.190 0.033 0.033 0.946
m=2 0.033 0.033 0.240 0.097 0.033 0.190 0.000 0.033 0.033 0.033 0.725
m=3 0.067 0.033 0.097 0.240 0.033 0.190 0.033 0.000 0.240 0.033 0.966
m=4 0.033 0.033 0.033 0.097 0.097 0.033 0.033 0.240 0.000 0.240 0.839
m=5 0.033 0.097 0.033 0.097 0.240 0.033 0.033 0.033 0.240 0.000 0.839
Total 0.73 0.582 1.379 1.521 0.965 1.589 1.248 1.703 2.047 1.418
TABLE V. CAPABILITY IMPACT FACTOR (
Cb
m ,p ,n ,q
)
q=1 q=2 q=3
Total n=1 n=2 n=1 n=2 n=3 n=1 n=2 n=3 n=4 n=5
p=1
m=1 0.000 0.217 0.190 0.083 0.033 0.083 0.083 0.083 0.067 0.033 0.872
m=2 0.217 0.000 0.033 0.083 0.217 0.033 0.033 0.033 0.083 0.083 0.815
p=2
m=1 0.217 0.033 0.000 0.067 0.033 0.083 0.190 0.067 0.033 0.033 0.756
m=2 0.190 0.033 0.067 0.000 0.217 0.033 0.033 0.083 0.190 0.083 0.929
m=3 0.033 0.217 0.033 0.217 0.000 0.033 0.033 0.083 0.190 0.083 0.922
p=3
m=1 0.430 0.033 0.273 0.190 0.033 0.000 0.217 0.190 0.033 0.033 1.432
m=2 0.067 0.033 0.217 0.033 0.033 0.067 0.000 0.033 0.033 0.033 0.549
m=3 0.217 0.083 0.083 0.273 0.067 0.190 0.033 0.000 0.190 0.190 1.326
m=4 0.033 0.067 0.033 0.258 0.258 0.033 0.033 0.067 0.000 0.067 0.849
m=5 0.033 0.430 0.033 0.083 0.273 0.033 0.033 0.217 0.190 0.000 1.325
Total 1.437 1.146 0.962 1.287 1.164 0.588 0.688 0.856 1.009 0.638
TABLE VI. SHARING IMPACT FACTOR (
Sb
m ,p ,n ,q
)
q=1 q=2 q=3
Total n=1 n=2 n=1 n=1 n=2 n=1 n=1 n=2 n=1 n=1
p=1
m=1 0.000 0.387 0.175 0.175 0.033 0.175 0.058 0.175 0.033 0.058 1.269
m=2 0.387 0.000 0.033 0.033 0.175 0.033 0.033 0.083 0.083 0.175 1.035
p=2
m=1 0.175 0.033 0.000 0.175 0.058 0.175 0.217 0.083 0.058 0.058 1.032
m=2 0.175 0.033 0.175 0.000 0.387 0.083 0.058 0.083 0.217 0.083 1.294
m=3 0.033 0.175 0.058 0.387 0.000 0.083 0.058 0.083 0.217 0.083 1.177
p=3
m=1 0.175 0.033 0.175 0.083 0.083 0.000 0.083 0.258 0.033 0.058 0.981
m=2 0.058 0.033 0.217 0.058 0.058 0.083 0.000 0.058 0.033 0.033 0.631
m=3 0.175 0.083 0.083 0.083 0.083 0.258 0.058 0.000 0.083 0.387 1.293
m=4 0.033 0.083 0.058 0.217 0.217 0.033 0.033 0.083 0.000 0.083 0.840
m=5 0.058 0.175 0.058 0.083 0.083 0.058 0.033 0.387 0.083 0.000 1.018
Total 1.269 1.035 1.032 1.294 1.177 0.981 0.631 1.293 0.840 1.018
TABLE VII. CAPABILITY LEVEL OF CASES IN EACH BUSINESS
𝒄𝒃𝟓
′′ 𝒄𝒃𝟒
′′ 𝒄𝒃𝟑
′′ 𝒄𝒃𝟐
′′ 𝒄𝒃𝟏
′′ 𝒄𝒃𝟑
′ 𝒄𝒃𝟐
′ 𝒄𝒃𝟏
′ 𝒄𝒃𝟐 𝒄𝒃𝟏 Parameter
0.08 0.08 0.40 0.78 0.40 0.22 0.22 0.40 0.78 0.78 Case 1
0.92 0.08 0.92 0.08 0.78 0.92 0.92 0.78 0.22 0.40 Case 2
0.60 0.92 0.50 0.03 0.08 0.22 0.22 0.08 0.08 0.08 Case 3
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TABLE VIII. MODEL PARAMETERS
Value Parameter Value Parameter Value Parameter Value Parameter
0.0002 𝒂𝟏 19,800 𝒄𝒙 0.15 𝒔𝟒
′′ 32,000,000,000 𝑴𝟏
′
0.0002 𝒂𝟐 56 𝒐𝒙 0.10 𝒔𝟓
′′ 48,000,000,000 𝑴𝟐
′
0.0020 𝒂′ 4.8 𝒇 0.515 𝑾𝑨𝑪𝑪 25,000,000,000 𝑴𝟑
′
0.0020 𝒂′′ 75,000,000 𝑪𝟏(𝒎𝒊𝒏) 2,700,000,000 𝑪𝟎 2,400,000,000 𝑴𝟏
′′
0.0100 𝒃𝟏 150,000,000 𝑪𝟐(𝒎𝒊𝒏) 150,000 𝑸𝟎 12,800,000,000 𝑴𝟐
′′
0.0100 𝒃𝟐 6,000,000 𝑲𝟐
′′(𝒎𝒊𝒏) 65 𝒑𝒕 2,400,000,000 𝑴𝟑
′′
0.0500 𝒃′′ 5,500,000 𝑲𝟒
′′(𝒎𝒊𝒏) 0.07 𝒎𝟏
′ 25,550,000,000 𝑴𝟒
′′
4,950,000 𝒄𝟏 250,000,000 𝑪𝒕-case1 0.08 𝒎𝟐
′ 1,250,000,000 𝑴𝟓
′′
3,700,000 𝒄𝟐 500,000,000 𝑪𝒕-case2 0.08 𝒎𝟑
′ 0.05 𝒔𝟏
′
3,050,000 𝒄′ 750,000,000 𝑪𝒕-case3 0.19 𝒎𝟏
′′ 0.05 𝒔𝟐
′
3,050,000 𝒄′′ 1.62 𝜼𝟐 0.41 𝒎𝟐
′′ 0.10 𝒔𝟑
′
0.031 𝒉 1.12 𝜼𝟒 0.15 𝒎𝟑
′′ 0.05 𝒔𝟏
′′
0.5 𝝉𝟐/𝝉𝟒 0.08 𝒎𝟒
′′ 0.05 𝒔𝟐
′′
0.42 𝜽 0.15 𝒎𝟓
′′ 0.15 𝒔𝟑
′′
The model we developed in this research is a highly
complex one with a NP-Hard type that requires meta-heuristic
methods to be solved. Therefore, we used non-dominant
genetic algorithm as one of the most efficient and applicable
multi-objective methods for obtaining appropriate answers
[31]. Studies have shown that the improved version of this
algorithm (NSGA-II) has better performance and less
computational complexity than the previous versions, and
provides better answers than the other presented algorithms
[32]. Using this algorithm, the model is solved by Matlab
software for each of the three cases in both EI and SI modes.
The initial population is 200, the number of generations is 100,
and the crossover rate is 0.8. The chromosome defined for
solving this model is a string of length 26, 10 of which (to enter
or not enter into a business) are Boolean variables. The rest
(investment variables) are continuous variables. The objective
function values for the answers set are shown in Figures 4 to 9
in the form of the Pareto front. Square polynomial fitting is
used in order to gain a better picture of answers. In order to
improve the results and reduce the impact of out-of-range
answers, bi-square method has been used for robust fitting.
Fig. 3. Pareto front of objective functions for the first case - SI mode
Fig. 4. Pareto front of objective functions for the first case - EI mode
Fig. 5. Pareto front of objective functions for the second case - SI mode
Fig. 6. Pareto front of objective functions for the second case - EI mode
Fig. 7. Pareto front of objective functions for the third case - SI mode
In Figures 9-11, values of each objective function for the
three cases are shown in both SI and EI modes.
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Fig. 8. Pareto front of objective functions for the third case - EI mode
Fig. 9. Z1 for the three cases in SI and EI modes
Fig. 10. Z2 for the three cases in SI and EI modes
Fig. 11. Z3 for the three cases in SI and EI modes
In order to analyze the results obtained from decision
variables, which represent entering or not entering into a
business, the simple mean of values in each set of answers is
calculated and presented separately for EI and SI modes in
Figures 12 and 13.
Fig. 12. Enter/not enter decision variable for the three cases - SI mode
Fig. 13. Enter/not enter decision variable for the three cases - EI mode
V. DISCUSSION AND CONCLUSION
The main achievement of this research is the structuring
and formulation of qualitative concepts of corporate strategy in
form of a quantitative optimization model. It can support top
management in the process of strategic decision making and
designing business portfolio.
Analyzing synergistic impact factors shows that having
engineering business in the portfolio has the greatest impact on
improving the capability-level of other businesses. On the other
hand, “Development and production” and “refining”
businesses, followed by level-2 businesses, have the most
positive impact on increasing the market share of other
businesses. Such pattern shows that specialized and knowledge
cores, which in the studied industry means engineering
capabilities, have a significant role in enhancing the firm's
capabilities even in upstream businesses. Hence, maintaining
such businesses in vertical integration structure instead of
outsourcing is feasible. For example, engaging in “subsurface
engineering” (k=1) that provides capabilities such as reservoir
engineering and geology can affect the firm's capabilities in the
“development and production” (i=1) and promote it. Moreover,
entering into upstream businesses of the value chain can create
internal markets for downstream businesses. In other words, in
addition to direct benefits, investing in an upstream-level
Engineering, Technology & Applied Science Research Vol. 8, No. 6, 2018, 3657-3667 3666
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business can indirectly lead to new sources of income for the
downstream businesses of a portfolio. Nevertheless, such
benefits should be evaluated considering the costs incurred by
entering the business, required investment and parenting costs
needed for holding management. Legal barriers or strategic
directions for assigning work to subsidiaries should also be
considered in this regard.
Findings also show that the portfolio of the level-2 firm
(case 2) performs better from the value adding point of view
compared to level-1 companies (case 1). Although these results
are obtained within our defined assumptions and constraints, it
shows that presence in higher-level businesses does not
necessarily mean more economic value added. Corporate
managers should choose the optimum portfolio by considering
internal factors such as the level of capabilities and external
factors such as market potentials, as well as the interactions
among businesses and their impact on each other. Besides, the
optimal diversification-concentration strategies for each type of
corporation could by proposed based on results:
• Type 1 (high level of competitive advantages and
capabilities in level-1 businesses): The portfolio should be
formed with a focus on level-1 capital-based businesses,
including “development and production” and “refinement”
along with outsourcing of level-2 E&C operations. In order
to play a better role as an employer, protecting corporate
investments, benefit from internal markets and reduce risk,
applying a “limited and relevant diversification” can be
considered by entering into some level-3 businesses,
especially engineering businesses.
• Type 2 (high level of competitive advantages and
capabilities in level-2 businesses): The best strategy for
these firms is “diversification”|. These firms would be
better placed in all level-2 E&C businesses, upstream and
downstream. It is also better for these companies to include
“engineering” in their business portfolio as it makes them
more capable and with better performance in level-2
contracting tasks.
• Type 3 (high level of competitive advantage and
capabilities in level-3 businesses): The appropriate strategy
for these firms is “focus”. These firms must refrain from
engaging in field development and production contracts,
investment, ownership of refineries and E&C businesses of
Level-2. On the contrary, they should focus on those
specialized engineering services in which they are more
capable and competitive.
The findings also confirm that portfolio business
performance (as a whole) is different from the total revenue-
expenditure structure of individual business. Presence in a
business can change the components of another business and,
consequently, its revenue-expenditure structure. This effect
does not necessarily mean that the values of the objective
functions are improved when considering the whole portfolio,
but could provide a more realistic picture of the portfolio's
value-adding potential.
VI. FUTURE WORK SUGGESTIONS
Given the wide range of stakeholders and decision criteria,
further objectives could be included in prospective models,
especially non-financial and non-economic ones such as
environmental impacts or sustainable development, which have
considerable importance in decision making for oil industry.
Also, criteria such as employment creation and energy security
that are of interest to national oil companies could be
considered in future optimizations. Moreover, the dynamics of
the relationship between variables over time periods can be
applied in the model. For example, a continuous presence in a
business can improve the market position in an upcoming
period, and it will provide the firm with a competitive
advantage compared to a newcomer. In addition, many of the
variables used as deterministic variables can actually be
defined as probabilistic variables, thus, the model becomes a
probabilistic optimization model, in which the risk concept will
be closer to real situations by covering issues beyond the
fluctuations of profitability as it is considered in this research.
REFERENCES
[1] L. G. Franko, “The death of diversification? The focusing of the world's
industrial corporates, 1980-2000”, Business Horizons, Vol. 47, No. 4,
pp. 41-50, 2004
[2] R. M. Grant, Contemporary Strategy Analysis: Text and Cases Edition,
John Wiley & Sons, 2016
[3] P. Ghemawat, “Competition and business strategy in historical
perspective”, Business History Review, Vol. 76, No. 1, pp. 37-74, 2002
[4] R. A. Proctor, J. S. Hassard, “Towards a New Model for Product
Portfolio Analysis”, Management Decision, Vol. 28, No. 3, 1990
[5] R. Mansini, W. Ogryczak, M. G. Speranza, “Twenty years of linear
programming based portfolio optimization”, European Journal of
Operational Research, Vol. 234, No. 2, pp. 518-535, 2014
[6] G. Johnson, K. Scholes, R. Whittington, Exploring Corporate Strategy:
Text & Cases, Pearson Education, 2008
[7] M. E. Porter, “From competitive advantage to corporate strategy”, in:
Managing the Multibusiness Company: Strategic Issues for Diversified
Groups, Cengage Learning EMEA, 1996
[8] J. R. Graham, M. L. Lemmon, J. G. Wolf, “Does corporate
diversification destroy value?”, The Journal of Finance, Vol. 57, No. 2,
pp. 695-720, 2002
[9] O. A. Lamont, C. Polk, “Does diversification destroy value? Evidence
from the industry shocks”, Journal of Financial Economics, Vol. 63, No.
1, pp. 51-77, 2002
[10] J. D. Martin, A. Sayrak, “Corporate diversification and shareholder
value: a survey of recent literature”, Journal of Corporate Finance, Vol.
9, No. 1, pp. 37-57, 2003
[11] J. A. Doukas, O. B. Kan, “Does global diversification destroy corporate
value?”, Journal of International Business Studies, Vol. 37, No. 3, pp.
352-371, 2006
[12] R. P. Rumelt, “Diversification strategy and profitability”, Strategic
Management Journal, Vol. 3, No. 4, pp. 359-369, 1982
[13] S. A. Mansi, D. M. Reeb, “Corporate diversification: what gets
discounted?”, The Journal of Finance, Vol. 57, No. 5, pp. 2167-2183,
2002
[14] N. Berger, J. D. Cummins, M. A. Weiss, H. Zi, “Conglomeration versus
strategic focus: Evidence from the insurance industry”, Journal of
Financial Intermediation, Vol. 9, No. 4, pp. 323-362, 2000
[15] S. P. Ferris, N. Sen, C. Y. Lim, G. H. Yeo, “Corporate focus versus
diversification: the role of growth opportunities and cashflow”, Journal
of International Financial Markets, Institutions and Money, Vol. 12, No.
3, pp. 231-252, 2002
Engineering, Technology & Applied Science Research Vol. 8, No. 6, 2018, 3657-3667 3667
www.etasr.com Kiamehr et al.: A Multi-Objective Optimization Model for Designing Business Portfolio in the Iranian …
[16] S. B. Suslick, D. Schiozer, M. R. Rodriguez, “Uncertainty and risk
analysis in petroleum exploration and production”, Terræ, Vol. 6, No. 1,
pp. 30-41, 2009
[17] D. P. Fichter, “Application of genetic algorithms in portfolio
optimization for the oil and gas industry”, SPE Annual Technical
Conference and Exhibition, Dallas, Texas, USA, October 1-4, 2000
[18] M. Shakhsi-Niaei, S. H. Iranmanesh, S. A. Torabi, “A review of
mathematical optimization applications in oil-and-gas upstream &
midstream management”, International Journal of Energy and Statistics,
Vol. 1, No. 2, pp. 143-154, 2013
[19] S. V. De Barros Bruno, C. Sagastizabal, “Optimization of real asset
portfolio using a coherent risk measure: application to oil and energy
industries”, Optimization and Engineering, Vol. 12, No. 1-2, pp. 257-
275, 2011
[20] Q. Xue, Z. Wang, S. Liu, D. Zhao, “An improved portfolio optimization
model for oil and gas investment selection”, Petroleum Science, Vol. 11,
No. 1, pp. 181-188, 2014
[21] Z. Lin, J. Ji, “The portfolio selection model of Oil/Gas projects based on
real option theory”, in: Lecture Notes in Computer Science, Vol. 4489,
pp. 945-952, Springer, Berlin, Heidelberg, 2007
[22] K. Sharma, S. Kumar, “Economic value added (EVA)-literature review
and relevant issues”, International Journal of Economics and Finance,
Vol. 2, No. 2, pp. 200-200, 2010
[23] D. Fountaine, D. J. Jordan, G. M. Phillips, “Using economic value added
as a portfolio separation criterion”, Quarterly Journal of Finance and
Accounting, Vol. 47, No. 2, pp.69-81, 2008
[24] P. Modesti, “EVA and NPV: some comparative remarks”, Mathematical
Methods in Economics and Finance, Vol. 2, pp. 55-70, 2007
[25] M. Chima, D. Hills, “Supply-chain management issues in the oil and gas
industry”, Journal of Business & Economics Research, Vol. 5, No. 6, pp.
27-36, 2011
[26] S. Tordo, B. S. Tracy, N. Arfaa, Natural Oil Companies and Value
Creation, World Bank Working Paper No. 218, The World Bank,
Washington DC, 2011
[27] Y. Y. Yusuf, A. Gunasekaran, A. Musa, M. Dauda, N. M. El-Berishy, S.
Cang, “A relational study of supply chain agility, competitiveness and
business performance in the oil and gas industry”, International Journal
of Production Economics, Vol. 147B, pp. 531-543, 2014
[28] M. S. Peters, K. D. Timmerhaus, R. E. West, Plant Design and
Economics for Chemical Engineers, McGraw-Hill Education, 2003
[29] T. Y. Chen, T. C. Ku, “Importance-Assessing Method with Fuzzy
Number-Valued Fuzzy Measures and Discussions on TFNs And TrFNs”,
International Journal of Fuzzy Systems, Vol. 10, No. 2, pp. 92-103, 2008
[30] W. Van Leekwijck, E. E. Kerre, “Defuzzification: criteria and
classification”, Fuzzy Sets and Systems, Vol. 108, No. 2, pp. 159-178,
1999
[31] Konak, D. W. Coit, A. E. Smith, “Multi-objective optimization using
genetic algorithms: A tutorial”, Reliability Engineering & System
Safety, Vol. 91, No. 9, pp. 992-1007, 2006
[32] K. Deb, S. Agrawal, A. Pratap, T. Meyarivan, “A fast elitist non-
dominated sorting genetic algorithm for multi-objective optimization:
NSGA-II”, Lecture Notes in Computer Science, Vol. 1917, pp. 849-858,
Springer, Berlin, Heidelberg, 2000