Content uploaded by Kanan Hasanov
Author content
All content in this area was uploaded by Kanan Hasanov on Mar 11, 2024
Content may be subject to copyright.
Advanced Mathematical Models & Applications
Vol.8, No.3, 2023, pp.502-528
A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL
MODEL FOR SELECTING OIL AND GAS INVESTMENT PROJECTS
UNDER UNCERTAINTY AND LIMITED RESOURCES
Dmitry Pervukhin1,ID Hadi Davardoost1∗, Dmitry Kotov1,
Yana Ilyukhina1,ID Kanan Hasanov2
1Saint Petersburg Mining University, Saint Petersburg, Russia
2Azerbaijan University of Architecture and Construction, Baku, Azerbaijan
Abstract. In this study, a multi-period, multi-objective mathematical model is presented for selecting oil and
gas investment projects based on the Sustainable Development Goals (SDGs) approach, considering resource lim-
itations. Based on the economic dimension of sustainability, the profit from the implementation of petrochemical
projects is maximized, and based on the environmental dimension, the amount of greenhouse gas emissions, energy
consumption, and produced waste is minimized. According to the social dimension, the number of job opportu-
nities, the number of people covered by insurance, the job satisfaction of employees, the project’s impact on the
regional economy, and the number of lost workdays is examined. The uncertainty of the strategic and operational
parameters of the model has also been considered, and to deal with the uncertainty, fuzzy possibility programming
(FPP) is used. The model is solved in GAMS optimization software with a two-stage approach based on fuzzy
programming and the best-worst group decision-making method (BWM). Numerical results confirm the effective-
ness of the proposed model and show that SDG will lead to a significant improvement in economic, environmental,
and social dimensions without significantly reducing the profits of the selected oil and gas projects.
Keywords: Sustainable Development Goals (SDGs), Project selection, Resource constraints, Uncertainty, Fuzzy
possibility planning (FPP), Best-Worst Method (BWM), Petrochemical industry.
AMS Subject Classification: 65-XX, 65Kxx, 65K10, 90-XX, 90Cxx.
Corresponding author: Hadi Davardoost, Saint Petersburg Mining University, 199106, Saint Petersburg, Rus-
sia, e-mail: s215133@stud.spmi.ru
Received: 15 July 2023; Revised: 14 October 2023; Accepted: 16 November 2023;
Published: 20 December 2023.
1 Introduction
Organizations’ managers are always faced with conflicts in making decisions at different strategic
and operational levels (Davardoost & Javadi, 2019) the quality and manner of these decisions will
guarantee the success and survival of organizations in the field of business and will overshadow
their competitive position. One of the critical determinations made by managers in petrochemi-
cal organisations is the selection of an optimal portfolio of investment projects from the available
options. In the absence of quantitative and economic methodologies guiding the project selection
process, there is a risk of misalignment between project outcomes and initial expectations, result-
ing in significant costs for both organizations and contractors. It is imperative for managers to
employ mathematical optimization models to arrive at optimal decisions, thereby enabling them
How to cite (APA): Pervukhin, D., Davardoost, H., Kotov, D., Ilyukhina, Y., & Hasanov K. (2023).
A sustainable development goals-based mathematical model for selecting oil and gas investment projects under
uncertainty and limited resources. Advanced Mathematical Models &Applications,8(3), 502-528.
502
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
to quantitatively assess the outcomes of their decision-making and available options. Hence, the
application of mathematical modelling in the assessment of oil and gas projects is of considerable
importance for managers functioning in this sector. Through the utilization of the most efficient
solution obtained from the mathematical model, managers can augment their capacity to make
informed decisions (Afanasyev et al., 2023; Bilbao-Terol et al., 2006; Golmakani & Fazel, 2011;
Kukharova et al., 2021; Liu & Gao, 2006). In general, the goal of the project selection problem
is to choose an optimal portfolio of several selected projects according to the limitations of time,
machinery, power, human capital, and other available facilities to achieve optimal goals. One
of the important and commonly used goals in this field is to maximize the profit of the project
and minimize the costs. Considering that the selection of oil and gas investment projects is
one of the most important organization’s decisions, paying attention only to the goals of the
internal project stakeholders, such as the project sponsor, the employer, contractors, the project
managers, the project consultant, and the main external stakeholders of the project, cannot be
of great benefit to the managers and companies. Therefore, it cannot ensure the success and
survival of the organization in the business environment. If an organization or company acts only
based on profit to decide regarding the selection of the project and the satisfaction of the external
stakeholders of the project, such as competitors, media, legislative organizations, environmen-
talists, sub-stakeholders, society, and citizens, if they do not pay attention, they may face a
challenge in the long run. Therefore, to fulfill the main goals of managers in choosing investment
projects, it is necessary to model the problem from the perspective of both internal and external
stakeholders of the project. Carrying out any project requires the consumption of various re-
newable and non-renewable resources such as manpower, machinery, raw materials, and required
equipment (Arefiev & Afanaseva, 2022). It is noteworthy that the execution of any oil and gas
venture results in the emission of greenhouse gases into the atmosphere (Fetisov et al., 2023;
Litvinenko et al., 2020; Pashkevich & Danilov, 2023). In recent years, there has been a growing
global awareness of pollution control in response to production and industrial activities, driven
by a desire to preserve land and its resources, promote economic development, ensure social wel-
fare, protect the environment, and enhance community security (Fetisov et al., 2023; Ilyushin,
2022; Ilyushin & Fetisov, 2022; Litvinenko et al., 2023). According to the available statistics
and reports, the emission of greenhouse gases around the world has increased by more than 80%
from 1970 to 2010, which is considered a great threat to the global ecosystem (Martirosyan &
Ilyushin, 2022). To reduce greenhouse gas emissions, different international agreements have
been made. For example, China and the United States, as the largest emitters of carbon dioxide
(CO2), announced their joint announcement on climate change in 2014 and policies to reduce
greenhouse gas emissions. Then, at the United Nations (UN) Climate Conference in 2015, a new
global agreement was made in which all participants pledged to reduce greenhouse gas emissions
to zero (Chen & Chen, 2017; Yurak et al., 2020). In light of growing environmental concerns,
business managers have devoted a significant portion of their efforts to executing effective invest-
ment projects that account for environmental considerations, in order to address these concerns
(Martirosyan et al., 2021) by implementing projects in addition to increasing profitable sales and
reducing costs (Kazanin & Drebenshtedt, 2017; Perdan & Azapagic, 2011).
Conversely, in the context of executing an investment initiative project, the organization’s
social responsibility towards employees, customers, and society should be considered with social
goals such as increasing job opportunities, stabilizing employment, and reducing the number
of injuries and lost days due to work accidents (Ilyushin et al., 2019; Moreno-Monsalve et al.,
2023). In recent years, there has been an increased focus on the concept of sustainability, which
involves balancing economic, social, and environmental requirements. With the growth of the
world population and the increase of human activity, sustainability has become an important issue
for governments, people, and environmentalists. Using sustainable development management for
organizations will have many benefits, including customer satisfaction, cost control, innovation,
and flexibility (Moreno-Monsalve et al., 2023; Rohmer et al., 2019; Sahebjamnia et al., 2018;
503
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
Taleizadeh et al., 2019). Although much research has been conducted in the field of investment
project selection, based on the results of the research background, limited research has been
conducted in the field of investment project selection according to Sustainable Development
Goals (SDGs). On the other hand, the decisions about selecting oil and gas investment projects
are among the strategic decisions of petrochemical organizations that are faced with considerable
uncertainty. The project selection problem encompasses numerous parameters, including the
potential profit yielded by project implementation, the availability of manpower, the quantity of
machines and raw materials necessary, the precise timing of activities, the requisite budget, and
the costs associated with both manpower and raw materials. The requirement for the machine’s
cost is faced with significant uncertainty (Teplyakova et al., 2022). Considering these parameters
in a certain way, the optimal solution to the problem may not be justified in real conditions.
Ben-Tal & Nemirovski (2000) demonstrated that even with a mere 0.001% uncertainty in the
parameters, the optimal solution derived from deterministic data is not sufficiently justified with
a significant probability. Consequently, the constraints of the problem may be violated. Hence,
it appears imperative to scrutinize the ambiguity surrounding the choice of investment ventures
(Ben-Tal & Nemirovski, 2000).
The aim of this research is to provide a mathematical model for selecting investment oil and
gas projects based on SDGs and considering the parameter’s uncertainty. In this model, the
goals of profit maximization, environmental impact minimization, and social impact maximiza-
tion will be considered simultaneously. Since the available resources for the implementation of
petrochemical projects are limited, in the mathematical model, the total budget available in a
period will be considered limited, and the real world’s limitations such as manpower, machines,
and consumable resources will also be considered. Decision-making related to the selection of
petrochemical projects is considered over a multi-period time horizon, and the investment and
selection of those projects in each period will be examined separately.
The advantage of a multi-period, multi-objective mathematical model for selecting oil and gas
investment projects compared with existing ones lies in its ability to comprehensively consider
various factors and objectives over time, leading to more informed and strategic decision-making.
This approach integrates multiple criteria and time periods, allowing for a holistic evaluation of
investment projects. The previous studies also emphasize the advantages of rule-oriented models
in decision support systems for oil and gas production companies, highlighting the need to utilize
knowledge base rule-oriented models for decision-making. This aligns with the multi-objective
nature of investment project selection, as it requires the consideration of diverse rules and criteria.
Furthermore, it underscores the adaptability of techniques preferred by organizations, indicating
that the multi-period, multi-objective mathematical model can be tailored to suit the specific
preferences and needs of the oil and gas company.
In conclusion, the advantage of the multi-period, multi-objective mathematical model for
selecting oil and gas investment projects compared with existing ones lies in its comprehensive
consideration of diverse criteria, rules, and time periods, leading to more robust and informed
decision-making processes.
The subsequent section of this manuscript delves into the background of the investigation,
while the third section introduces the suggested mathematical framework. The fourth section
presents a potential approach utilizing fuzzy programming to address the indeterminate nature
of the parameters. The fifth section of the study delves into the methodology employed for
resolving the model. The sixth and seventh sections entail the numerical results and sensitivity
analysis, respectively. The final section provides conclusions and recommendations for future
research.
504
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
2 Research background
In the literature on the selection of investment projects, various mathematical models have
been developed for the selection of projects. This section provides a comprehensive review
of the literature pertaining to the process of selecting investment projects. For this purpose,
Table 1 presented below provides a summary of the solving methods proposed by scholars. It is
noteworthy to mention that in the selection of investment projects, since numerous parameters
of the real world are subject to uncertainty, mathematical modeling also takes uncertainty into
account. To investigate uncertainty, various methods such as Monte Carlo simulation, stochastic
programming, fuzzy theory, robust optimization, and hybrid approaches have been used.
While SDGs have been the subject of numerous research articles in recent years, the matter
of selecting oil and gas investment projects has received comparatively less attention. Therefore,
the characteristics of the reviewed articles are shown in Table 2. As can be seen in most of the
research, only the economic dimension in the selection of projects with the aim of minimizing
the implementation costs or maximizing the profit from the implementation of the project has
been investigated, and other main dimensions of the SDGs, including environmental and social
dimensions, have received less attention. Among the reviewed articles, only Habibi et al. (Habibi
et al., 2019) used SDGs to select the suppliers of materials needed for the projects, and Reza
Hosseini et al. (RezaHoseini et al., 2020) used SDGs to determine the desirability of the selected
projects. Although in the real world it is rare to determine the exact value of the parameters,
in most of the articles the parameters are assumed to be definite. Also, among the various
methods to deal with the uncertainty of parameters, areas such as possible fuzzy optimization
have not been considered at all. Interrelationships between projects have not been investigated
in most studies. In this research, a model for selecting oil and gas investment projects based
on SDGs is proposed in conditions of uncertainty, given the interdependent nature of projects
and resource constraints, the present study proposes a model that innovatively addresses these
factors as below which is mostly modeled on Zarinpour’s work:
1. Providing a mathematical framework for the selection of petrochemical investment projects
over a multi-period time horizon. The model considers various real-world constraints,
including budgetary limitations, manpower availability, machinery capacity, raw material
availability, and supplier capacity,
2. Investigating mutual relationships between projects using complementary economic con-
straints and incompatible options at the same time,
3. Examining the SDGs in the selection of oil and gas investment projects, including the
economic, environmental, and social goals,
4. Examining job opportunities, injuries, and lost days due to work accidents, the number
of people covered by insurance, the impact of project selection on the improvement of the
regional economy, and the social welfare of employees in the function of the social goal,
5. Investigating greenhouse gas emissions, energy consumption, and waste produced in the
review function for environmental purposes,
6. Investigating the uncertainty of real-world parameters and using the fuzzy possibility ap-
proach based on the "Me" criterion to deal with uncertainty in the project selection prob-
lem,
7. Using a combined solution approach, including the Best-Worst group method (BWM) to
determine the weight of environmental and social factors and the interactive fuzzy pro-
gramming method to solve the multi-objective mathematical model.
505
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
Table 1: Summary of models and proposed solving methods by scholars since 2010
Authors(year) Proposed model Proposed solving
method
Ref.
Rabbani et al.(2010) A multi-objective mathematical model for project selection,
in which the objectives of project benefit maximization, risk
minimization and total cost were investigated
Particle swarm
optimization
algorithm
(Rabbani et al.,
2010)
Shakhsi-Niaei et
al.(2011)
A project selection model under the uncertainty considering
a limited budget. Firstly, they ranked the candidate projects
through Monte Carlo simulation and a multi-criteria decision-
making approach, and in the second stage, they proposed an
integer programming model to select the final set of projects
Mixed approach (Shakhsi-Niaei et
al., 2011)
Khalili-Damghani et
al.(2012)
A multi-objective model for selecting projects considering
profit and risk objectives
The TOPSIS
method and the
epsilon constraint
method
(Khalili-Damghani
et al., 2012)
Khalili-Damghani
et al.(2013)
A multi-period multi-objective model for pro ject selection un-
der limited resource conditions
Fuzzy-TOPSIS
implementation
(Khalili-Damghani
et al., 2013)
Zaraket et
al.(2014)
A mathematical model for selecting software projects and re-
source allocation, in which universities, software companies
and potential projects of a country are examined with the
aim of profit maximization
Meta-Heuristic
methods
(Zaraket et al.,
2014)
Huang and
Zhao(2014)
Investigated the problem of selection and timing of research
and development projects under the conditions of uncertainty
of net income and investment costs
Genetic algorithm (Huang & Zhao,
2014)
Huang et al.(2014) A mean-variance optimization model for the optimal project
selection problem based on resource and budget constraints,
considering the uncertainty of initial costs and net cash flows
Meta-Heuristic
methods
(Huang et al., 2014)
Shafahi and
Haghani(2014)
An optimization model for the selection of contracting
projects, in which the importance of activities performed by
contractors is used as the most important non-monetary eval-
uation criterion
Genetic algorithm
and Monte Carlo
simulation
(Shafahi & Haghani,
2014)
Toufighian and
Naderi(2015)
This study proposes a bi-criteria framework for project selec-
tion and scheduling that aims to simultaneously optimize the
expected profit of the project and minimize resource utiliza-
tion.
Meta-Heuristic
methods
(Tofighian &
Naderi, 2015)
Huang et al.(2016) A mean-variance model and a mean-semi-variance model for
the problem of selecting and scheduling optimal projects by
considering the relationship and order of time sequence be-
tween projects
Meta-Heuristic
methods
(Huang et al., 2016)
Tang et al(2017) A mathematical model for selecting oil and gas projects under
budget and production capacity constraints
Quadratic plan-
ning model and
preference theory
(Tang et al., 2017)
Shariatmadari et
al. (2017)
This study proposes two distinct methodologies for project
selection and scheduling, namely an integrated resource man-
agement approach utilising mixed integer programming, and
a hybrid approach combining heuristic algorithm and gravity
search algorithm.
Meta-Heuristic
methods
(Shariatmadari et
al., 2017)
Amirian and
Sahraeian(2017)
A mathematical model for the problem of project selection
and scheduling using the theory of net cash flows of projects
based on gray data
Monte Carlo sim-
ulation and algo-
rithm based on
frog jump
(Amirian &
Sahraeian, 2017)
Kumar et
al.(2018)
Investigated the problem of project selection and planning
with the aim of maximizing the expected profit and consid-
ered two types of interdependence, i.e., constraints of incom-
patible options and constraints of economic complementarity
Meta-Heuristic
methods
(Kumar et al., 2018)
Shafahi and
Haghani(2018)
A mathematical model for project selection and scheduling,
based on which some projects can be implemented in differ-
ent phases, in which maximizes the net present value of fu-
ture investments under budget constraints and reinvestment
strategies
Hybrid integer
programming
model
(Shafahi & Haghani,
2018)
Habibi et al.(2019) A model for ordering materials and scheduling projects, in
which the suppliers of materials required for projects are se-
lected based on sustainability criteria
Fuzzy sequential
analysis method
(Habibi et al., 2019)
Miralinaghi et
al.(2020)
A two-level mathematical model for the selection and schedul-
ing of road construction projects based on game theory, in
which an optimal set of projects is selected and scheduled in
the first level, and in the second level, and the travel delay
time in roads is minimized
Game theory
methods
(Miralinaghi et al.,
2020)
Abbasi et al.(2020) A project selection model for the development of new prod-
ucts in which a balanced scorecard is used to select criteria.
They also used a two-objective model to select projects with
the objectives of profit maximization and risk minimization
Meta-Heuristic
methods
(Abbasi et al., 2020)
Tavana et
al.(2020)
An approach based on multi-criteria decision making and
mathematical modeling to evaluate and select information
technology projects. They evaluated and ranked the projects
and then selected the best projects using a two-objective
mathematical model with the objectives of profit maximiza-
tion and project value maximization
The fuzzy TOP-
SIS method
(Tavana et al., 2020)
Rezahoseini et
al.(2020)
A model for selecting and scheduling projects in which the
attractiveness of projects is determined based on a utility
function dependent on sustainability and projects splitting
Utility function
dependent
(RezaHoseini et al.,
2020)
Mavrotas and
Makryelios(2021)
An approach based on Monte Carlo simulation and mathe-
matical modeling to select R&D projects considering budget
constraints
Monte Carlo
simulation and
mathematical
modeling
(Mavrotas &
Makryvelios, 2021)
Zolfaqhari and
Mousavi(2021)
A project selection and scheduling model considering resource
management, in which the uncertainty of parameters is mod-
eled using an interval-valued fuzzy random uncertainty
Fuzzy methods (Zolfaghari &
Mousavi, 2021)
Hamidi Hesar-
sorkh et al.(2021)
A model for selecting R&D projects in the arbitration indus-
try, in which financial planning and outsourcing policy are
considered. Also, they considered the uncertainty of the pa-
rameters
Probabilistically
robust optimiza-
tion models
(Hesarsorkh et al.,
2021)
Zarinpour and
Zarinpour,(2022)
A model for selecting and scheduling projects in which the
attractiveness of projects is determined based on a utility
function dependent on sustainability and projects splitting
Fuzzy sequential
analysis method
(Zarinpour et al.,
2022)
506
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
Table 2. Characteristics of reviewed scholarly articles in the field of project selection with the approach of the
SDGs from 2010 until present
3 Mathematical model
3.1 Statement of the problem
In this research, a multi-objective mathematical model is presented for choosing investment oil
and gas projects using the SDGs approach. Since the available resources for the project’s imple-
mentation are limited, in the mathematical model, the total available budget is considered for
a limited period, and other real-world limitations such as manpower, machinery (Yungmeister
et al., 2021), and consumables are also considered respectively (Yungmeyster et al., 2022). The
amount of investment and the projects chosen for each period are both determined based on the
decisions made in relation to the selection of projects, which are made with a long-term time hori-
zon. In the proposed model, the interrelationships between the projects, the uncertainty of the
parameters, and the project’s raw material suppliers’ capacity are examined. The assumptions
of the proposed problem are as follows:
1. Decisions related to the selection of projects can be made over several time periods.
2. Complementary economic restrictions are considered in the selection of investment projects.
3. The manpower and raw materials required to carry out investment projects and project’s
raw material suppliers’ capacity in each of the time periods is limited.
4. Some investment projects have incompatible options, so by choosing one of them, the next
incompatible option will be removed.
5. The uncertainty in the model parameters is considered.
The sets defined in the mathematical model are as follows:
507
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
J: set of existing projects;
T: set of time periods;
R: set of raw materials;
M: set of machines;
L: set of human resources;
S: set of suppliers;
K: set of amenities for employees;
Hj: set of incompatible projects with the project j
Ej: set of economic complementary projects of project j.
3.2 Economical objective function
The main goal of choosing oil and gas investment projects is to maximize the profit, which is as
follow:
Max Z1=T R −T C, (1)
where the total revenue from the selection of projects is marked with T R and the total cost of
implementing the projects is marked with T C, which expression 2 is considered as below:
T R =X
jX
t
˜pjt xjt ,(2)
where ˜pjt is the expected profit of the project jat time tand xj t is a binary variable, where
it is equal to 1 if project j is selected at time t, otherwise it is considered zero. To calculate
T C total system costs including fixed investment, raw material supply, manpower, machinery,
travel, and amenities costs are considered. The fixed investment cost of the project can comprise
of expenses related to the acquisition of equipment and machinery essential for the project’s
execution, infrastructure development, land procurement, construction of buildings, landscaping,
and procurement of vehicles, and the cost of issuing permits and initial feasibility studies. This
type of cost is expressed according to expression :
X
jX
t
˜
F cjt xjt ,(3)
where ˜
F cjt is the fixed investment cost to implement project jat time t.
The cost of supplying raw materials consists of the purchase cost and the cost of ordering
raw materials which are procured from different suppliers. The cost of supplying raw materials
is calculated using expression 4:
X
rX
sX
jX
t
˜pcsrtyr sjt +X
rX
sX
jX
t
˜ocrst ursj t,(4)
where ˜pcsrt is the cost of purchasing raw material rfrom supplier sat time t,yrsjt is the amount
of raw material type rsupplied by supplier sfor project jat time t,˜ocrst is the fixed cost of
ordering raw material rsupplied by supplier sat a time t, and ursjt is the binary variable that is
equal to 1 if supplier sis selected to supply raw material type rfor project jat time t, otherwise
it is considered zero.
To implement the project, the cost of manpower is calculated based on the man-hour accord-
ing to the following expression 5:
X
lX
jX
t
˜
lcltwhlxjt,(5)
where ˜
lclt is the cost per hour of labor lat time tand whlis the working hours of labor type l
in each period.
508
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
Also, the cost of machines is calculated based on machine-hours required for the implemen-
tation of the project according to expression 6:
X
mX
jX
t
˜
Mcmt whmxj t,(6)
where ˜
Mcmt is the cost per hour of machine type mat time tand whmis the working hours of
machine type min each period.
Furthermore, the cost for transporting raw materials from the supplier to the project site is
calculated according to the following expression 7:
X
rX
sX
jX
t
˜
T crsjt dsj yrsj t,(7)
where ˜
T crsjt is the transportation cost of the raw material type rfrom the supplier sfor the
implementation of the project jin time tand dsj is the distance between the supplier sand the
project implementation site j.
Finally, the cost of amenities for the employees involved in the project is also calculated
according to the following: X
kX
jX
t
˜
Sckjt okj t,(8)
where ˜
Sckjt is the cost of providing any type of amenities kfor project employees jat time tand
okjt is the binary variable equal to 1 in case of providing any type of amenities kfor the project
employees jat time t, and otherwise zero.
Considering that in evaluating the economic feasibility of the projects the period and the time
value of money are very effective factors, the concept of discount rate has been used. According
to the provided information, it can be inferred that the first expression will be elaborated in the
subsequent manner: (ir is the discount rate in percentage)
Max Z1=X
t
1
(1 + ir)t−1
X
j
˜pjt xjt −X
j
˜
F cjt xjt −X
sX
rX
j
˜pcsrtyr sjt −
−X
rX
sX
j
˜ocrst ursj t−X
lX
j
˜
lcltwhlxjt −X
mX
j
˜
Mcmt whmxj t−
−X
rX
sX
j
˜
T crsjt dsj yrsj t −X
kX
j
˜
Sckjt okj t
.
(9)
3.3 Environmental objective function
To execute a project, it is imperative to procure requisite raw materials, which necessitates
the utilization of vehicles for the purpose of transporting materials from suppliers. The trans-
portation of raw materials results in the emission of significant quantities of greenhouse gases,
including carbon dioxide, methane, sulfur dioxide, nitrogen oxide, heavy metals, and volatile
organic compounds (Fetisov et al., 2023). These emissions pose a severe threat to human health.
The emission of greenhouse gases resulting from the combustion of fossil fuels is widely recognized
as the primary contributor to global warming and consequential alterations in the Earth’s climate
and soil (Martirosyan & Ilyushin, 2022; Shammazov et al., 2023; Vasilyeva, 2023; Zhang et al.,
2018). Conversely, the transportation of raw materials by vehicles necessitates the utilization
of fossil fuels. The global populace’s requirement for non-renewable energy sources is escalating
at a rapid pace, surpassing the capacity of current energy reservoirs to cater to this mounting
509
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
demand. According to a projection (Mirhosseini et al., 2011), the global energy demand is ex-
pected to increase twofold or even threefold by the year 2050. As per the prognostications, the
worldwide utilization of oil is anticipated to escalate from 86 million barrels per diem in 2007
to 104 million barrels per day in 2030 (Brink & Marx, 2013; Ilyushin & Asadulagi, 2023). The
preservation of fossil fuels has become an imperative need considering their depletion and the
pressing environmental issues (Afanaseva et al., 2023; Kazakov et al., 2022).
To mitigate the quantity of greenhouse gas emissions resulting from the conveyance of raw
materials, the fuel consumption associated with the transportation of materials from suppliers
to the designated project site, and the waste generated by the utilization of raw materials in the
chosen projects, we shall employ expressions 10, 11, and 12, correspondingly.
X
rX
sX
jX
t
˜ghrsj dsj yrsj t,(10)
X
rX
sX
jX
t
˜ersj dsj yr sjt ,(11)
X
rX
jX
t
˜wgrj xj t,(12)
where ˜ghrsj is the amount of greenhouse gas emitted to transport raw material type rfrom
supplier sto the project j,˜ersj is the amount of fuel required to transport the raw material type
rfrom supplier sto project j, and ˜wgrj is the percentage of waste produced due to the use of
raw material type rin project j.
According to the importance of greenhouse gas emissions, fuel consumption, and the produc-
tion of waste, the environmental objective function will be as follows:
Min Z2=W e1
X
rX
sX
jX
t
˜ghrsj dsj yrsj t
+W e2hPrPsPjPt˜ersj dsj yr sjt i+
+W e3
X
rX
jX
t
˜wgrj xj t
.
(13)
Here W e1, W e2,and W e3are the weights of greenhouse gas emissions, the weight of the amount
of fuel consumed, and the weight of the amount of waste produced, respectively.
3.4 Social objective function
With the implementation of any investment project, the organization’s social responsibility to-
wards internal and external stakeholders should be considered. The GRI report [36] has been
used to consider the social dimension. One of the most important responsibilities of investors to-
wards society is to increase the number of job opportunities. To implement an investment project,
different human resources, such as project sponsors, employers, project managers, project con-
sultants, project contractors, main project shareholders, and workers, are needed. It is worth
noting that some of the required labor force is required on a constant basis from the beginning to
the end of the project, but some of them will be employed for a short period of time. The number
of fixed and variable job opportunities created by selecting investment projects is calculated as
expressions (14) and (15). Then, the number of idle working days that are lost due to injuries
and work hazards is calculated as belowX
jX
t
˜
fojtxj t,(14)
GRI is an independent international organization that provides sustainability reports based on all SDG
aspects.
510
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
X
jX
t
˜vojt xjt,(15)
X
jX
t
˜
Idjt xjt,(16)
where ˜
fojt is the number of fixed job opportunities created by choosing project jat a time t,
˜vojt is the number of variable job opportunities created by choosing project jat a time t, and
˜
Idjt is number of idle working days caused by choosing project jat a time t.
Given that project employers and contractors frequently hire erratic labor for numerous
projects, insurance typically covers a small number of people. Therefore, to increase the number
of people covered by insurance (objective function 17), to improve the economic situation of
the project implementation area (objective function 18), and to increase the level of employee
satisfaction, considering welfare amenities (objective function 19) as parts of the social objective
function is considered respectively:
X
jX
t
˜
fscjtxj t,(17)
X
jX
t
˜pjt xjt ,(18)
X
kX
jX
t
˜
Jskj tok jt ,(19)
where ˜
fscjt is the number of workers covered by insurance by choosing project jat a time t,
˜pjt is the impact of the project’s implementation jin time ton the economy of the region, and
˜
Jskj t is the employee’s job satisfaction as a result of welfare services type kin project jat time
t.
Considering the weight of each of the project’s social responsibility objectives, the social
objective’s function will be as follows:
Max Z3=W s1hPjPt(˜
fojt + ˜vojt)xj ti+W s2h−PjPt˜
Idjt xjt +PjPt˜
fscjtxj ti+
+W s3hPjPt˜pjt xjt i+W s4hPkPjPt˜
Jskj tok jt i,
(20)
where W s1represents the weight assigned to the number of job opportunities created, W s2
represents the weight assigned to safety and health activities for employees, W s3represents
the weight assigned to the economic development of the region, and W s4represents the weight
assigned to employee amenities.
3.5 Constraints of the proposed problem
The constraints to the problem are taken as
X
t
xjt ≤1,(21)
X
tt+f
dujxjt ≤T+ 1,(22)
X
je
λrj xjt ≤βr t,∀r, t, (23)
511
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
X
jeγmj xjt ≤e
δmt,∀m, t, (24)
X
jeτlj xjt ≤e
Ωlt,∀l, t, (25)
X
t
xjt +X
t
xht ≤1,∀j, h ∈Hj,(26)
X
t
xjt =X
t
xkt,∀j, k ∈Ej,(27)
X
rX
sX
t
yrsjt =X
tX
re
λrj xjt ,∀j, (28)
X
sX
j
yrsjt =βr t,∀r, t, (29)
yrsjt ≤˜caprs ursj t,∀r, s, j, t, (30)
ursjt ≤xj t,∀r, s, j, t, (31)
xjt ∈ {0,1},∀j, t, (32)
yrsjt ≥0,∀r, s, j, t, (33)
ursjt ∈ {0,1},∀r, s, j, t, (34)
okjt ∈ {0,1},∀k, j, t, (35)
βrt ≥0,∀r, t. (36)
Constraint 21 guarantees that each project is selected only once in each period. According to
constraint 22, each project must be completed within the planned time horizon. Constraint 23
specifies that the total raw materials required to carry out the selected projects should not exceed
the available raw materials in any period (e
λrj is the required type rraw material for the project
jin each period, and βrt is the amount of primary material type rat time t). Constraint 24
states that the working hours of the machines required for the selected projects do not exceed
the available machine-hours in any period (eγmj is the required machine-hours type mfor project
jin each period, and e
δmt is machine-hours available type mat time t). Based on the constraint
25, the man-hours required to carry out the selected projects do not exceed the available man-
hours in any period (eτlj is the number of man-hours required for labor lfor project jin each
period, and e
Ωlt is man-hours available type lat time t). Constraint 26 is related to incompatible
project options: if the projects are incompatible, only one of them will be selected. Constraint 27
expresses the restriction of economic complementarity between projects. Constraint 28 specifies
that in each project, the total raw materials purchased from suppliers are equal to the raw
materials needed to complete that project. Constraint 29 specifies that the total raw material
purchased from suppliers is equal to the available raw material in each period. According to
the constraint 30, the number of raw materials purchased must be less than the capacity of the
suppliers. Constraint 31 specifies that only if a project is selected, suppliers will be selected
to provide raw materials. The constraint of 32 to 36 specifies the constraints of the problem’s
decision variables.
512
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
4 A probabilistic fuzzy programming approach
In the previous section’s proposed model, some parameters are uncertain. Approaches such as
random optimization (RO), fuzzy optimization (FO), stable optimization, and hybrid approaches
can be used to deal with parameter uncertainty. In this study, the fuzzy optimization method
(FOM) is used to deal with the uncertainty in the parameters of the model. In fuzzy mathematical
programming (FMP) models, fuzzy confidence coefficients and membership functions are used
to express the uncertainty of parameters (Xu & Zhou, 2013; Zarrinpoor et al., 2018). Numerous
researchers have used the fuzzy-probabilistic method that Xu and Zhou (Xu & Zhou, 2013)
first proposed because of its widespread success. This method relies on strong mathematical
concepts such as expected distance and the expected value of fuzzy numbers. In this method,
it is assumed that all non-deterministic parameters follow the triangular distribution function.
Consider the possibility space (θ, P (θ), P oS ) where θ, P (θ),and P oS specify an arbitrary
set, a set function of θ, and a possibility criterion, respectively. To determine the values of non-
deterministic parameters between optimistic and pessimistic constraints, Xu, and Zhou (Zhang
et al., 2018) used the Me criterion as follow:
M e (A) = Nec (A) + ς(P os (A)−N ec (A)) ,(37)
where A is an arbitrary set in P(θ),and ςis an optimistic-pessimistic parameter that reflects the
decision-makers opinions. Functions P os (A) and N ec (A)specify the necessity and possibility
of set Ain probabilistic space, respectively. In the following, the approach of Xu and Zhou
(2013) is briefly described. Consider the following linear programming model:
Min ˜
Cx
˜
Ax ≥˜
b
˜
Nx ≤˜
d
x≥0.
(38)
In this model, non-deterministic parameters are considered triangular fuzzy numbers (TFN). In
probabilistic planning based on criterion 1, the functions of expected value, chance limit, and
possibility limit are used. So, we have:
Min ˜
Cx
M e {˜
Ax ≥˜
b} ≥ α
M e {˜
Nx ≤˜
d} ≥ β
x≥0,
(39)
where αand βare the minimum levels of satisfying the possible constraints. Xu, and Zhou
converted the above model into upper approximation model (UAM) and a lower approxima-
tion model (LAM), and then, they proposed the deterministic equivalent (DE) model of the
probabilistic models UAM and LAM, which are as follows:
Upper Approximation Model (UAM)
M in E[˜
C]x
P os {˜
Ax ≥˜
b} ≥ α
P os {˜
Nx ≤˜
d} ≥ β
x≥0
(40)
Lower Approximation Model (LAM)
M in E[˜
C]x
N ec {˜
Ax ≥˜
b} ≥ α
N ec {˜
Nx ≤˜
d} ≥ β
x≥0
(41)
513
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
The deterministic equivalent model of the probabilistic model UAM is in the form
Min 1−c
2C1+1
2C2+c
2C3x
A2x+ (1 −α)(A3−A2)x≥b2−(1 −α)(b2−b1)
N2x−(1 −β)(N2−N1)x≤d2+ (1 −β)(d3−d2)
x≥0.
(42)
The deterministic equivalent model of the probabilistic model LAM is
Min 1−c
2C1+1
2C2+c
2C3x
A2x+α(A2−A1)x≥b2+ (1 −α)(b3−b2)
N2x+ (1 −β)(N3−N21)x≤d2−β(d2−d1)
x≥0.
(43)
Considering the possible planning method based on criteria, the deterministic equivalent
model of the proposed non-deterministic problem based on UAM will be as follows
Max Z1=X
t
1
(1 + ir)t−1[X
j1−ς
2p(1)
jt +1
2p(2)
jt +ς
2p(3)
jt xj t−
X
j1−ς
2F c(1)
jt +1
2F c(2)
jt +ς
2F c(3)
jt xj t−
X
sX
rX
j1−ς
2pc(1)
srt +1
2pc(2)
srt +ς
2pc(3)
srtyr sjt −
X
rX
sX
j1−ς
2oc(1)
rst +1
2oc(2)
rst +ς
2oc(3)
rstur sjt −
X
lX
j1−ς
2lc(1)
lt +1
2lc(2)
lt +ς
2lc(3)
lt whlxjt−
X
mX
j1−ς
2Mc(1)
mt +1
2Mc(2)
mt +ς
2Mc(3)
mtwhmxjt−
X
rX
sX
j1−ς
2T c(1)
rsjt +1
2T c(2)
rsjt +ς
2T c(3)
rsjt dsj yrsj t−
X
kX
j1−ς
2Sc(1)
kjt +1
2Sc(2)
kjt +ς
2Sc(3)
kjt okj t];
(44)
Min Z2=W e1
X
rX
sX
jX
t1−ς
2gh(1)
rsj +1
2gh(2)
rsj +ς
2gh(3)
rsj dsj yrsj t
+
W e2
X
rX
sX
jX
t1−ς
2e(1)
rsj +1
2e(2)
rsj +ς
2e(3)
rsj dsj yrsj t
+
W e3
X
rX
jX
t1−ς
2wg(1)
rj +1
2wg(2)
rj +ς
2wg(3)
rj xjt
;
(45)
Max Z3=W s1hPjPt1−ς
2fo(1)
jt +1
2fo(2)
jt +ς
2fo(3)
jt xj t +PjPt1−ς
2vo(1)
jt +1
2vo(2)
jt +ς
2vo(3)
jt xj ti+
W s2h−PjPt1−ς
2Id(1)
jt +1
2Id(2)
jt +ς
2Id(3)
jt xj t +PjPt1−ς
2fsc(1)
jt +1
2fsc(2)
jt +ς
2fsc(3)
jt xj ti+
W s3hPjPt1−ς
2p(1)
jt +1
2p(2)
jt +ς
2p(3)
jt xj ti+W s4hPkPjPt1−ς
2js(1)
kjt +1
2js(2)
kjt +ς
2js(3)
kjt okj ti.
(46)
514
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
Subject to (21), (26), (27), (29), (31)-(36)
X
tt+hdu(2)
j−(1 −β)du(2)
j−du(1)
jixjt ≤T+ 1,∀j(47)
X
jhλ(2)
rj −(1 −β)λ(2)
rj −λ(1)
rj ixjt ≤βr t,∀r, t (48)
X
jhγ(2)
mj −(1 −β)γ(2)
mj −γ(1)
mj ixjt ≤δ(2)
mt + (1 −β)δ(3)
mt −δ(2)
mt ,∀m, t (49)
X
jhτ(2)
lj −(1 −β)τ(2)
lj −τ(1)
lj ixjt ≤Ω(2)
lt + (1 −β)Ω(3)
lt −Ω(2)
lt ,∀l, t (50)
X
rX
sX
t
yrsjt ≥X
tX
r
λ(2)
rj xjt ,∀j(51)
X
rX
sX
t
yrsjt ≤X
tX
r
λ(3)
rj xjt ,∀j(52)
yrsjt ≤hcap(2)
rs + (1 −β)cap(3)
rs −cap(2)
rs iursj t,∀r, s, j, t. (53)
The deterministic equivalent model of the proposed non-deterministic problem based on LAM
will be as follows:
Max E (Z1),
Min E (Z2),
Max E (Z3).
Subject to (21), (26), (27), (29), (31)-(36), (51), (52)
X
tt+hdu(2)
j+ (1 −β)du(3)
j−du(2)
jixjt ≤T+ 1,∀j(54)
X
jhλ(2)
rj + (1 −β)λ(3)
rj −λ(2)
rj ixjt ≤βr t,∀r, t (55)
X
jhγ(2)
mj + (1 −β)γ(3)
mj −γ(2)
mj ixjt ≤δ(2)
mt −βδ(2)
mt −δ(1)
mt ,∀m, t (56)
X
jhτ(2)
lj + (1 −β)τ(3)
lj −τ(2)
lj ixjt ≤Ω(2)
lt −βΩ(2)
lt −Ω(1)
lt ,∀l, t (57)
yrsjt ≤hcap(2)
rs −βcap(2)
rs −cap(1)
rs iursj t,∀r, s, j, t. (58)
5 Solution method
In this study, a two-step solution method is used. In the first stage, the importance of envi-
ronmental and social criteria is determined using the best-worst method (BWM). In the second
step, an interactive fuzzy programming method will be used to transform the multi-objective
mathematical programming problem into a single-objective problem.
515
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
5.1 The Best-Worst Method (BWM)
BWM was introduced in 2015 to determine the weight of decision-making problem criteria
(Rezaei, 2015). In this study, considering that this method only uses the preferences of a decision
maker, to determine the weight of the criteria based on the opinions of a group of decision mak-
ers, the BWM of Omrani et al. (2020) has been used. The steps of this method are summarized
as follows:
1. Step 1. Determine the important criteria for the decision problem.
2. Step 2. determine the best and worst criteria from each decision maker’s perspective.
3. Step 3. Specify the preference of the best criterion (B) over the rest of the criteria based
on the opinion of the decision maker (r) with numbers 1 to 9 as follows:
Ar
B= (ar
B1, ar
B2, . . . , ar
Bn).(59)
4. Step 4. Specify the preference of other criteria over the worst criteria (W) based on the
decision maker’s opinion (r) with numbers 1 to 9 as follows:
Ar
W= (ar
1W, ar
2W, . . . , ar
nW ).(60)
5. Step 5. Considering ar
Bo, the preference of the best criterion (B) over criterion obased on
the opinion of decision maker rand ar
oW , the preference of the criterion oover the worst
criterion (W) based on the opinion of the decision maker (r), determine the optimal weight
of each criterion based on the following model:
M in X
r
ξr(61)
|ωB−ar
Boωo| ≤ ξr,∀o, r (62)
|ω0−ar
oW ωW| ≤ ξr,∀o, r (63)
X
0
ωo= 1,(64)
ωo≥0.(65)
Considering that the above-mentioned model is nonlinear, its linear form is written as follows:
M in X
r
ξr(66)
Subject to (64), (65)
ωB−ar
Boωo≤ξr,(67)
ωB−ar
Boωo≥ −ξr,∀o, r (68)
ωo−ar
oW ωW≤ξr,(69)
ωo−ar
oW ωW≥ −ξr,∀o, r (70)
516
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
5.2 Interactive fuzzy programming (IFP) method
To solve multi-objective problems, there are various methods, such as the Epsilon constrained
method (ECM), the LP-metric method, and the weighted sum method (WSM). In this study,
the interactive fuzzy programming method (IFPM) proposed by Torabi and Hassini (Torabi &
Hassini, 2008) is used to solve multi-objective problems. In this approach, positive ideal solutions
(PIS) and negative ideal solutions (NIS) for the objective functions of the problem are calculated
as follows:
ZP IS
1=Min Z1=M ax Z1, ZN I S
1,(71)
ZP IS
2=Max Z2=M in Z2, ZN I S
2,(72)
ZP IS
3=Min Z3=M ax Z3, ZN I S
3.(73)
The linear membership function (LMF) for each of the objective functions is also defined as
follows:
µ1(Z1) =
1, Z1> ZP IS
1
Z1−ZNI S
1
ZP IS
1−ZNI S
1
, ZNIS
1≤Z1≤ZP IS
1
0, Z1< ZNIS
1
(74)
µ2(Z2) =
1, Z2< ZP IS
2
ZNI S
2−Z2
ZNI S
2−ZP IS
2
, ZP IS
2≤Z2≤ZNIS
2
0, Z2> ZNIS
2
(75)
µ3(Z3) =
1, Z3> ZP IS
3
Z3−ZNI S
3
ZP IS
3−ZNI S
3
, ZNIS
3≤Z3≤ZP IS
3
0, Z3< ZNIS
3
(76)
The following expressions are used to convert the multi-objective model into a single-objective
model:
M ax λ (x) = ϕλ0+ (1 −ϕ)X
h
$hµh(x)(77)
λ0≤µh(x),∀h(78)
x∈F(x), λ0, ϕ ∈[0,1] .(79)
where $h,F(x)and ϕdetermine the relative importance of objective function h, the solution
space of the problem and the compensation coefficient, respectively. Also, λ0= minhµh(x)and
µh(x)determine the membership degrees of objective function h.
6 Numerical results
In this section, solution methods are used to explain the numerical results of the proposed model’s
solution. Table 3 shows the values of the input parameters in numerical examples. To determine
the weight of the components of the environmental and social objective functions, the opinions
of five experts in the field of investment projects were used.
517
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
Table 3. Values of the input parameters in numerical examples
Parameters Quantity Parameters Quantity
e
pjt[100000000, 500000000]
e
Ωlt [0, 30]
e
Fcjt[3000000, 21000000] dsj [0, 150]
e
pcsrt [2000, 5000] ˜ersj [5, 20]
e
ocrst [5000, 6000] ˜ghrsj [1, 5]
f
Mcmt[1000, 4000] ˜
fojt [3, 10]
lclt[8000, 30000] ˜vojt [4, 10]
e
Sckjt [3000, 12000] ˜
Idj t [5, 8]
e
Tcrsjt [10, 30] ˜
jskj t [0, 0.8]
ir10% ˜pjt [0.02, 0.04]
e
λrj[0, 20] whl[0, 8]
eτlj[0, 10] whm[0, 8]
eγmj[0, 20] ˜capr s [200, 1000]
e
δmt[0, 50] ˜
duj[1, 10]
Table 4 shows the preference of the best criterion (B) over other criteria and the preference
of other criteria over the worst criterion (W) for environmental and social factors. In this table,
the amount of greenhouse gas emissions is shown with (e1), the amount of energy consumption
with (e2), and the amount of produced waste with (e3). And, in the same table, the prefer-
ence of decision makers according to social criteria is presented. In this table, the number of
job opportunities created by (s1), safety and health activities for employees by (s2), economic
development of the region by (s3), and amenities by (s4) are demonstrated. Tables 5 also shows
the optimal weight of environmental and social criteria.
Table 4. The preference of decision makers according to environmental and social criteria
Decision
Makers
The best and worst criteria The criteria
e1e2e3s1s2s3s4
DM 1The best criteria (e2) and (s2)6199154
The worst criteria (e3) and (s1)7911976
DM 2The best criteria (e1) and (s3)1789516
The worst criteria (e3) and (s1)8611695
DM 3The best criteria (e2) and (s2)5197159
The worst criteria (e3) and (s4)6915961
DM 4The best criteria (e2) and (s3)4199516
The worst criteria (e3) and (s1)7911796
DM 5The best criteria (e1) and (s3)1685419
The worst criteria (e3) and s4)8715691
Table 5. The optimal weight of environmental and social criteria
Criteria e1e2e3s1s2s3s4
The weight of the criteria 0.4908 0.2908 0.2181 0.1851 0.3333 0.3333 0.1481
Five different examples are used for numerical results. The model is coded in GAMS opti-
mization software (Released May 18, 2023). The size of the sets of numerical examples is shown
in Table 6, and the numerical results obtained from solving the model are shown in Table 7.
In Table 7, (DE) specifies the value of the objective function in linear mode. As can be seen,
the profit from the implementation of projects in all numerical examples in the UAM model is
greater than that in the LAM model. Because the UAM model is based on an optimistic view,
the profit from the implementation of projects (ς) increases with the increase in the optimistic
opinions of the decision makers. When the profit of the projects increases, more projects will
be selected, and more raw materials will be needed to implement the projects. Vehicles are
used to transport raw materials from suppliers to the project site which results in large amounts
518
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
of greenhouse gases and energy. Therefore, the value of the environmental objective function
increases. The value of the social objective function also increases in proportion to the profit of
the project. Because, when more projects are selected, more job opportunities will be created.
Since the focus is mostly on the economic dimension in the project selection models, the
impact of sustainability dimensions on the selection of investment projects has been investigated.
Table 8 shows the results based on the third numerical example. In this table, SM is a proposed
model based on SDGs, and PM is a model considering the maximization of expected profit. As
can be seen, considering the SDGs, the result of the economic objective function in deterministic
models (UAM and LAM) will decrease by 0.13%, 1.19%, and 0.13%, respectively, though it
will significantly improve the environmental and social objective functions. The destructive
environmental effects in the deterministic models (UAM and LAM) in the PM model are 2.31,
2.82, and 2.25 times of those of the model considering sustainability, respectively. The social
objective function of the deterministic and UAM models in the SM case has been improved by
95.4 and 98.97 percent, respectively, compared to the PM case. The social objective function of
LAM is also 2.06 times that of PM in the SM case.
Table 6. The size of the sets of numerical examples
Numerical examples |J| |T| |R| |M| |L| |S| |K|
15732232
210 8 5 4 3 4 3
315 9 7 5 4 5 4
421 11 9 6 5 6 5
528 13 11 7 6 7 6
Table 7. The numerical results obtained from solving the model.
Table 8. Comparison of the proposed model and profit maximization model for model 3
D LAM UAM
PM SM PM SM PM SM
Z1 3.214945E+09 3.210700E+09 2.766536E+09 2.733912E+09 3.214971E+09 3.210752E+09
Z2 297095.431 128851.352 278935.149 98732.595 264165.827 117210.973
Z3 37.321 72.927 34.934 71.818 37.404 74.423
m1 1.000 0.999 1.000 0.988 1.000 0.987
m2 0.605 0.829 0.592 0.856 0.639 0.863
m3 0.423 0.826 0.448 0.921 0.451 0.877
519
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
7 Sensitivity analysis
This section presents an analysis of the variations in the objective function concerning the pa-
rameters of ϕ, discount rate (ir), available person-hours, and available machine-hours, utilizing
numerical example number 5.
7.1 The effect of ϕon the objective functions
To investigate the effect of ϕon the objective functions, the value of the degree of membership
in each function has been investigated. Table 9 shows the effect of ϕon the objective functions.
As can be seen, with the increase in the value of the membership degree of the first objective
function, the membership degree of the second objective function decreases and the membership
degree of the second objective function increases. The degree of membership in the third objective
function also has no special trend. Of course, in each of the deterministic models, UAM and
LAM, for some values of ϕ, the membership degree of the function remains unchanged. Also,
the results of the investigation of effect of ϕon the objective functions shows that results from
DE, UAM and LAM are convergent to 0.870 (Figure 1).
Table 9. The effect of ϕon the objective functions
ϕD LAM UAM
m1 m2 m3 m1 m2 m3 m1 m2 m3
00.999 0.829 0.826 0.988 0.856 0.921 0.999 0.840 0.898
0.1 0.999 0.829 0.826 0.988 0.856 0.921 0.999 0.840 0.898
0.2 0.999 0.829 0.826 0.988 0.856 0.921 0.987 0.863 0.877
0.3 0.999 0.829 0.826 0.988 0.856 0.921 0.987 0.863 0.877
0.4 0.999 0.829 0.826 0.988 0.856 0.921 0.987 0.863 0.877
0.5 0.999 0.829 0.826 0.988 0.856 0.921 0.987 0.863 0.877
0.6 0.910 0.849 0.883 0.988 0.856 0.921 0.987 0.863 0.877
0.7 0.868 0.861 0.873 0.920 0.879 0.886 0.987 0.863 0.877
0.8 0.868 0.861 0.873 0.920 0.879 0.886 0.877 0.877 0.880
0.9 0.868 0.861 0.873 0.920 0.879 0.886 0.877 0.877 0.880
10.868 0.861 0.865 0.892 0.879 0.879 0.877 0.877 0.880
Figure 1: The results of the investigation of effect of ϕon the objective functions
520
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
7.2 The Effect of discount rate (ir) on the objective functions
The effect of the discount rate (ir) on the objective functions is shown in Table 10 and figure
2. As can be seen, with the increase in the ir, the total profit decreases. Also, in some cases,
the environmental objective function and the social objective function are relatively reduced and
remain constant. It should be noted that the discount rate is one of the most influential param-
eters on the profit obtained from the oil and gas project’s implementation which by considering
it, a profitable project may be considered uneconomical. Considering that both the income and
expenses of the investor are affected by the discount rate (ir), profitable projects should be
selected according to the discount rate (ir) and the time factor (t).
Table 10. The effect of the discount rate (ir) on the objective functions
irD LAM UAM
Z1 Z2 Z3 Z1 Z2 Z3 Z1 Z2 Z3
5% 3.706272E+09 122862.295 74.208 3.279311E+09 98732.595 71.818 3.963227E+09 117210.973 74.423
10% 3.010700E+09 118851.352 72.927 2.733912E+09 98732.595 71.818 3.210752E+09 117210.973 74.423
15% 2.475420E+09 113102.470 71.913 2.328027E+09 97971.445 70.421 2.677894E+09 96795.550 71.309
20% 2.121001E+09 113102.470 71.913 2.000735E+09 97971.445 70.421 2.285416E+09 96795.550 71.309
25% 1.815055E+09 107071.860 70.953 1.735980E+09 97971.445 70.421 1.978719E+09 93977.590 70.393
The results of the analysis show that the closest exponential trend line for the objective
functions is y= 4E+ 09e−0.178x, R2= 0.995 (Figure 2).
Figure 2: The effect of the discount rate (ir) on the objective functions
7.3 The impact of available machine-hours and maximum available
person-hours on objective functions
The impact of the maximum available machine hours is shown in Table 11. In this table, the first
column shows the percentage of maximum machine-hour changes compared to the base state. By
increasing the available machine hours in each period, more projects can be implemented, and
the profit from the implementation of investment projects in the oil and gas industry increases.
As the number of selected projects increases, the environmental objective function and the social
objective function also increase. In general, time is considered as an important factor in the
profitability of the selected oil and gas projects, and if the machine hours available in the initial
time periods of the project can provide the machine hours required by the project, a high profit
will be obtained for the investors.
Also, the effect of the maximum available man-hours is shown in Table 12. As it can be
seen, by increasing the maximum number of available man-hours, the necessary manpower to
complete the projects is provided in less time, and the projects become profitable sooner than
521
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
expected. Furthermore, by increasing the maximum available man-hours compared to the base
case, as profitability increases, the economic impact of the project on the region and the number
of available job opportunities increase, and as a result, the social objective function increases
compared to the base case. With the increase in available man-hours, as more projects are
selected, the amount of energy consumption and greenhouse gas emissions will increase, and the
objective environmental function will increase, respectively.
Table 11. The impact of the maximum available machine hours
% D LAM UAM
Z1 Z2 Z3 Z1 Z2 Z3 Z1 Z2 Z3
-20 2.860279E+09 104865.812 72.343 2.456912E+09 77091.073 67.057 2.906881E+09 109696.826 73.605
-10 2.906878E+09 120567.874 72.570 2.546337E+09 82988.835 69.123 2.994517E+09 110234.723 74.510
03.210700E+09 128851.352 72.927 2.733912E+09 98732.595 71.818 3.210752E+09 117210.973 74.423
10 3.231657E+09 129761.187 73.422 2.816691E+09 116453.761 75.285 3.239712E+09 118921.188 75.634
20 3.254746E+09 131275.894 77.075 2.844017E+09 117065.666 77.617 3.254757E+09 119379.594 77.773
Table 12. The effect of the maximum available man-hours
% D LAM UAM
Z1 Z2 Z3 Z1 Z2 Z3 Z1 Z2 Z3
-20 2.678142E+00 111749.693 70.974 2.524386E+00 94778.300 71.269 2.705919E+00 104271.254 71.678
-10 2.816719E+00 126699.774 71.891 2.671828E+00 97126.124 71.547 2.816723E+00 115391.996 72.285
03.210700E+00 128851.352 72.927 2.733912E+00 98732.595 71.818 3.210752E+00 117210.973 74.423
10 3.230857E+00 129687.173 79.409 2.994522E+00 100251.176 74.651 3.351887E+00 117878.958 79.060
20 3.288020E+00 130486.734 79.508 3.178685E+00 111155.371 76.661 3.380361E+00 118258.236 79.786
8 Conclusion
In this study, the multi-objective planning problem of choosing investment projects considering
real-world limitations such as manpower, machinery, and consumables was presented. To select
investment projects, in addition to the economic objective function that maximizes the profit
from the implementation of the oil and gas projects, environmental and social objectives were also
considered. The proposed model was considered a multi-cycle mathematical programming model.
Based on the environmental dimension, the amount of greenhouse gas emissions, the amount of
energy consumed to provide the required raw materials, and the amount of waste produced
were minimized. Based on the social dimension, the number of job opportunities created by the
selected projects, the number of people covered by insurance, the job satisfaction of employees
because of the provision of welfare services, the impact of the project on the region’s economy,
and the number of lost working days were minimized. Also, the capacity of the suppliers to
provide the raw materials needed by the projects and the costs of purchasing and ordering the raw
materials were considered. Considering that in the real world, many parameters are uncertain and
random in nature, the uncertainty of the parameters was also considered. To transform the non-
deterministic model into a deterministic equivalent model, the fuzzy probability programming
approach based on the Me criterion was used, and two LAM and UAM models were developed. To
check the effectiveness of the proposed model, five different numerical examples were considered,
and the results were presented based on economic, social, and environmental objective functions.
In the end, the sensitivity analysis of the key parameters was presented.
Based on the numerical results, it can be stated that the presented mathematical model
provides a suitable tool for decision-making regarding the evaluation and selection of projects for
the senior managers of organizations and enables them to get the highest profit by choosing the
best set of projects and thereby overshadow their competitive position accordingly. Since the
UAM model is based on an optimistic view, in most of the numerical examples, the profit from
the implementation of the projects is greater than the LAM and the deterministic equivalent
model.
In UAM model, more projects are selected, so as the profit is higher, more energy will be
consumed and more greenhouse gases will be emitted, so the environmental objective function in
most numerical examples in UAM model is also higher than in LAM model. Also, UAM model
has a higher social objective function than LAM model and is a deterministic model. Therefore,
522
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
based on the numerical results, it can be stated that considering the SDGs will significantly
improve the environmental and social dimensions of sustainability without having a significant
impact on the profit of the project’s implementation.
The results of this research show that if there is uncertainty in the model’s parameters, they
cannot be ignored. Because, the profitability of the investor is greatly affected, and the amount
of profit will be less or more than the actual amount. The discount rate (ir) is one of the most
influential parameters in investment; considering it, an economic project has a chance to may
be considered uneconomical. Therefore, its exact amount should be determined according to the
type of project so that the investor can choose profitable projects in the shortest possible time. In
general, by increasing the maximum machine hours and the maximum person hours available, it
becomes possible to carry out investment projects in a shorter period, and consequently, the profit
from the project’s implementation increases. Therefore, to design an effective project selection
mathematical model, it is necessary to consider real-world constraints such as renewable and
non-renewable resources for the implementation of projects to obtain an accurate estimate of the
implementing projects’ benefit.
9 Recommendations for the future research
According to the proposed model in this article, future research directions for researchers in the
fields of investment and project management are suggested as follows:
In the proposed model, the maximum machine-hour and person-hour available in each period
are considered parameters. It would be very interesting for future research to consider these
parameters as decision variables. In the proposed model, the effect of loans, sanctions, currency
exchange rate, and other financing sources on the implementation of projects can be considered.
In this study, fuzzy probabilistic programming was used to deal with uncertainty. For future
research, other approaches such as robust optimization and stochastic planning (logic-based
Bender’s decomposition (LBBD) can be used to deal with uncertainty and compare the results
with the possible fuzzy planning approach.
References
Abbasi, D., Ashrafi, M., & Ghodsypour, S.H. (2020). A multi objective-BSC model for new
product development project portfolio selection. Expert Systems with Applications, 162,
113757.
Afanaseva, O., Bezyukov, O., Pervukhin, D., & Tukeev, D. (2023). Experimental Study Results
Processing Method for the Marine Diesel Engines Vibration Activity Caused by the Cylinder-
Piston Group Operations. Inventions, 8(3), 71.
Afanasyev, M., Pervukhin, D., Kotov, D., Davardoost, H., & Smolenchuk, A. (2023). System
Modeling in Solving Mineral Complex Logistic Problems with the Anylogic Software Environ-
ment. Transportation Research Procedia, 68, 483-491.
Amirian, H., Sahraeian, R. (2017). Solving a grey project selection scheduling using a simulated
shuffled frog leaping algorithm. Computers & Industrial Engineering, 107, 141-149.
Arefiev, I.B., Afanaseva, O.V. (2022). Implementation of Control and Forecasting Problems of
Human-Machine Complexes on the Basis of Logic-Reflexive Modeling. In System Analysis in
Engineering and Control (pp. 187-197). Springer.
Ben-Tal, A., Nemirovski, A. (2000). Robust solutions of linear programming problems contami-
nated with uncertain data. Mathematical Programming, 88, 411-424.
523
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
Bilbao-Terol, A., Pérez-Gladish, B., & Antomil-Lbias, J. (2006). Selecting the optimum portfolio
using fuzzy compromise programming and Sharpe’s single-index model. Applied Mathematics
and Computation, 182 (1), 644-664.
Brink, J., Marx, S. (2013). Harvesting of Hartbeespoort Dam micro-algal biomass through sand
filtration and solar drying. Fuel, 106, 67-71.
Chen, J.-X., Chen, J. (2017). Supply chain carbon footprinting and responsibility allocation
under emission regulations. Journal of Environmental Management, 188, 255-267.
Davardoost, H., Javadi, M. (2019). Complexity and Conflict Management in Iran’s Oil and Gas
Projects Evidence from One of the South Pars Gas Field Development Phases. International
Conference on Innovations in Business administration and Economics.
Fetisov, V., Davardoost, H., & Mogylevets, V. (2023). Technological Aspects of Methane–
Hydrogen Mixture Transportation through Operating Gas Pipelines Considering Industrial
and Fire Safety. Fire, 6 (10), 409.
Fetisov, V., Gonopolsky, A.M., Davardoost, H., Ghanbari, A.R., & Mohammadi, A.H. (2023).
Regulation and impact of VOC and CO2 emissions on low?carbon energy systems resilient to
climate change: A case study on an environmental issue in the oil and gas industry. Energy
Science & Engineering, 11 (4), 1516-1535.
Fetisov, V., Gonopolsky, A.M., Zemenkova, M.Y., Andrey, S., Davardoost, H., Mohammadi,
A.H., & Riazi, M. (2023). On the Integration of CO2 Capture Technologies for an Oil Refinery.
Energies, 16 (2), 865.
Golmakani, H.R., Fazel, M. (2011). Constrained portfolio selection using particle swarm opti-
mization. Expert Systems with Applications, 38 (7), 8327-8335.
Habibi, F., Barzinpour, F., & Sadjadi, S.J. (2019). A mathematical model for project schedul-
ing and material ordering problem with sustainability considerations: A case study in Iran.
Computers & Industrial Engineering, 128, 690-710.
Hesarsorkh, A.H., Ashayeri, J., & Naeini, A.B. (2021). Pharmaceutical R&D project portfo-
lio selection and scheduling under uncertainty: A robust possibilistic optimization approach.
Computers & Industrial Engineering, 155, 107114. Huang, X., Xiang, L., & Islam, S. M. (2014).
Optimal project adjustment and selection. Economic Modelling, 36, 391-397.
Huang, X., Zhao, T. (2014). Project selection and scheduling with uncertain net income and
investment cost. Applied Mathematics and Computation, 247, 61-71.
Huang, X., Zhao, T., & Kudratova, S. (2016). Uncertain mean-variance and mean-semivariance
models for optimal project selection and scheduling. Knowledge-Based Systems, 93, 1-11.
Ilyushin, Y.V. (2022). Development of a Process Control System for the Production of High-
Paraffin Oil. Energies, 15 (17), 6462.
Ilyushin, Y.V., Asadulagi, M.A.M. (2023). Development of a Distributed Control System for
the Hydrodynamic Processes of Aquifers, Taking into Account Stochastic Disturbing Factors.
Water, 15 (4), 770.
Ilyushin, Y.V., Fetisov, V. (2022). Experience of virtual commissioning of a process control
system for the production of high-paraffin oil. Scientific Reports, 12 (1), 18415.
Ilyushin, Y.V., Pervukhin, D.A., & Afanaseva, O.V. (2019). Application of the theory of systems
with distributed parameters for mineral complex facilities management. ARPN Journal of
Engineering and Applied Sciences, 14 (22), 3852-3864.
524
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
Kazakov Yu.A., Garufullin, D., Korotkova, O.Y., & Agaguena, A. (2022). Analysis of the mobile
complex structure for organogenic materials mining by in-pit method. Mining informational
and analytical bulletin, 6, 317-330.
Kazanin, O.I., Drebenshtedt, K. (2017). Mining education in the XXI century: global challenges
and prospects. Journal of Mining Institute, 225 (0), 369. https://doi.org/10.18454/pmi.
2017.3.369
Khalili-Damghani, K., Sadi-Nezhad, S., & Tavana, M. (2013). Solving multi-period project selec-
tion problems with fuzzy goal programming based on TOPSIS and a fuzzy preference relation.
Information Sciences, 252, 42-61.
Khalili-Damghani, K., Tavana, M., & Sadi-Nezhad, S. (2012). An integrated multi-objective
framework for solving multi-period project selection problems. Applied Mathematics and Com-
putation, 219 (6), 3122-3138.
Kukharova, T.V., Utkin, V.A., & Pershin, I.M. (2021). Modeling of a Decision Support System
for a Psychiatrist Based on the Dynamics of Electrical Conductivity Parameters. 2021 IEEE
Conference of Russian Young Researchers in Electrical and Electronic Engineering (ElCon-
Rus).
Kumar, M., Mittal, M.L., Soni, G., & Joshi, D. (2018). A hybrid TLBO-TS algorithm for
integrated selection and scheduling of projects. Computers & Industrial Engineering, 119, 121-
130.
Litvinenko, V.S., Petrov, E.I., Vasilevskaya, D.V., Yakovenko, A.V., Naumov, I.A., & Ratnikov,
M.A. (2023). Assessment of the role of the state in the management of mineral resources.
Journal of Mining Institute, 259 (0), 95-111. https://doi.org/10.31897/PMI.2022.100
Litvinenko, V.S., Tsvetkov, P.S., Dvoynikov, M.V., & Buslaev, G.V. (2020). Barriers to imple-
mentation of hydrogen initiatives in the context of global energy sustainable development.
Journal of Mining Institute, 244(0), 428-438. https://doi.org/10.31897/pmi.2020.4.5
Liu, M., Gao, Y. (2006). An algorithm for portfolio selection in a fric-
tional market. Applied Mathematics and Computation, 182 (2), 1629-1638.
https://doi.org/https://doi.org/10.1016/j.amc.2006.05.048
Martirosyan, A.V., Ilyushin, Y.V. (2022). The Development of the Toxic and Flammable Gases
Concentration Monitoring System for Coalmines. Energies, 15 (23), 8917.
Martirosyan, A.V., Ilyushin, Y.V. (2022, August). Modeling of the Natural Objects’ Temperature
Field Distribution Using a Supercomputer. In Informatics (Vol.9, No.3, p. 62). MDPI.
Martirosyan, A.V., Kukharova, T.V., & Fedorov, M.S. (2021). Research of the Hydrogeological
Objects’ Connection Peculiarities. 2021 IV International Conference on Control in Technical
Systems (CTS)
Mavrotas, G., Makryvelios, E. (2021). Combining multiple criteria analysis, mathematical pro-
gramming and Monte Carlo simulation to tackle uncertainty in Research and Development
project portfolio selection: A case study from Greece. European Journal of Operational Re-
search, 291 (2), 794-806.
Miralinaghi, M., Seilabi, S.E., Chen, S., Hsu, Y.-T., & Labi, S. (2020). Optimizing the selection
and scheduling of multi-class projects using a Stackelberg framework. European Journal of
Operational Research, 286 (2), 508-522.
525
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
Mirhosseini, M., Sharifi, F., & Sedaghat, A. (2011). Assessing the wind energy potential locations
in province of Semnan in Iran. Renewable and Sustainable Energy Reviews, 15 (1), 449-459.
Moreno-Monsalve, N., Delgado-Ortiz, M., Rueda-Varyn, M., & Fajardo-Moreno, W.S. (2023).
Sustainable development and value creation, an approach from the perspective of project
management. Sustainability, 15 (1), 472.
Omrani, H., Amini, M., & Alizadeh, A. (2020). An integrated group best-worst method–Data
envelopment analysis approach for evaluating road safety: A case of Iran. Measurement, 152,
107330.
Pashkevich, M.A., Danilov, A.S. (2023). Ecological security and sustainability. Journal of Mining
Institute, 260 (0), 153-154. https://pmi.spmi.ru/index.php/pmi/article/view/16233
Perdan, S., Azapagic, A. (2011). Carbon trading: Current schemes and future developments.
Energy Policy, 39(10), 6040-6054.
Rabbani, M., Bajestani, M.A., & Khoshkhou, G.B. (2010). A multi-objective particle swarm
optimization for project selection problem. Expert Systems with Applications, 37(1), 315-321.
Martirosyan, A.V., Ilyushin, Y.V. (2022, August). Modeling of the Natural Objects’ Temperature
Field Distribution Using a Supercomputer. In Informatics (Vol. 9, No. 3, p. 62). MDPI.
Rezaei, J. (2015). Best-worst multi-criteria decision-making method. Omega, 53, 49-57.
RezaHoseini, A., Ghannadpour, S.F., & Hemmati, M. (2020). A comprehensive mathematical
model for resource-constrained multi-objective project portfolio selection and scheduling con-
sidering sustainability and projects splitting. Journal of Cleaner Production, 269, 122073.
Rohmer, S., Gerdessen, J.C., & Claassen, G. (2019). Sustainable supply chain design in the
food system with dietary considerations: A multi-objective analysis. European Journal of
Operational Research, 273 (3), 1149-1164.
Sahebjamnia, N., Fathollahi-Fard, A.M., & Hajiaghaei-Keshteli, M. (2018). Sustainable tire
closed-loop supply chain network design: Hybrid metaheuristic algorithms for large-scale net-
works. Journal of Cleaner Production, 196, 273-296.
Shafahi, A., Haghani, A. (2014). Modeling contractors’ project selection and markup decisions
influenced by eminence. International Journal of Project Management, 32(8), 1481-1493.
Shafahi, A., Haghani, A. (2018). Project selection and scheduling for phase-able projects with
interdependencies among phases. Automation in Construction, 93, 47-62.
Shakhsi-Niaei, M., Torabi, S.A., & Iranmanesh, S.H. (2011). A comprehensive framework for
project selection problem under uncertainty and real-world constraints. Computers & Indus-
trial Engineering, 61(1), 226-237.
Shammazov, I.A., Batyrov, A.M., Sidorkin, D.I., & Van Nguyen, T. (2023). Study of the Effect
of Cutting Frozen Soils on the Supports of Above-Ground Trunk Pipelines. Applied Sciences,
13 (5), 3139. https://doi.org/10.3390/app13053139
Shariatmadari, M., Nahavandi, N., Zegordi, S.H., & Sobhiyah, M.H. (2017). Integrated resource
management for simultaneous project selection and scheduling. Computers & Industrial Engi-
neering, 109, 39-47.
Taleizadeh, A.A., Haghighi, F., & Niaki, S.T.A. (2019). Modeling and solving a sustainable
closed loop supply chain problem with pricing decisions and discounts on returned products.
Journal of Cleaner Production, 207, 163-181.
526
D. PERVUKHIN et al.: A SUSTAINABLE DEVELOPMENT GOALS-BASED MATHEMATICAL...
Tang, B.-J., Zhou, H.-L., & Cao, H. (2017). Selection of overseas oil and gas projects under low
oil price. Journal of Petroleum Science and Engineering, 156, 160-166.
Tavana, M., Khosrojerdi, G., Mina, H., & Rahman, A. (2020). A new dynamic two-stage mathe-
matical programming model under uncertainty for project evaluation and selection. Computers
& Industrial Engineering, 149, 106795.
Teplyakova, A., Azimov, A., Alieva, L., & Zhukov, I. (2022). Improvement of manufacturability
and endurance of percussion drill assemblies: Review and analysis of engineering solutions.
MIAB. Mining Inf. Anal. Bull., 9, 120-132.
Tofighian, A.A., Naderi, B. (2015). Modeling and solving the project selection and scheduling.
Computers & Industrial Engineering, 83, 30-38.
Torabi, S.A., Hassini, E. (2008). An interactive possibilistic programming approach for multiple
objective supply chain master planning. Fuzzy Sets and Systems, 159 (2), 193-214.
Vasilyeva M.A., Volchikhina A.A., Kuskildin R.B. (2023). Improvement of water segregation in
backfilling. MIAB. Mining Inf. Anal. Bull., 4, 125-139. (In Russian). https://doi.org/10.
25018/0236_1493_2023_4_0_125.
Vasilyeva M.A., Volochkina, A., Kuskildin, R.B. (2023). Improvement of water segregation
in backfilling. Mining Informational and Analytical Bulletin, 4, 125-139. https://doi.org/10.
25018/0236_1493_2023_4_0_125.
Xu, J., Zhou, X. (2013). Approximation based fuzzy multi-objective models with expected objec-
tives and chance constraints: Application to earth-rock work allocation. Information Sciences,
238, 75-95.
Yungmeister, D., Gasimov, E., & Isaev, A. (2021). Substantiation of the design and parameters
of the device for regulating the air flow in down-the-hole hammers of roller-cone drilling rigs.
MIAB, 6 (2), 251-267. https://doi.org/10.25018/0236_1493_2022_62_0_251
Yungmeyster, D., Isaev, A. & Gasymov, E.. (2022). Substantiation of dth air drill ham-
mer parameters for penetration rate adjustment using air flow. Gornyi Zhurnal, 72-77. doi:
10.17580/gzh.2022.07.12.
Yurak, V.V., Dushin, A.V., & Mochalova, L.A. (2020). Vs sustainable development: scenarios for
the future. Journal of Mining Institute, 242 (0), 242. https://doi.org/10.31897/pmi.2020.
2.242
Zaraket, F.A., Olleik, M., & Yassine, A.A. (2014). Skill-based framework for optimal software
project selection and resource allocation. European Journal of Operational Research, 234 (1),
308-318.
Zarinpour, N., Naimeh, Zarinpur, & Mohammadi, A.H. (2022). Presenting a mathematical model
for selecting investment projects based on sustainable development goals under conditions of
uncertainty and limited resources. Industrial Engineering and Management, 38 (1), 51-66.
Zarrinpoor, N., Fallahnezhad, M.S., & Pishvaee, M.S. (2018). The design of a reliable and robust
hierarchical health service network using an accelerated Benders decomposition algorithm.
European Journal of Operational Research, 265 (3), 1013-1032.
Zhang, S., Liu, L., Zhang, L., Zhuang, Y., & Du, J. (2018). An optimization model for carbon
capture utilization and storage supply chain: A case study in Northeastern China. Applied
Energy, 231, 194-206.
527
ADVANCED MATHEMATICAL MODELS & APPLICATIONS, V.8, N.3, 2023
Zolfaghari, S., Mousavi, S.M. (2021). A novel mathematical programming model for multi-mode
project portfolio selection and scheduling with flexible resources and due dates under interval-
valued fuzzy random uncertainty. Expert Systems with Applications, 182, 115207.
528
