A Multi-Criteria Model For Sustainable Development Goals Using Fuzzy Goal Programming-Application For Egypt

Background: Sustainable development necessitates the implementation of policies that integrate various competing economic, environmental, energy, and social objectives. Multi-Criteria Decision Analysis using goal programming is a popular and widely used technique to study decision problems with multiple conflicting objectives. Fuzzy goal programming models are the most appealing choice since real-life situations frequently contain imprecise information. Results: This article proposes fuzzy goal programming model that combines optimal resource allocation with prospective goals for economic development, electricity consumption, employment, and greenhouse gas emission reduction in Egypt's primary economic sectors. The presented model analyses the prospects for improvement, the effort required, and the implementation of sustainable development strategies. The model also offers valuable insights to decision makers for both strategic planning and investment allocations towards sustainable development. We validate the model by applying it to Egypt's important economic sectors to meet the country's 2030 sustainable development goals. Conclusion: The model implies that Egypt's objective of GDP growth will not be met, and that further research and preparation is required. It also recommends that Egypt take some required measures in the direction of renewable technologies, such as solar and wind energy, which have enormous potential for achieving sustainability goals. This can also aid in meeting greenhouse gas emission targets, as well as meeting power consumption targets. The model


Background Introduction
Sustainable development (SD) is defined as development that meets current demands without jeopardizing future generations' ability to meet their own needs.The United Nations General Assembly in September 2015 formally adopted 17 Sustainable Development Goals () 1 .Planning for sustainable development requires integrating conflicting criteria on economics, energy, environment and social aspects.The main objective of the United Nations is to achieve these goals in every sector by 2030.Sustainable development practices help countries grow in ways that are adaptive to the challenges posed by climate change, which in turn help protect the natural resources important to our future generations [1].
With a population of approximately 104 million people, Egypt is the most populous Arab country.Its per capita GDP is estimated at $3,740.Egypt is a low-middle-income country, with poverty rates of 32.5% 2 .Between 1993 and 2019, Egypt's average unemployment rate was at 10.75 percent, with the highest rate of 13.40 percent in the third quarter of 2013, and the lowest rate of 7.50 percent in the second quarter of 2019. 345  Economic growth and energy consumption are linked because higher levels of energy consumption lead to higher levels of economic growth; similarly, energy consumption and pollution are linked.
Energy consumption is deemed sustainable if it meets current demands without jeopardizing future generations' needs.Environmental concerns such as greenhouse gas emissions, as well as social and economic aspects such as energy poverty, are frequently included in definitions of sustainable energy.More than 70% of the greenhouse gas emissions that cause climate change are attributed to the global energy system, which is 85% reliant on fossil fuels.Some neighboring countries' average per capita electrical energy consumption is ten times that of Egypt [2].Electricity usage per capita is expected to peak in 2020.More than 750 million people do not have access to electricity, and over 2.6 billion people cook using harmful fuels like wood or coal. 6 Reducing greenhouse gas emissions to levels consistent with the Paris Agreement will necessitate a system-wide transformation in energy production, distribution, storage, and consumption.The sustainable energy system is likely to see a shift towards using more electricity in sectors such as transportation and heating, energy conservation, and the use of hydrogen produced from low-emission energy sources.
Resource planning problems often involve economic, environmental and social objectives that are in conflict with one another.There is an intimate connection between energy, environment, and sustainable development, as Dincer and Rosen [3] point out.Goal programming techniques have been used to apply multi-criteria decision models to a variety of energy planning, energy resource allocation, building energy management, transportation energy management, and energy project planning [4,5].The importance of sustainable consumption and production in the SDGs was examined by Akenji et al [6], as well as how sustainable consumption and production objectives could be expressed efficiently in this evolving global policy framework.Han et al [7] proposed a multi-objective optimization model for determining viable technologies for producing electricity and treating CO2 with the goal of maximizing predicted revenues while minimizing financial risk.San Cristóbal [8] looked at how GHG emission targets can be met and how they affect the mix of manufacturing activity in Spain, using a GP model to minimize GHG emissions, waste emissions, energy requirements, and maximize employment and output levels across important economic sectors.Flores et al. [9] proposed a mathematical programming methodology for energy investment planning.
In order to maximize the Net Present Value over time, the model incorporates renewable and non-renewable demands, new energy facility sources, and the present amount of fossilfuel reserves.Gupta et al. [10] created a fuzzy goal programming model that allocates resources optimally by accomplishing future goals in terms of gross domestic product, electricity consumption, and greenhouse gas emissions.Chang [11] used a goal programming approach to identify the key CO2 generating industries in order to optimize production structure in order to meet China's emission reduction targets.Schult et al. [12] proposed mixed integer linear programming methods for solving large-scale input-output systems that represent an optimal allocation of global resources for a more sustainable global economy.Pal et al. [13] propose a linear GP approach for dealing with interval data uncertainty in thermal power generation and dispatch challenges.Balaman and Selim [14,15] use multiple fuzzy goal programming (FGP) methodologies to solve their model, which is a multi-objective optimization problem of biomass to energy supply chains in an uncertain environment.In the United Arab Emirates, Jayaraman et al. [16,17] created a mathematical model that incorporates optimal resource allocation to simultaneously achieve anticipated goals on economic development, energy consumption, workforce, and GHG emission reduction.

methodology and case study
In this section, we presented a multi-criteria fuzzy goal programming model that combines optimal resource allocation with projected goals for economic development, energy consumption, workforce, and Green House Gases emission reduction by 2030, as applied to Egypt's important economic sectors.

Multi-Criteria Fuzzy Goal Programming Formulation
Making decisions in the face of several, frequently contradictory and incommensurable factors is referred to as multi-criteria decision making (MCDM).Goal programming is a popular MCDM technique based on the distance function notion, in which the decision-maker (DM) seeks out the solution that reduces the absolute deviation between the objective's achievement level and its aspiration level.It was first used in the context of executive compensation by (Charnes et al, 1955) [18].The phrase 'goal programming' was not in use at the time, and the paradigm was viewed as a linear programming adaption.(Charnes and Cooper, 1961) [19] provide a more formal framework of goal programming.The technique was further developed by (Ijiri, 1965) [20], and seminal textbooks by (Lee, 1972) [21] and (Ignizio, 1976) [22] popularized it as an operational research tool.
GP is a multi-objective optimization problem that balances a trade-off between conflicting purposes.It is an extension of linear programming that can handle multiple objectives.It's also used to undertake three different types of analysis: • Determine the degree to which the goals may be met with the resources available.
• Determine the resources needed to achieve a specific set of goals.
• Providing the most satisfactory solution under a variety of resource constraints and goal priorities.The GP model is a powerful and versatile decision-making technique that has been applied to a wide range of decision-making problems involving multiple objectives, including economics, accounting, engineering, agriculture, marketing, transportation, finance, and other types of competing situations.

Mathematical formula for goal programming:
As we mentioned, the purpose of GP is to reduce the gap between goal achievement and expectations., say   (), X=( 1 ,  2 , … ,   ), and these acceptable aspiration levels,   (i = 1, 2, ..., K).Therefore, GP can be expressed as follows: Minimize (1) Subject to: x Where Z i is linear function of the i th goal and g i is the aspiration level of i th goal.
Here,  is the total number of goals,  is the right-hand side of the constraint coefficient,   () is the k-th objective and   is the aspiration level of the k-th goal.Equation (1) can be formulated as follows: Minimize Subject to: Where d i + , d i − ≥ 0 are, respectively under and over deviations of i th goal.
Any optimization model that represents real-world situations includes a lot of parameters whose values are assigned through expert opinion, and in the traditional approach, they are required to specify an accurate value for the parameters.However, both the experts and the decision-maker often do not know the value of those criteria with precision.If exact values are suggested, they are merely statistical inferences based on previous data, and their stability is questionable, hence the problem's parameters are typically determined by the decision maker in an uncertain area.As a result, the knowledge of experts' opinions on the parameters is beneficial as fuzzy data that aids the decision maker in an open-ended area.Because the market is dynamic, determining the best decision criteria is tough; nevertheless, fuzzy linked data can assist in determining the best answer.This makes us resort to fuzzy numbers which deal with uncertain information [23,24].
Aspiration levels are considered exact, predictable, and well-known in GP formulations.However, the parameters in some decision-making (DM) scenarios can be hazy, imprecise, or unpredictable.In fact, there are many decision-making circumstances in which the DM lacks comprehensive information on some parameters, particularly the GP model's target values.(Narasimhan, 1980) [25] presented a Fuzzy Goal Programming (FGP) formulation based on the concept of membership functions to cope with such a circumstance.The interval [0, 1] is used to define these functions.When the i-th goal is achieved and the decision multi criterion is completely satisfied, the membership function for that goal has a value of 1; otherwise, the membership function has a value between 0 and 1.
Fuzzy goal programming is an extension of traditional goal programming that is used to handle decision issues involving many objectives in an uncertain environment.A general mathematical model of the fuzzy goal programming model can be stated as: where  is   −dimensional decision vector.The symbol ≥ (the type of fuzzy-max) referring to that   should be approximately greater than or equal to the aspiration level   signifies that the decision-maker is satisfied even if less than   up to a certain limit.The symbol ≤ (the type of fuzzy-min) referring to that   () should be approximately less than or equal to the aspiration level   up to a certain tolerance limit.The symbol ≅ (the type of fuzzy-equal) referring to that Z i (X) should be in the vicinity of the aspiration g i signifies that the decision-maker is satisfied even if greater than (or less than)   up to a certain limit.For fuzzy-min, the membership function is defined as: Where   is the upper tolerance limit.Where   is the lower tolerance limit for the k-th fuzzy goal   (X) .The linear membership function for the fuzzy constraint is given by: Egypt has the largest population density in the Arab world and one of the largest economies in it.While the economy was centralized and led by the state during the era (1956)(1957)(1958)(1959)(1960)(1961)(1962)(1963)(1964)(1965)(1966)(1967)(1968)(1969)(1970)(1971)(1972)(1973), reforms in the nineties of the twentieth century aimed to reduce the state's role in the economy, and to adopt principles market-oriented economy, and Egypt's integration into the global economy.Between 2000 and 2010, the Egyptian economy grew at a rate of 32 9.4 percent annually, and the country's GDP expanded from $144 billion to more than $231 billion by 2010.During the same period, its per capita GDP grew from about $7,400 to $9,800, or about 3 percent annually, while the (Gini index) for Egypt, a measure of inequality, remained consistently low [26].
Egypt has succeeded in achieving most of the Millennium Development Goals, a set of eight global goals that ran from 2000 to 2015, and ranged from country requirements to halve extreme poverty to reduce the spread of HIV/AIDS and achieve universal primary education.According to the Millennium Development Goals (UNDESA, 2017a), Egypt reduced extreme poverty (population living on less than $25.1 a day) by more than 62 percent between 1990 and 2008, and has succeeded in meeting targets within the framework of the first goal of the Millennium Development Goals.By 2010, the net primary education enrollment rate in Egypt was 97 percent.The under-five mortality rate decreased by more than 74 percent between 1990 and 2013.The tuberculosis mortality rate decreased by more than 81 percent.Clean water and sanitation extended to more than 95 percent of the population.Population However, some targets remained unmet, particularly those related to Millennium Development Goal 3, "Promote gender equality and empower women".The ratio of girls to boys in primary education has converged, but has not reached the target of gender parity by 2013.During the same time frame, the share of women working in the non-agricultural sector decreased by 9 percent, declining to about 19 percent in 2013 [26].
Egypt's population is expected to grow by nearly 24 percent, rising from 93.8 million in 2015 to 122.6 million by 2030.With this growth, the country will remain somewhat youth.In 2030, 30 percent of the population will be under 15 years of age and more than 60 percent will be of working age (from 15 to 64).The Egyptian economy is expected to grow by 5 to 6 percent annually over the projected horizon, with a gross domestic product of $571 billion by 2030.GDP increased from $10,250 in 2015 to $14,270 by 2030, or roughly the level of Brazil in 2018.This growth is expected to reduce poverty and expand the middle class.In 2030, less than ten million people will live in poverty (according to define the population living below the current national poverty line in Egypt, which is equivalent to less than $3.40 per day in 2011 (compared to 2015, while the middle-class population (those living on between $10 and $50 a day) is expected to increase to more than double by 2030.
Egypt may also face economic challenges such as the informal economy, unemployment, and low participation of women in the labor force.It is expected to decline Informal employment as a percentage of the non-agricultural labor force increased from 47 percent today to 36 percent by 2030.An additional 2.5 million people are expected to work in the informal sector.Women's participation in work, which today stands at about 20 percent, is not expected to grow significantly.
It is expected that human development in terms of the health and education of the population will improve steadily.And to increase educational attainment, as measured by the average years of schooling in Egypt, from 1.7 years in 2015 (6.5 for women and 7.8 for men) to 5.8 years in 2030 (8 for women and 9 for men).Thus, it is even in time when educational attainment increases in all fields, female achievement will continue to lag behind.The average life expectancy is expected to increase from 71.3 years to 74 years in 2030.The under-five mortality rate will decrease from 22 deaths per 1,000 live births in 2015 to 14.7 by 2030 7 .

Data Collection and Model Formulation
In this paper, we considered employment as a decision variable, which is very important for sustainable development.The following goals related to gross domestic product, electricity consumption and greenhouse gas emissions are among the main goals for achieving the Sustainable Development Goals which are essential for the successful operation of the modern economy.

 Gross domestic product (GDP)
Sector wise GDP are published by Ministry of Planning and Economic Development -National Accounts Data and IMF. 89In some cases the most updated entry was unavailable, and we used the estimated annual percentage growth rate of GDP based on constant growth in local currency.Table (1) presents the sector wise per capita estimates of GDP with reference to the year 2019.

 Electricity consumption (EC)
The per capita estimates for electricity consumption across the sectors in Giga watt hour (Gwh) are summarized in Table (1).The sectorial data for electricity consumption was obtained from Ministry of Electricity and Renewable Energy with reference to the year 2019. 10 Green House Gases emissions (GHG) GHG emission data was obtained from the United Nations Framework Convention on Climate Change (UNFCCC) 11 , Climate Watch 12 and CAIT with reference to year the 2018. 13Table 1 summarizes the sector specific per capita GHG emissions in Giga Grams of CO2 equivalent.To estimate the value of greenhouse gas emissions in 2030, we used the conclusion shown in the paper presented by (Lamia Abdullah, 2020) which states 14"to reduce total emissions by 20% by 2030" due to the absence of a formally measured target that can be relied upon in estimating the value of GHG in 2030.

 Number of employees (NE)
The number of employees across the economic sectors were obtained from International Labour Organization 15 , Central Agency for Public Mobilization and Statistics. 16and UNDP.Table )1( presents the number of employees (in thousands) employed in each sector.The annual growth percentage of labor was used to project the data with reference to year 2019.We have used the following law to find the number of employees in 2030 because there is no specific value in any source.
Number of employees = labor force * (1 -unemployment rate) Note: GHG Emissions in manufacturing (*) and construction (**) together is 41.12 Table (2) presents the projected goal values for the year 2030 with the corresponding growth rates for the four criteria.The GDP growth rates were estimated based on data from Egypt Vision 2030estimated also were across the four sectors .Electricity consumption growth rates 17from Energy Strategy 2035.The number of employees were estimated based on CAPMS and UNDP and similarly GHG emissions were estimated based on the research paper introduced by (Lamia Abdullah, 2020) and UNFCCC.Also; we used the following rule to find the value of compound annual growth rate formula.

Compound annual growth rate= [ending value/ beginning value]
1 number of years -1.

Model Formulation
In our model, we make use of a formulation as a multi-objective integer linear programming model to determine the optimum allocation of employees across different economic activities to maintain GDP growth, electricity consumption and GHG emissions.The objectives are formulated as follows: , Subject to: Here, the following symbols are used:  Objective function  1 optimizes the per-capita gross domestic product across the j-th economic sector. Objective function  2 optimizes the per-capita gross electricity consumption across the jth economic sector. Objective function  3 optimizes the per-capita greenhouse gas emissions across the j-th economic sector.   is the number of employees in the j-th contributing sectors.   is the current employment in the j-th sector.   is the employment goal in the j-th sector. ()  is the gross domestic product in the j-th sector. ()  is the electricity consumption in the j-th sector. ()  is the GHG emissions in the j-th sector. ()  is the GDP goal for sustainable development.

Results and Discussion
We apply the fuzzy goal programming approach presented in Section 3 to the above model formulation.The numerical optimization software LINGO is used to solve the resulting optimization problem.Tables 4,5 show the optimal compromise of objective values with optimal employment in several sectors.

Table ( 1
). Sectoral contribution of economic sectors to the identified goals.

Table ( 3
). Lower & Upper tolerance limit of goals