Optimization and Forecasting Modelling to Analyse India’s Pursuit of the Sustainable Development Goals in Agenda 2030 ^†

Abstract

The Sustainable Development Goals (SDGs), set in Agenda 2030, are examined in this study, along with India’s progress towards attaining them, and creative solutions based on forecasting and optimization modelling are presented. We investigate the complex alternatives between economic development, mainly focusing on GDP, sustainability—environmental concerns—and employment—a problem at the core of India’s sustainable development. We examine India’s development across several sectors like agriculture, mining, trades, construction, and so on, using a lexicographic goal programming framework, developing a hierarchical structure with four different levels and prioritizing the most important goal. Decisions are made from the highest priority level to the lowest priority level. Research goes beyond assessment by providing practical solutions to problems. A numerical study highlight the applicability of our strategy. By emphasizing the relevance of coordinating progress across decision-making levels for a more equal, prosperous, and sustainable future by 2030, this research delivers customized, context-aware solutions to accelerate India’s achievement of the SDG goals.

1. Introduction

At the United Nations in September 2015, people from all over the world came together to support Agenda 2030, a bold plan of action with 169 targets and 17 goals designed to solve the urgent social, economic, and environmental issues facing humanity. This agenda resonates with India, a country at a key juncture in its development, as it aligns with its national ambitions for gender equality, inclusive growth, poverty eradication, improved healthcare and education, and the adoption of renewable energy and resilient infrastructure. India’s commitment to the Sustainable Development Goals (SDGs) demonstrates its resolve to guarantee fair development while preserving the environment for coming generations.

India’s 2030 Agenda is a multimodal strategy that includes poverty reduction, digital connection, healthcare improvement, infrastructure development, renewable energy transition, sustainable development, and education reform. India hopes to promote inclusive development and lessen the effects of climate change by concentrating on sustainable economic growth, energy transition, reducing greenhouse gas emissions, and providing equitable employment opportunities. This all-encompassing paradigm emphasises how crucial it is to strike a balance between social justice, environmental conservation, and economic development in order to create a resilient and sustainable future for everybody.

The study endeavours to accomplish several key research objectives as follows:

• Identifying and incorporating future goals such as economic growth (GDP), energy consumption, greenhouse gas emission (GHG), and employment into the analytical framework, ensuring a holistic assessment of India’s development trajectory;
• Establishing a hierarchical structure to prioritize each goal based on their significance and constraints, ensuring an organized approach to goal designation and analysis;
• Implementing lexicographic goal programming techniques to address the entirety of the problem and evaluate the efficiency and effectiveness of the developed model.

2. Literature Review

Biermann et al. [1] proposed a novel global governance approach for SDGs, while Ali et al. [2] and Jayaraman et al. [3] examined the implications of the SDGs with the help of stochastic goal programming in 2021. Gupta et al. [4] proposed a linear programming framework with multi-criterion modelling to examine the SDGs. Chui et al. [5] developed a multi-objective optimization framework pertaining to energy sustainability in smart cities. Ali et al. [6] developed a framework for India’s achievement of the SDGs with the help of a multi-objective approach. With the help of the consensus-based expert elicitation method, Vinuesa [7] explores AI’s impact of the SDGs and their targets. Several other authors also contributed so many remarkable contributions in the context of the SDGs: Modibbo et al. [8] used multi-objective goal programming for SDGs in the context of Nigeria, Khan et al. [9] explained a neutrosophic solution approach for SDGs, and Ghaffar et al. [10] helped gain a better understanding of the relationships network in SDGs related to India.

3. Materials and Methods

We discussed the forecasting as well as the optimization technique for analysing SDGs with the help of ARIMA, MOOP, and lexicographic programming.

3.1. ARIMA Model for Time-Series Analysis

GDP, GHG emissions, electricity consumption, and employment all are time-dependent data and hence, for forecasting them, the time series method is used. The time series analysis is a useful technique and is used to comprehend and forecast trends in sequential data. For forecasting GDP, GHG emissions, electricity consumption, and employment, we use the auto-regressive integrated moving average (ARIMA) model in our work, as introduced by Box and Jenkins [11], founded on an organized, iterative procedure for choosing the most appropriate model to predict unknown parameters.

3.2. Multi-Objective Optimization Problem

The multi-objective programming problems (MOPP) are concerned with finding a compromise as a solution for two or more objectives. The general mathematical model for a multi-objective optimization problem can be represented as follows:

Given a set of decision variables $x=\left(x_1,x_2\dots .,x_n\right)$ and a set of m objective functions $f_i\left(x\right), i=\mathrm{1,2}\dots ,m,$ multi-objective optimization problem is to find a vector of decision variables $x^{*}$ that minimizes or maximizes the objective function simultaneously, subject to a given constraints $g_j\left(x\right), where j=\mathrm{1,2}\dots ..,k$.

• Minimize or maximize $f\left(x\right)=(f_1\left(x\right),f_2\left(x\right),\dots ..,f_m\left(x\right))$
• Subject to constraints:

  $$\begin{gathered} g_j\left(x\right)\le 0, j=\mathrm{1,2},\dots .,k \\ x\ge 0 \end{gathered}$$

3.3. Lexicographic Goal Programming

In lexicographic goal programming (LGP), the objective functions is ranked in order of their importance from best to worst. The optimum solution $x^{*}$ is then obtained by optimizing the highest-order objective functions and proceeding according to the priority of importance of the objective functions. Let us suppose, we want to optimize $f\left(\underset{\_}{x}\right)=(f_1\left(x\right),f_2\left(x\right),\dots ..,f_k\left(x\right))$ subject to set of defined constraints $g_j\left(\underset{\_}{x}\right)\le 0, j=\mathrm{1,2},\dots .,m.$ Here, $f_1\left(x\right)$ and $f_k\left(x\right)$ were defined as most and least important objective functions, respectively. Then, we firstly solve the problem:

• Optimize $f_1\left(x\right)$
• Subject to $g_j\left(x\right)\le 0, j=\mathrm{1,2},\dots ,m$
• and obtained solution ${\underset{\_}{x}}_1^{*}$ and ${f_1\left(\underset{\_}{x}\right)}^{*}$. Next problem is,
• Optimize $f_2\left(x\right)+d_1^{-}-d_1^{+}$
• Subject to $g_j\left(x\right)\le 0, j=\mathrm{1,2},\dots ,m$

  $$f_1\left(x\right)+d_1^{-}-d_1^{+}=f_1\left(x^{*}\right)$$

  where $d_i=|f_i\left(x\right)-f_i\left(x^{*}\right)|$
• and obtain solution $x_2^{*}$ and $f_2\left(x_2^{*}\right)$ and so on.
• The procedure is repeated until all k objectives have been solved. Hence, the generalized problem of LGP is
• Optimize $f_1\left(\underset{\_}{x}\right), i=\mathrm{1,2},\dots .,k$
• Subject to; $g_j\left(x\right)\le 0; j=\mathrm{1,2},\dots .,m$

  $$f_l\left(x\right)=f_l^{*}; l=\mathrm{1,2},\dots .,i-1$$

  The final solution $x_k^{*}$ is obtained as the desired solution of the problem.

3.4. Case Study

The Intended Nationally Determined Contributions (INDC) report submitted by India to the UNFCCC outlined several commitments and initiatives concerning GDP, carbon emissions, electricity use, and employment. India’s INDC aimed to combat climate change while promoting sustainable development, emphasizing the key elements given below:

• GDP (gross domestic product): India’s INDC noted the importance of economic growth for addressing poverty eradication and social and economic development challenges.
• Carbon emissions: India committed to reducing its GDP emissions intensity by 33–35 percent by 2030 compared to 2005 levels, reflecting a commitment to reducing greenhouse gas emissions per unit of GDP.
• Electricity consumption: While not directly mentioned, India emphasized the importance of renewable energy sources in its climate action plans. It pledged to generate 40% of its total installed electric power capacity from non-fossil fuel-based energy sources by 2030, indicating a strong commitment to expanding renewable energy sources like solar and wind power.
• Number of employees: Although not explicitly stated, India’s focus on economic development, industrial expansion, and clean energy industries has potential implications impacting employment generation. The promotion of sustainable practices and clean technologies aimed to create indirect employment opportunities in sectors such as clean energy, afforestation, and climate resilience.

India’s INDC remains committed to addressing climate change while maintaining economic growth, emphasising the importance of sustainable practises, carbon intensity reduction, and the transition to cleaner energy sources. Various sectors in India, including agriculture, mining, manufacturing, power, construction, transportation, commerce, finance, and community, contribute differently to the economy, as illustrated in

Table 1. Sustainable Development Goals by sector.

Sectors	GDP 2022 1	Carbon Emission 2020	Electricity Consumption 2022	Number of People in Employment 2022 2
Agriculture, forestry, and fishing	684.38	741.92	334,433.8	255,956.454
Mining and quarrying	55.25	204.49	87,531.11	2409.002
Manufacturing	489.13	234.73	420,420.7	45,469.911
Electricity, gas, water supply	91.52	1121.98	26,266.34	3613.503
Constructions	242.70	274.72	227,564.9	72,872.309
Trade, repair, hotels and restaurants	254.23	85.35	148,642.8	75,883.560
Transport, storage, communication, broadcasting	556.59	276.44	18,589.1	35,532.778
Financial, real estate, and professional services	747.43	162.49	483,066.6	33,726.027
Community, social, and personal services	244.06	64.83	111,484.6	49,384.539

¹ Planning Commission, Govt of India. ² Ministry of Labour and Employment, India.

, which displays sectoral contribution data from the previous year and

Table 2. Sustainable Development Goals in India.

Goals	GDP 2022	Carbon Emission 2020	Electricity Consumption 2022	Number of People in Employment 2022
Values	3365	3167	1,858,000	574,848
2030 Goals	4695	5700	2,684,750	742,032

Source: INDC Report of India, UNFCC 2015.

gives the India’s SDG goals in the coming 2030 year.

3.5. Formulation

The final SDG optimization model with numerical values is as follows:

Objective functions of SDGs:

G1 = 0.002674 x1 + 0.022935 x2 + 0.010757 x3 + 0.025327 x4 + 0.00333 x5 + 0.00335 x6 + 0.015664 x7 + 0.022162 x8 + 0.004942 x9

G2 = 0.002899 x1 + 0.084886 x2 + 0.005162 x3 + 0.310496 x4 + 0.00377 x5 + 0.001125 x6 + 0.00778 x7 + 0.004818 x8 + 0.001313 x9

G3 = 1.30660 x1 + 36.33500 x2 + 9.24612 x3 + 7.26894 x4 + 3.122790 x5 + 1.958827 x6 + 0.523154 x7 + 14.323258 x8 + 2.257480 x9

G4 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9

SDG constraints:

0.002674 x1 + 0.022935 x2 + 0.010757 x3 + 0.025327 x4 + 0.00333 x5 + 0.00335 x6 + 0.015664 x7 + 0.02216 x8 + 0.00494 x9 ≤ 4695

0.002899 x1 + 0.084886 x2 + 0.005162 x3 + 0.310496 x4 + 0.00377 x5 + 0.001125 x6 + 0.00778 x7 + 0.00481 x8 + 0.00131 x9 ≤ 5700

1.306604 x1 + 36.33500 x2 + 9.24612 x3 + 7.26894 x4 + 3.12279 x5 + 1.95882 x6 + 0.52315 x7 + 14.32325 x8 + 2.25748 x9 ≤ 2,684,750

x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 ≤ 742,032

255,956.454 ≤ x1 ≤ 330,183.8257

2409.002 ≤ x2 ≤ 3107.61258

45,469.911 ≤ x3 ≤ 58,656.18519

3613.503 ≤ x4 ≤ 4661.41887

72,872.309 ≤ x5 ≤ 94,005.27861

75,883.56 ≤ x6 ≤ 97,889.7924

35,532.778 ≤ x7 ≤ 45,837.28362

33,726.027 ≤ x8 ≤ 43,506.57483

49,384.539 ≤ x9 ≤ 63,706.05531

where x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, x₉ are the number of employees in each sector and G_i, i = 1, 2, 3, 4 are the different objective goals of GDP, carbon emission, electricity consumption, and number of people in employment, respectively.

4. Results

Based on the above methodology, the summarized forecasted target values for India’s SDGs using ARIMA models are given in

Table 3. Forecasted estimated values of ARIMA models.

Goals	ARIMA	AIC	BIC	RMSE	2030 Values Est
GDP	(0,2,3)	726.97	735.41	84.96	4636.184
GHG carbon emission	(1,1,0)	261.85	264.03	81.27	2045.658
Electricity consumption	(0,2,1)	512.56	514.65	40,963.95	2,505,835
Number of people in employment	(1,1,0)	785.13	788.4	11,545,926	676,682,580

, and the optimum solution for a lexicographic model for SDGs using LINGO software is as shown in

Table 4. Optimum solution for lexicographic SDG model.

Decision Variables
x1	x2	x3	x4	x5	x6	x7	x8	x9
255,956	2409	45,470	10,143	151,614	75,884	35,533	62,608	102,415
Objective Values	G1 = 4695		G2 = 5700		G3 = 2,684,750		G4 = 742,031

.

5. Discussion and Conclusions

The forecasted values of ARIMA models says that GDP will be around USD 4636 billion at the end of the year 2030, while GHG carbon emissions is all about 2046 million metric tonnes, and that the electricity consumption will reach around 2,505,835 Gigawatt hours. However, at the end of the year 2030, the number of people in employment will be approximately 680 million, which is a positive sign towards India achieving its SDGs and SDG targets.

The LINGO results, combined with the hierarchical priorities assigned to each factor, show an effective trade-off between economic growth (GDP), sustainability (emissions and electricity consumption), and job creation. Using lexicographic goal programming, this solution demonstrates the discovery of solutions that meet a variety of objectives and constraints. The findings indicate that, while all goals can be achieved with minor changes to current policies, concentrated effort will be required to meet the targets by 2030. Interestingly, the first goal, GDP, outperforms expectations, indicating successful economic growth. Furthermore, the significant reduction in carbon emissions demonstrates effective environmental stewardship, which is critical for addressing climate change. The third goal, which calls for increased electricity efficiency, promises financial savings and a lower environmental impact, especially if it is generated by renewable energy. Furthermore, the significant increase in employment opportunities represented by the fourth goal is positive for socioeconomic development and community welfare.

However, prioritising emissions reduction and energy efficiency may have had an impact on GDP, potentially affecting the production levels or costs. Nonetheless, such trade-offs occur frequently in complex systems. In conclusion, while the optimization process produced positive results, increasing outputs may necessitate changes in trade-offs and resource allocation. Nonetheless, this model can help policymakers make informed decisions about resource allocation, technology adoption, and economic policies in a variety of sectors, ensuring sustainable and inclusive development.

As a conclusion, our study underscores the fact that sustainable development is not an unattainable ideal but an actionable goal that can be achieved through careful planning, responsible decision making, and a commitment to the well-being of both present and future generations.