## 1 Introduction  
There is a significant contribution from small and medium-sized enterprises (SMEs) toward a country's sustainable development. SMEs differ from large enterprises in various parameters, such as factory size, manpower involved, yearly turnover, the financial year, size, etc., [1]. The different ways of classifying micro, small, and medium enterprises (MSMEs), and SMEs, vary from country to country [2]. SMEs also differ in terms of the types of skills required, organizational structure, culture, types of resources, total assets involved, etc. SMEs are among the most important economic units globally and contribute more than larger organizations, economically, in terms of providing employment, adding value, and contributing to the GDP of the country [3]. SMEs are attempting to move toward sustainable business practices globally, thus promising profitability, resilience, and positive social and environmental impacts [4]. SME industrial growth boosts a nation's economy. According to a World Bank report, SMEs account for up to 60% of total employment [5]. SMEs, either formal or informal in their structure, contribute to gross domestic product (GDP). Similarly, various Indian enterprises classified as MSMEs also contribute to the national socio-economic development and GDP [6]. In India, MSMEs provide around 8% of the national GDP. They also contribute around 45% of the manufacturing output and approximately 40% of the country's exports [7]. The government's financial help in terms of soft loans and grants appears insufficient to expand MSME operations [8]. SMEs also face slow growth due to the various challenges of insufficient resources, such as skilled manpower, state-of-the-art equipment, revolutionary digital technology, competitive sales and marketing strategies, research and development (R&D) efforts, lack of information technology (IT) infrastructure, etc., [9]. Global challenges and fierce competition force manufacturing industries and organizations to improve their ability to use lean manufacturing [10]. The prevailing stiff competition in the business world is forcing Indian SMEs to look for better management and manufacturing practices to survive [11]. To fight local and global competitiveness and provide long-term sustainability, various strategic approaches are adopted by SMEs. For many probable reasons, lean implementation in SMEs is crucial for waste minimization and value addition. However, without prior knowledge of many lean barriers, lean implementation in SMEs results in unsuccessful attempts. The role of each lean barrier is significant during lean implementations. The implementation of lean production in SMEs presents many barriers on practical, theoretical, financial, and organizational levels [12]. Hence research on lean barriers (LBs) is essential for successful lean implementation in SMEs [13]. Many SMEs only have a limited understanding and awareness of lean principles and practice [11]. Further, there is a need to understand the importance of understanding LBs so that their respective levels of importance in lean implementation may be evaluated [14]. Researchers should also prioritize and analyze LBs to gain a better understanding and improve interpretation for successful lean implementation [15]. LBs in SMEs must be eliminated for successful lean implementation. Several studies across the globe attempted to identify LBs [10; 16; 17]. Apart from these several studies, there appear to be no studies suggesting the relationship modeling of lean implementation barriers for SMEs in the manufacturing sector. Further, lean implementation barriers require classification into various categories to help entrepreneurs understand the LBs, and their influence needs further investigation. Hence, it is essential to model lean implementation barrier relationships to provide a good understanding of LBs for successful lean implementation in SMEs.