Within operation management, how does the application of lean principles and Six Sigma methodologies enhance process efficiency and quality control in manufacturing and service industries? Additionally, how do supply chain management strategies, such as just$-$in$-$time inventory and vendor$-$managed inventory systems, optimize resource utilization and mitigate risks? By delving into these theoretical underpinnings, we can gain deeper insights into the mechanisms driving operational excellence and competitive advantage in modern businesses across diverse sectors$.$