"How do various theories in operations management, such as Lean, Six Sigma, and Total Quality Management, contribute to optimizing processes and enhancing efficiency within organizations? Explore the fundamental principles underlying each theory, their applications across different industries, and their impact on productivity, quality, and cost$-$effectiveness. Additionally, consider contemporary trends like agile methodologies and Industry $4\mathrm{.}0,$ and their integration with traditional operations management theories. How do these theories address challenges such as supply chain disruptions, technological advancements, and changing consumer demands? Lastly, analyze the role of leadership and organizational culture in implementing and sustaining effective operations management practices."