How does the Theory of Constraints $($TOC$)$ influence decision$-$making and performance improvement in Operations Management? Analyze its principles in optimizing processes, identifying bottlenecks, and managing constraints to enhance efficiency. Evaluate the application of TOC in various industries, considering its impact on production scheduling, inventory management, and supply chain coordination. Discuss how TOC integrates with other operational management methodologies like Lean and Six Sigma, highlighting synergies and potential conflicts. Explore case studies illustrating successful implementation of TOC strategies and their outcomes in terms of cost reduction, lead time reduction, and overall operational performance enhancement.