Theory of Constraints $($TOC$)$ contribute to optimizing operations management? Specifically, how does it address bottlenecks, throughput, and inventory management within manufacturing and service industries? Additionally, what are the key principles of TOC, such as identifying and exploiting constraints, subordinating everything to the constraint, and elevating the system's constraint? How do these principles apply to various operational scenarios, and what are the implications for decision$-$making, resource allocation, and performance measurement within organizations? Finally, how can TOC be integrated with other operational management approaches like Lean and Six Sigma to achieve synergistic improvements in efficiency and effectiveness?