Robots are increasingly utilized in manufacturing and logistics, where bin-picking has become crucial for managing randomly placed objects. However, traditional methods often rely on expensive 3D vision systems, have limited adaptability to unstructured environments, and primarily focus on the picking process, neglecting the placing tasks. To address these challenges, this study presents a cost-effective system that combines a depth camera, YOLO-based instance segmentation, and optimization-based inverse kinematics for real-time object detection and stable manipulation. In the placing stage, an adaptive algorithm detects empty tray holes and generates grid patterns, ensuring reliable placement even in the presence of tray misalignments, occupied slots, or partial occlusions. Experimental validation revealed a 91% success rate in mixed-object environments during picking tasks and a 94% success rate for placing tasks, even with tray displacement and occlusion conditions. The results demonstrate that the system maintains stable performance across both picking and placing processes while minimizing reliance on expensive hardware and complex initial setups. By enhancing flexibility and scalability, the proposed approach offers a practical solution for intelligent automation and can serve as a foundation for broader applications in assembly, logistics, and service robotics.