Abstract: This study combines a three-stage non-exact positioning algorithm with a Genetic Annealing (GASA) algorithm to address the rectangular blank layout problem for standard-sized textured panels in the furniture manufacturing industry under process constraints. To optimize the "one-cut" production strategy considering sawing requirements and panel texture alignment, we propose an improved hybrid heuristic algorithm. This algorithm integrates a three-stage non-exact positioning method with a metaheuristic GASA algorithm enhanced by two-point mutation and simulated annealing cooling. It specifically tackles constraints such as large-scale nested layouts, diverse blank sizes, and non-rotational texture alignment in furniture production. Experimental validation using benchmark cases and real-world production scenarios demonstrates that the proposed three-stage hybrid heuristic algorithm achieves higher material utilization rates compared to single-stage positioning strategies. In multi-category nested layout problems with texture constraints, the algorithm outperforms three-stage non-exact algorithms, two-stage heuristic algorithms, and homogeneous three-stage hybrid algorithms by average utilization improvements of 5.98%, 5.09%, and 3.31%, respectively. Furthermore, when transitioning from non-textured to textured cutting scenarios, the homogeneous three-stage hybrid algorithm exhibits a material utilization decline rate approximately three times faster than the proposed method. These results confirm the broad applicability and stability of the three-stage non-exact hybrid heuristic algorithm across diverse "one-cut" panel cutting scenarios.