The nested partitions (NP) method is a powerful optimization technique effective for solving large-scale discrete optimization problems, particularly in manufacturing and service industries. It is applicable to both operational and planning problems and has been used in diverse areas such as radiation therapy, data mining, and product design. The NP method is well-suited for complex problems where traditional methods struggle, including mixed integer programs (MIPs) and combinatorial optimization problems (COPs). It combines the benefits of mathematical programming and metaheuristics, providing a flexible framework for integrating heuristics and mathematical programming methods. The NP method uses a decomposition approach similar to branch-and-bound, partitioning the feasible solution space into promising and complementary regions, and generating primal feasible solutions from each subregion to achieve upper bounds. This approach ensures robustness and efficiency in finding optimal or near-optimal solutions.The nested partitions (NP) method is a powerful optimization technique effective for solving large-scale discrete optimization problems, particularly in manufacturing and service industries. It is applicable to both operational and planning problems and has been used in diverse areas such as radiation therapy, data mining, and product design. The NP method is well-suited for complex problems where traditional methods struggle, including mixed integer programs (MIPs) and combinatorial optimization problems (COPs). It combines the benefits of mathematical programming and metaheuristics, providing a flexible framework for integrating heuristics and mathematical programming methods. The NP method uses a decomposition approach similar to branch-and-bound, partitioning the feasible solution space into promising and complementary regions, and generating primal feasible solutions from each subregion to achieve upper bounds. This approach ensures robustness and efficiency in finding optimal or near-optimal solutions.