Research on the Optimization of Uncertain Multi-Stage Production Integrated Decisions Based on an Improved Grey Wolf Optimizer

Defect-rate uncertainty creates cascading operational challenges in multi-stage production, often driving inefficiency and misallocation of labor, materials, and capacity. To confront this, we develop a multi-stage Production Integrated Decision (MsPID) framework that unifies quality inspection and shop-floor decision-making within a single computational model. The framework couples a two-stage sampling inspection policy-used to statistically learn and control defect-rate uncertainty via estimation and rejection rules-with a multi-process, multi-part production decision model. Optimization is carried out with an Improved Grey Wolf Optimizer (IGWO) enhanced with Latin hypercube sampling (LHS) for uniformly diverse initialization; an evolutionary factor mechanism that blends simulated binary crossover (SBX) among three leadership-guided parents (Alpha, Beta, Delta) to strengthen global exploration in early iterations and focus exploitation later; and a greedy, mutation-assisted opposition learning step applied to the lowest-performing quartile of the population to effect leader-informed local refinement and accept only fitness-improving moves. Experiments show the method identifies minimum-cost policies across six single-stage benchmark cases and yields a total profit of 43,800 units in a representative multi-stage scenario, demonstrating strong performance in uncertain environments. Sensitivity analysis further clarifies how recommended decisions adapt to shifts in estimated defect rates, finished product prices, and swap/changeover losses. These results highlight how bio-inspired intelligence can enable adaptive, efficient, and resilient integrated production management at scale.