A Study on Multi-Stage Quality Control in Production Based on Dynamic Programming and Simulated Annealing Algorithm

This paper investigates the multi-stage quality control problem in production processes based on dynamic programming and the simulated annealing algorithm. A comprehensive multi-stage dynamic decision-making model has been developed to address the multi-stage decision-making problems in corporate production. The model covers various scenarios, including component procurement, component inspection, product assembly, finished product inspection, and the handling of non-conforming products, with the goal of maximizing corporate profits. Building on the single-stage dynamic decision-making model, the model is further extended to a multi-stage model, considering 8 types of components and 2 assembly stages, involving 16 decision points. The model is implemented using MATLAB, and a nested loop structure is employed to simulate the traversal process of the multi-stage decision-making model, verifying the correctness and rationality of the model. Given the large number of possible decision schemes $(65,536)$ in the multi-stage model, the simulated annealing algorithm is used for optimization. The simulated annealing algorithm, with its ability to handle nonlinear and discrete decision spaces, and its probabilistic capability to escape local optima and find the global optimum, significantly reduces computational effort. Ultimately, using MATLAB and the simulated annealing algorithm, the optimal maximum profit result of 43.55 yuan was obtained, which is consistent with the result derived from exhaustive search. This demonstrates the effectiveness and practicality of the model in solving complex and large-scale optimization problems.