Decision Analysis Based on Enterprise Production Process

Abstract

This paper mainly studies the decision-making problems encountered by enterprises in the production process, including whether to inspect parts and finished products, and how to handle unqualified parts and finished products. By applying operations research and statistical knowledge, and adopting dynamic programming and one-sided hypothesis testing methods, relevant decision-making problems are effectively solved. In this paper, the authors propose a sampling inspection method to parameterize the defect rate of parts and optimize decision-making schemes for different production stages. Finally, the study analyzes the impact of various decisions on the economic benefits of enterprises, constructs corresponding models using dynamic programming, and derives optimal solutions under various decisions. For the first problem, based on the basic principles of statistics, this paper uses one-sided hypothesis testing to detect whether the defect rate of parts exceeds the nominal value. In the case of a large sample size, the central limit theorem is cleverly applied to approximate the binomial distribution to the normal distribution, thereby simplifying the calculation process. And based on the principle of sampling inspection, detailed judgments are made on whether to accept or reject parts under different confidence levels. When studying the second problem, this paper cleverly adopts the dynamic programming method to conduct detailed decision analysis on the three key stages of the enterprise production process: part inspection, finished product inspection, and unqualified product handling. And through the reverse analysis method, starting from the final product, the decision-making of each stage is gradually optimized to ensure that the risk is minimized while controlling costs. By evaluating the relationship between inspection costs and potential losses, as well as the specific impact of different handling methods for unqualified products on the economic benefits of enterprises, the goal is to maximize economic benefits while ensuring product quality. The third problem further enhances the complexity of decision-making based on the second problem, considering multiple processes and multiple parts to optimize decision-making in the multi-stage production process. This problem still adopts the reverse analysis method of dynamic programming to construct a more complex dynamic programming model, comprehensively considering the inspection costs, unqualified product handling costs, and potential market risks of each production stage. In the process of model construction, in-depth analysis is conducted on how to effectively handle parts, semi-finished products, unqualified semi-finished products, finished products, and unqualified finished products at different production stages, including different decisions for each stage. Through careful analysis, it provides enterprises with an optimal decision-making scheme for multiple processes and multiple parts.