Optimal Design of Decision Problem in The Production Process

Abstract

Based on the production decision problem of the "Higher Education Society Cup" national College students Mathematical Contest in Modeling, this paper presents an optimization scheme to solve the sampling detection and production decision of two kinds of spare parts in the production process of enterprises. By establishing the production decision model and cost optimization model, the binomial distribution model is used to test the hypothesis, and the relationship between the minimum sampling quantity and the real defective rate is determined, which improves the detection efficiency and reduces the cost. A production decision model with binary code is constructed, which considers many cost factors, optimizes the model by decision tree and dynamic programming, and obtains the optimal strategy and net profit expectation. The whole calculation strategy of multi-process and multi-parts is proposed. The model is further optimized by simulated annealing and genetic algorithm, and the maximum profit of a single finished product is obtained. By integrating all models, a cost optimization model based on sampling inspection defective rate is proposed, which takes the posterior distribution of defective rate as the key basis to provide a more accurate decision analysis and optimization path for enterprises.