Production Optimization Decision Problem Based on Multi-Stage Linear Programming and Alternative Complementarities

Reasonable allocation and utilization of resources in modern industrial production is the key to improve production efficiency and reduce costs. As an effective mathematical optimization tool, multi-stage linear programming is widely used in production planning, inventory management, supply chain optimization and other fields. The article first establishes the objective function and considers the sales and planting costs. Then, the article proposes six constraints, including the cultivated area of arable land, the relationship between crop yield and sales, the minimum value of the cultivated area of a crop, the concentration of crop cultivation, the limitation of crop cultivation in the same plot, and the cultivation interval of legume crops. The article considers complementarity and competition of legume crops, substitution of cereal crops, competition of root crops, complementarity of vegetable crops and complementarity of mushroom crops by constructing a multi-stage planning model. By constructing the mutual exclusion and complementarity matrix, the planting decision is optimized and the production efficiency is improved. The model proposed in this paper can effectively solve the problem of resource allocation in agricultural production and provide scientific decision support for agricultural production by considering the substitutability and complementarity between crops.