Research on Crop Planting Optimization Based on Linear Programming

Abstract

In the face of challenges posed by population growth and climate change, modern agriculture urgently needs scientific optimization of cropping schemes to increase yields, reduce costs, and achieve efficient allocation of resources and stable economic benefits. This study proposes an optimized crop cultivation scheme for a rural village in North China in response to the challenges posed by population growth and climate change. By analyzing agricultural data for the year 2023 and considering a crop rotation system, this paper develops a model that maximizes profits while ensuring sustainable development. The optimization model contains 11 constraints and employs a weighted objective with 0.5 as the threshold value for the three objective groups. Under the stagnant sales scenario, the seven-year average profit increases by $1,631,900 compared to 2023, with an additional cost of $112,500. In the 50% price reduction scenario, profits increase by $1,376,100 and costs increase by $147,100. Using Monte Carlo simulation with 10,000 iterations to account for uncertainty in sales, acreage, costs, and prices, the most common scenario showed a seven-year average increase in profits of $1,240,900 and an increase in costs of $84,900. The proposed scenarios are highly adaptable and can be optimized according to the actual situation.