Optimizing Planting Planning Based on Linear Programming Pulp Model

Jia Cao; Min Tan; Qiangwei Wu; Yikun Zhou

doi:10.54097/ngr06q05

Authors

Jia Cao
Min Tan
Qiangwei Wu
Yikun Zhou

DOI:

https://doi.org/10.54097/ngr06q05

Keywords:

Linear Programming, Pulp Model, Optimization Problem, Gibbs Sampling, Random Growth Rate.

Abstract

To achieve sustainable rural economic development and make full use of cultivated land resources, solve the problem of rural land planting planning and improve planting benefits. Based on the data in Problem C of the 2023 mathematical modeling competition, the concept of random growth rate is introduced to deal with the uncertainty of growth rate. The Gibbs sampling algorithm is used to screen the random growth rate to make it more in line with the actual situation. A pulp linear programming model is established. The decision variables are set as binary variables. The objective function is determined as maximizing the total income of crops. According to different land types (flat dry land, terraced fields, slopes, irrigated land, ordinary greenhouses, intelligent greenhouses, etc.), planting constraint conditions are set, including the number of planting seasons and types of planted crops. At the same time, the constraints of legume rotation and non-negative and binary variable constraints are considered. Finally, the model is solved based on the pulp algorithm. Through data processing and model calculation, the results of two situations are obtained. The first situation is that excess products are unsalable and cause waste. The second situation is that the excess products are sold at 50% of the sales price in 2023. The incomes of vegetables, grains and edible fungi and the total income in each year from 2024 to 2028 under the two situations are calculated respectively. For example, the total income in 2024 under the first situation is 595,766.81, and the total income in 2024 under the second situation is 2,921,016.2. The total income in the second situation is generally higher than that in the first situation, indicating that selling the excess products at a reduced price can improve planting benefits. This research provides a basis for optimizing planting strategies. In the future, more factors can be included to improve planting planning and promote rural economic development.

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