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Web of Proceedings - Francis Academic Press

A Multi-objective Planning Model for Planting Programmes Based on Monte Carlo Simulation and Complementary Substitution Constraints

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DOI: 10.25236/icetmr.2024.003

Author(s)

Baoquan Cui, Sen Fan, Gaofeng Han

Corresponding Author

Baoquan Cui

Abstract

In order to optimise the use of arable land resources, enhance production efficiency and promote the sustainable development of rural economy, this paper studies the crop planting planning problem in a village in the mountainous region of North China, and establishes an optimal planting model for the period from 2024 to 2030, and the study designs three problem-solving models for the open cropland and greenhouse respectively according to the arable land conditions of the village, and carries out analyses and comparisons. In this paper, a multi-objective linear programming model is firstly proposed, aiming at maximising the crop cultivation returns between 2024 and 2030, deriving a compact lower bound on the returns by combining the mean value inequality and the Lagrange multiplier method, and maximising this lower bound to achieve the robustness of the returns. In addition, the model considers a minimum area constraint to ensure that all planted areas do not fall below a pre-determined minimum value and the remaining area is optimally allocated according to the economic benefits of the crop.Then, based on the multi-objective linear programming model, this paper further considers uncertainty and potential planting risks (e.g. market price fluctuations, climate change, fluctuations in planting costs, pest and disease risks, etc.), and solves the optimal planting scheme under dynamic constraints through Monte Carlo simulation to cope with market, climate and cost uncertainties while ensuring risk management capability.Finally, alternative and complementary relationships between crops are incorporated. The constructed substitutability and complementarity matrices were combined with Spearman's correlation analysis so as to optimise the cropping returns and to find the two most correlated characteristics as yield per acre versus cropping cost to build the complete model

Keywords

Monte Carlo Simulation, Complementarity Gains, Substitution Constraints, Lagrange Multiplier Method, Minmax Optimisation