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Robust Crop Planning under Uncertainty: Aligning Economic Optimality with Agronomic Sustainability

Runhao Liu, Ziming Chen, You Li, Peng Zhang

TL;DR

This work addresses long-horizon agricultural planning under spatial heterogeneity, temporal dynamics, and multi-source volatility. It introduces the Multi-Layer Robust Crop Planning Framework (MLRCPF), which embeds explicit crop–crop interactions into a three-layer architecture (spatial, temporal, robust uncertainty) and unifies them into a distributionally robust optimization. The approach yields sustainable checkerboard rotations that restore soil fertility and improves worst-case profitability relative to baselines, by leveraging agronomic complementarities and diversification. Validation on a North China high-mix dataset demonstrates significant resilience and economic viability, highlighting the practical value of embedding domain-specific priors into robust optimization for complex agricultural systems.

Abstract

Long-horizon agricultural planning requires optimizing crop allocation under complex spatial heterogeneity, temporal agronomic dependencies, and multi-source environmental uncertainty. Existing approaches often treat crop interactions, such as legume-cereal complementarity, which implicitly or rely on static deterministic formulations that fail to guarantee resilience against market and climate volatility. To address these challenges, we propose a Multi-Layer Robust Crop Planning Framework (MLRCPF) that integrates spatial reasoning, temporal dynamics, and robust optimization. Specifically, we formalize crop-to-crop relationships through a structured interaction matrix embedded within the state-transition logic, and employ a distributionally robust optimization layer to mitigate worst-case risks defined by a data-driven ambiguity set. Evaluations on a real-world high-mix farming dataset from North China demonstrate the effectiveness of the proposed approach. The framework autonomously generates sustainable checkerboard rotation patterns that restore soil fertility, significantly increasing the legume planting ratio compared to deterministic baselines. Economically, it successfully resolves the trade-off between optimality and stability. These results highlight the importance of explicitly encoding domain-specific structural priors into optimization models for resilient decision-making in complex agricultural systems.

Robust Crop Planning under Uncertainty: Aligning Economic Optimality with Agronomic Sustainability

TL;DR

This work addresses long-horizon agricultural planning under spatial heterogeneity, temporal dynamics, and multi-source volatility. It introduces the Multi-Layer Robust Crop Planning Framework (MLRCPF), which embeds explicit crop–crop interactions into a three-layer architecture (spatial, temporal, robust uncertainty) and unifies them into a distributionally robust optimization. The approach yields sustainable checkerboard rotations that restore soil fertility and improves worst-case profitability relative to baselines, by leveraging agronomic complementarities and diversification. Validation on a North China high-mix dataset demonstrates significant resilience and economic viability, highlighting the practical value of embedding domain-specific priors into robust optimization for complex agricultural systems.

Abstract

Long-horizon agricultural planning requires optimizing crop allocation under complex spatial heterogeneity, temporal agronomic dependencies, and multi-source environmental uncertainty. Existing approaches often treat crop interactions, such as legume-cereal complementarity, which implicitly or rely on static deterministic formulations that fail to guarantee resilience against market and climate volatility. To address these challenges, we propose a Multi-Layer Robust Crop Planning Framework (MLRCPF) that integrates spatial reasoning, temporal dynamics, and robust optimization. Specifically, we formalize crop-to-crop relationships through a structured interaction matrix embedded within the state-transition logic, and employ a distributionally robust optimization layer to mitigate worst-case risks defined by a data-driven ambiguity set. Evaluations on a real-world high-mix farming dataset from North China demonstrate the effectiveness of the proposed approach. The framework autonomously generates sustainable checkerboard rotation patterns that restore soil fertility, significantly increasing the legume planting ratio compared to deterministic baselines. Economically, it successfully resolves the trade-off between optimality and stability. These results highlight the importance of explicitly encoding domain-specific structural priors into optimization models for resilient decision-making in complex agricultural systems.

Paper Structure

This paper contains 18 sections, 25 equations, 7 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction and Related Work
  2. Proposed Method
  3. Problem Formulation
  4. Overview
  5. Layer 1: Spatial Heterogeneity Layer
  6. Layer 2: Temporal Dynamics Layer
  7. Layer 3: Robust Uncertainty Layer
  8. Unified Optimization Model
  9. Experimental Evaluation
  10. Case Study: High-Mix Agricultural Planning
  11. Instance Construction
  12. Experimental Setup
  13. Results and Analysis
  14. Discussion
  15. Mechanisms of Agronomic Recovery
  16. ...and 3 more sections

Figures (7)

  • Figure 1: Overview of proposed MLRCPF.
  • Figure 2: Visualization of the crop interaction matrix $M$ derived from agronomic constraints.
  • Figure 3: Spatio-temporal crop allocation plan generated by the Deterministic Baseline (2024).
  • Figure 4: Spatio-temporal crop allocation plan generated by the proposed framework (2024).
  • Figure 5: Sensitivity analysis of worst-case profit with respect to the uncertainty radius ($\rho$).
  • ...and 2 more figures