Multi-objective planning model for sustainable agri-food supply chains: balancing profitability and fairness
提出了一个整合盈利性与多维公平性的多目标规划模型，用于可持续农业食品供应链，通过随机规划处理产量和价格不确定性，并比较了多种优化算法。
Smallholder agriculture constitutes an integral component of the global agri-food system; however, smallholders remain susceptible to systemic risks arising from socio-economic inequities and uncertainty in production and markets. This study proposes a multi-objective planning model for sustainable agri-food supply chains that integrates profitability with multi-dimensional fairness. Fairness is represented through three dimensions: distributional fairness, financial-risk resilience, and service fairness. The problem is formulated as a mixed-integer non-linear programming model, incorporating multi-period and multi-product decisions across planting, harvesting, packing, storage, sorting, and transport stages. To capture uncertainty in crop yield and market price, a scenario-based stochastic programming approach was developed and compared with a deterministic benchmark. The model was solved using Non-dominated Sorting Genetic Algorithm (NSGA-II), Multi-Objective Particle Swarm Optimisation (MOPSO), and Multi-Objective Whale Optimisation Algorithm (MOWOA), and the ϵ-constraint method. Computational experiments demonstrate that the stochastic model achieves more robust fairness outcomes under uncertainty while maintaining comparable expected profit. Furthermore, sensitivity analyses reveal how fairness-weight preferences and structural constraints shape the trade-offs between profitability and the three fairness dimensions. These findings provide actionable insights for contract design, resource allocation and fairness-oriented decision-making in sustainable agri-food supply chains.