Optimal allocation of agricultural water in the event of droughts is an important global problem. In addressing this problem, many aspects, including the welfare of farmers, the economy, and the environment, must be considered. Under this backdrop, our work focuses on several resource-matching problems accounting for agents with multi-crop portfolios, geographic constraints, and fairness. First, we address a matching problem where the goal is to maximize a welfare function in two-sided markets where buyers' requirements and sellers' supplies are represented by value functions that assign prices (or costs) to specified volumes of water. For the setting where the value functions satisfy certain monotonicity properties, we present an efficient algorithm that maximizes a social welfare function. When there are minimum water requirement constraints, we present a randomized algorithm which ensures that the constraints are satisfied in expectation. For a single seller--multiple buyers setting with fairness constraints, we design an efficient algorithm that maximizes the minimum level of satisfaction of any buyer. We also present computational complexity results that highlight the limits on the generalizability of our results. We evaluate the algorithms developed in our work with experiments on both real-world and synthetic data sets with respect to drought severity, value functions, and seniority of agents.

翻译：干旱期农业用水的优化配置是一个重要的全球性问题。在解决这一问题时，必须考虑农民福祉、经济收益和生态环境等多个方面。在此背景下，本研究聚焦于考虑多作物组合农户、地理约束与公平性的资源匹配问题。首先，我们解决了一个在双边市场中的匹配问题，其目标是最大化社会福利函数——其中买方需求与卖方供给通过价值函数进行表征，该函数为特定水量赋予价格（或成本）。针对价值函数满足特定单调性的场景，我们提出了一个能最大化社会福利函数的高效算法。当存在最低用水需求约束时，我们设计了一个随机算法以确保约束条件在期望意义下成立。对于具有公平约束的单一卖方-多买方场景，我们构建了一个能最大化任意买方最小满意度的效率算法。此外，我们还给出了计算复杂度结果，揭示了所得结论推广性的理论极限。我们通过真实与合成数据集，针对干旱严重程度、价值函数及农户优先级等维度，对提出的算法进行了实验评估。