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：干旱期间农业用水的优化分配是一个重要的全球性问题。在解决该问题时，需综合考量农民福利、经济与环境等多方面因素。在此背景下，本研究聚焦于若干考虑多作物组合持有者、地理约束及公平性的资源匹配问题。首先，我们解决了一个匹配问题，其目标是在双边市场中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（对特定水量赋予价格或成本）表征。针对价值函数满足特定单调性质的情形，我们提出了一种高效算法以最大化社会福利函数。在存在最低水量约束时，我们设计了一种随机化算法，可确保约束条件在期望意义上得到满足。针对带公平约束的单一卖方与多买方场景，我们提出了一种最大化任意买方最小满意度的高效算法。此外，我们给出了计算复杂性理论结果，揭示了本方法推广性的局限。基于现实与合成数据集、干旱严重程度、价值函数及代理优先权等因素的实验，我们对所提算法进行了评估。