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This work addresses task planning under uncertainty for precision agriculture applications whereby task costs are uncertain and the gain of completing a task is proportional to resource consumption (such as water consumption in precision irrigation). The goal is to complete all tasks while prioritizing those that are more urgent, and subject to diverse budget thresholds and stochastic costs for tasks. To describe agriculture-related environments that incorporate stochastic costs to complete tasks, a new Stochastic-Vertex-Cost Aisle Graph (SAG) is introduced. Then, a task allocation algorithm, termed Next-Best-Action Planning (NBA-P), is proposed. NBA-P utilizes the underlying structure enabled by SAG, and tackles the task planning problem by simultaneously determining the optimal tasks to perform and an optimal time to exit (i.e. return to a base station), at runtime. The proposed approach is tested with both simulated data and real-world experimental datasets collected in a commercial vineyard, in both single-and multi-robot scenarios. In all cases, NBA-P outperforms other evaluated methods in terms of return per visited vertex, wasted resources resulting from aborted tasks (i.e. when a budget threshold is exceeded), and total visited vertices.Index Terms-Planning, robotics and automation in agriculture and forestry, scheduling and coordination, task and motion planning. I. INTRODUCTIONA UTONOMOUS agricultural mobile robots become increasingly more capable for persistent missions like monitoring crop health [1] and sampling specimens [2] across extended spatio-temporal scales to enhance efficiency and productivity in precision agriculture [3]. An autonomous robot (or a team of them) needs to perform certain tasks in distinct locations of the environment subject to a specific budget [4] on the actions Manuscript