This paper presents a scalable solution with adjustable computation time for the joint problem of scheduling and assigning machines and transporters for missions that must be completed in a fixed order of operations across multiple stages. A battery-operated multi-robot system with a maximum travel range is employed as the transporter between stages and charging them is considered as an operation. Robots are assigned to a single job until its completion. Additionally, The operation completion time is assumed to be dependent on the machine and the type of operation, but independent of the job. This work aims to minimize a weighted multi-objective goal that includes both the required time and energy consumed by the transporters. This problem is a variation of the flexible flow shop with transports, that is proven to be NP-complete. To provide a solution, time is discretized, the solution space is divided temporally, and jobs are clustered into diverse groups. Finally, an integer linear programming solver is applied within a sliding time window to determine assignments and create a schedule that minimizes the objective. The computation time can be reduced depending on the number of jobs selected at each segment, with a trade-off on optimality. The proposed algorithm finds its application in a water sampling project, where water sampling jobs are assigned to robots, sample deliveries at laboratories are scheduled, and the robots are routed to charging stations.

翻译：本文针对需要在多阶段固定操作顺序完成的任务，提出了一种具有可调计算时间的可扩展解决方案，用于机器与运输车的联合调度与分配问题。采用具有最大行驶距离限制的电池驱动多机器人系统作为阶段间的运输车，并将充电过程视为一项操作。机器人被分配至单个作业直至其完成。此外，操作完成时间假设取决于机器和操作类型，但与作业无关。本研究旨在最小化包含运输车所需时间与能量消耗的加权多目标函数。该问题属于带运输的可扩展流水车间调度变体，已被证明是NP完全的。为提供解决方案，时间被离散化，解空间按时间划分，作业被聚类为不同组别。最终，在滑动时间窗口内应用整数线性规划求解器，以确定分配方案并生成最小化目标的调度。计算时间可根据每个分段的选定作业数量减少，但需以最优性为代价。所提出的算法应用于水质采样项目，其中水质采样作业被分配给机器人，实验室的样品交付被调度，且机器人被引导至充电站。