  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.
