Scheduling Single AGV in Blocking Flow-Shop with Identical Jobs

We consider a flow-shop with m stations (machines) and n identical jobs that need to be processed on each station. The processing time of every job on station i is p_i. After a job is processed on a station i, it needs to be transported by an automated guided vehicle (AGV) to the next station i + 1. There is only one AGV. We assume no buffers, i.e., when the AGV transports a job to a station, the station needs to be empty. Furthermore, an AGV can transport at most one job at a time, non-preemptively, i.e., it cannot leave the job in the middle of transportation. The transportation times between the stations are given and are independent of whether the AGV carries a job or not. We study the problem of scheduling the single AGV such that all jobs are processed and the makespan is minimized. We provide a characterization of feasible schedules, and use it to derive an integer linear program (ILP) for the problem. We observe that solving the ILP requires a rather large amount of computation time even for very small instances. We use the ILP-formulation to design a rolling-window based heuristic that scales up and provides close-to-optimum schedules, as demonstrated by experimental evaluation that also involves comparison to two natural greedy algorithms.