A diophantine set-driven approach to part sets cycle time scheduling and repetitive flow balancing

The problem studied in this paper is a cyclic job-shop problem with multiple AGVs. Job batches, which follow specific production routes, are processed in order of their operations on multiple machines with standard processing times, and the fleet of AGVs perform the transportation operations of moving job batches between the workstations. In this system, part sets of items are produced at fixed time intervals. In the adopted model, a layer of station-to-station transport, which is a network of local loops connecting subsets of workstations serviced cyclically by dedicated AGVs, and a layer of repetitive production flows which comprise task batches following a given set of production routes are distinguished. A set of nonlinear Diophantine equations describes the relationship between the elements of the structure of the system and its potential behavior. The resulting Diophantine sets enable fast evaluation, although limited to integers, of production flow parameters including part sets, cycle time and takt time, as well as repetitive-flow balancing aimed at maximization of the rate of system resource utilization. The high efficiency of the proposed Diophantine-set-driven approach is a consequence of omitting the time-consuming calculation of task timing and sequencing.