Minimizing total weighted tardiness in a dynamic flowshop with variable processing times

This research is motivated by the problem of meeting customer due dates in a multi-product flowshop production environment subject to processing time variability. The production environment under study requires the enforcement of permutation sequences wherein the operating sequences of jobs are the same on every machine. Permutation schedules often find applicability in real world situations, such as those factories with conveyors between machines for material transfer and assembly lines performing the final assembly of bulky products. Permutation schedules allow for a planned, smooth, continuous flow of jobs. We investigate such situations where each machine needs to be operated based on a first in first out (FIFO) rule. Good non-permutation schedules would outperform their permutation counterparts except in the case of two machines where optimal permutation schedules can be determined. The number of feasible schedules in a non-permutation wherein every job visited every machine is (n!) ^m. However, in the permutation case the search space is reduced to n!. The problem of identifying good permutation schedules is itself difficult. Therefore, flowshop research has typically assumed a permutation restriction on job sequences. Jobs are released into the flowshop at the beginning of every shift. Within each scheduling horizon, many jobs are present at various workstations in the flowshop. Therefore, the permutation sequence is fed into a subroutine that constructs schedules for each workstation in the flowshop while considering current shop status at the time of scheduling. Two methods are tested for scheduling jobs, both of which generate permutation sequences for the flowshop: a modified Apparent Tardiness Cost (ATC) heuristic and a genetic algorithm (GA). As new jobs arrive to the flowshop over time, the problem was investigated over a rolling horizon. Having generated a schedule for a given time horizon (planning period), we modify the schedule in response to the undesirable effects of variability. The modified schedule is now executed in the flowshop. The question is if/when to initiate rescheduling so that total weighted tardiness is minimized. A method to generate individual machine schedules using permutation sequences is developed. Due to the stochastic nature of jobs processing times the flowshop is expected to deviate from the planned schedule, thereby warranting rescheduling. Three different rescheduling triggering mechanisms that use information on the difference between actual and expected job completion times on critical machines are proposed. Finally the permutation schedule requirement was relaxed to access the cost of this requirement. A simulation-based experimental study is carried out to study the performance of the above methods with respect to minimizing total weighted tardiness.