Scheduling with uncertain processsing times: Applying β-robust schedule on two-machine flow-shop with constraints

Scheduling of jobs is momentous to augment production rate, reduce production expenses, trim down jobs completion times etc. However, changes in the sequence of jobs on machines as well as the uncertainties in actual processing times of jobs produces variations in the performance of flow-shop schedule. In these circumstances, the risk of attaining schedules' performance level inferior than a certain limit is an imperative evaluator for the efficiency of jobs schedule. To muddle through the risk in two-machine flow-shop where total flow-time is considered as a performance measure, a constraint based ß-robust schedule is anticipated to minimize the risk of exceeding total flow-time from a certain limit. The presented constraints are applied for scheduling of jobs in two-machine flow-shop of a manufacturing company in China. Result reveals that the proposed constraints yield a schedule with maximum probability of attaining total flow-time less than a threshold and the obtained schedule has minimum risk of exceeding total flow-time from a certain limit.