Robust optimization of Flow Shop Scheduling with Uncertain Processing Time

The flow shop scheduling (FSS) problem is a classic NP-hard combinatorial problem. Owing to the processing time of an operation is usually uncertain in practice, a scenario-based robust optimization model is established for the FSS problem with uncertain processing time. The optimization goal of this model is to minimize the combination of expected processing time and the deviation of makespan for all scenarios. Then, a mixed integer linear programming (MILP) model is derived to minimize the objective, and two more constraints are added to ensure the validation of the model. Based on this model, the global best solutions of the small sized cases are obtained by LINGO. To solve the mid-to-large sized cases, a new algorithm called master-apprentice evolutionary algorithm (MAE) is adopted. The comparison between MAE and state-of-the-art metaheuristics illustrates the effectiveness of the MAE.