Robust optimization for minimizing total tardiness on unrelated parallel machine scheduling

This paper investigates a scheduling problem with due times for unrelated parallel machines, incorporating uncertain setup times and processing times. The tardiness of jobs can be easily overlooked in production scheduling problems when dealing with uncertainty, potentially leading to disruptions in the production plan and longer production cycles. To address this issue, we propose a robust model to minimize the total tardiness while considering the uncertainty of setup times and processing times, as well as incorporating the constraint of due times. We then convert the model into a linear robust formulation and solve it using Gurobi. Through experimental comparisons between the deterministic model and the proposed robust model under uncertain conditions, the results demonstrate that the robust model exhibits superior performance in handling uncertain situations.