Two-stage robust mixed integer programming problem with objective uncertainty

Many real problems with uncertain parameters can be modeled as two-stage robust mixed integer programming problems (RMIPs). Due to the complex nature of this kind of problems, this paper focuses on the two-stage RMIPs with objective uncertainty. Based on the results that the augmented Lagrangian is a strong dual for integer programming Boland and Eberhard (Math Program 150(2):491-509, 2015), we present the upper and lower bounds. In a special case, we show that the two-stage RMIPs can be equivalently reformulated as a solvable minimax problem.