A robust optimization solution to bottleneck generalized assignment problem under uncertainty

We consider two versions of bottleneck (or min–max) generalized assignment problem (BGAP) under capacity uncertainty: Task–BGAP and Agent–BGAP. A robust optimization approach is employed to study this issue. The decision maker’s degree of risk aversion and the penalty weighting parameter are incorporated into the objective function. A state-of-the-art linearization method is introduced to deal with the mathematical model and find the solution scheme. Two penalties of weighting parameters that realize the trade-off between solution robustness and model robustness are obtained. Illustrative examples are presented with managerial implications highlighted for decision-making considerations.