Distributionally robust single machine scheduling with the total tardiness criterion.

•A distributionally robust optimization (DRO) model is adopted to minimize the total tardiness criterion for machine scheduling.•An explicit expression is derived as an upper bound approximation for the robust objective.•Branch-and-bound and beam search algorithms are proposed to solve the problem.•Experimental results confirm the efficacy of the proposed algorithms.•Simulation experiments verify the effectiveness of the proposed DRO model.