Batch Scheduling and Robust Batch Scheduling to Minimize Maximum Lateness

We consider the problem of scheduling jobs on a batching machine to minimize maximum lateness. Two batch processing modes, serial batch (s-batch) and parallel batch (p-batch), are considered. We first describe the exact algorithms for the s-batch and p-batch scheduling problems. We then present a robust extension to classical problems in which uncertain processing times are represented by a budgeted uncertainty set. Given a solution, we demonstrate efficient algorithms to evaluate the solution under its worst-case scenario for both s-batch and p-batch robust scheduling problems. For the s-batch robust scheduling problem, we propose an exact algorithm that has the same time complexity as the classical problem. For the p-batch robust scheduling problem, we design a heuristic algorithm that provides both upper and lower bounds on the optimal value. Computational results show that the proposed heuristic performs satisfactorily.