Single machine lot scheduling with maintenance activity

We study a single-machine lot scheduling problem. In this setting, the producer receives orders of different sizes that should be processed in lots. The total size of the orders assigned to a specific lot cannot exceed its capacity, and order splitting is permitted. The processing times of the lots are identical. Moreover, we assume that a fixed maintenance activity is performed, and during the maintenance time, no production is feasible. The objective function is the minimum total weighted completion times of the orders. An extension in two directions is also studied. The first is optional job rejection, in which the scheduler has the option to process only a subset of the orders. The other orders are rejected, and the scheduler is penalized accordingly. The objective function remains total weighted completion time, subject to an upper bound on the total permitted rejection cost. The second extension is rate-modifying maintenance, in which the production rate is improved when the system resumes. Pseudo-polynomial dynamic programming solution algorithms are introduced for these NP-hard problems. Large-size instances are shown to be solved efficiently.