A lower bounding method for earliness and tardiness minimization on a single batch processing machine

In this research, the problem of scheduling a single batch processing machine with non-identical job sizes is considered. The objective is to minimize the total earliness and tardiness of all the jobs. A batch processing machine can process a group of jobs simultaneously as a batch as long as its capacity is not violated. The processing time of a batch is equal to the maximum processing time of all the jobs in the batch. Since the problem under study is shown to be NP-hard, a lower bounding method based on column generation is proposed. The proposed lower bound can be used for evaluating the performance of the heuristic and metaheuristic algorithms developed for the research problem. The computational experiments are designed to analyze the performance of the proposed lower bound. The results show that the column generation approach can considerably generates better lower bound than the best known lower bounding method in the literature.