Research on the batch scheduling on the single machine using the JIT technique

We consider a scheduling model in which several batches of jobs need to be processed by a single machine. During processing, no tardy jobs are allowed, so only earliness penalties and the machine processing cost are to be considered, the objective of which is to minimize the processing cost. To solve this problem, we provide two lemmas and three rules about batching jobs and deciding the start time of each batch, on the basis of which a heuristic algorithm is put forward. The results of experiment show the algorithm is efficient.