New Lower Bounds for the Optimal Makespan on a Single Batch Processing Machine

This paper considers minimizing makespan (Cmax) on a single batch-processing machine. A batch-processing machine can process a group of jobs simultaneously, as long as the total size of jobs in the batch does not exceed the machine capacity (B). For each job, we assume a specific job size and job processing time. The processing time of a batch is just the longest processing time of all jobs in the batch. We introduce two new procedures for obtaining lower bounds of the optimal makespan, entitled LB2 and LB3, respectively. We prove that both of the new bounds are tighter than the only existing bound called LB1. We also prove that LB3 is at least as tight as LB2.