MINIMIZING TOTAL WEIGHTED COMPLETION TIME ON A SINGLE BATCH PROCESSING MACHINE

We study the problem of scheduling jobs on a single batch processing machine to minimize the total weighted completion time. A batch processing machine is one that can process a number of jobs simultaneously as a batch. The processing time of a batch is given by the processing time of the longest job in the batch. We present a branch and bound algorithm to obtain optimal solutions and develop lower bounds and dominance conditions. We also develop a number of heuristics and evaluate their performance through extensive computational experiments. Results show that two of the heuristics consistently generate high‐quality solutions in modest CPU times.