Minimizing the makespan for different volume parallel batch-processing machines problem with release times and job sizes

This paper considers the scheduling problem of different volume parallel batch-processing machines. The problem is inspired by the realistic burn-in operation environment in semiconductor manufacturing where jobs with nonidentical job sizes are not released for process at a time and ovens do not have equal capacity. In this study, two lower bounds, a mixed integer programming (MIP) model, and a genetic algorithm (GA) are proposed. In the GA, (m-1) genes in each chromosome with (n+m-1) genes were used as flags to separate jobs for each machine. Additionally, a dynamic programming (DP) algorithm is applied to group the jobs into batches for each machine. Experimental results showed that the lower bound was stronger than the optimal linear solutions (C-max(LP)) obtained by the MIP model where integer constraints were released, although the lower bound is very straightforward. Furthermore, the proposed GA could be capable of obtaining significantly good solutions in the shortest time.