A New MIP Model for Parallel-Batch Scheduling with Non-identical Job Sizes

Parallel-batch machine problems arise in numerous manufacturing settings from semiconductor manufacturing to printing. They have recently been addressed in constraint programming (CP) via the combination of the novel sequenceEDD global constraint with the existing pack constraint to form the current state-of-the-art approach. In this paper, we present a detailed analysis of the problem and derivation of a number of properties that are exploited in a novel mixed integer programming (MIP) model for the problem. Our empirical results demonstrate that the new model is able to outperform the CP model across a range of standard benchmark problems. Further investigation shows that the new MIP formulation improves on the existing formulation primarily by producing a much smaller model and enabling high quality primal solutions to be found very quickly.