A new method for a class of parallel batch machine scheduling problem

This paper studies the scheduling problem of jobs with release times, non-identical sizes, and incompatible job families on unrelated parallel batch machines. The capacities of batch machines and the processing times of each job on the batch machines are different. The processing time of one batch is equal to the longest processing time of jobs in this batch. Different types of jobs are not allowed to be assigned into the same batch, which is known as incompatible job families. Mixed integer linear programming and constraint programming (CP) models are proposed. A new batch-based local search method is designed and an iterated greedy (IG) algorithm is developed to avoid unreasonable exchanging of jobs during the local search. Numerical results show that the CP method can obtain high quality solutions in the small-scale instances. For the large-scale instances, the IG algorithm with the new local search method has a competitive performance.