Solving the unrelated parallel batch machine scheduling problem with mixed-integer programming

In this study, the problem of scheduling jobs with arbitrary sizes and non-zero release times on a set of unrelated parallel batch processing machines with different capacities is discussed. Three mixed-integer programming models with different objective functions are developed to solve the problem. Corresponding models aim at minimizing (i) the total flow time, (ii) the makespan and (iii) the total tardiness, respectively, which are considered to be among the most important objectives in scheduling problems. In order to test the validity and applicability of the proposed solution approach, different datasets are generated using some rules in the literature. The results obtained by solving the mathematical programming models with these data sets are analyzed in terms of some performance parameters.