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This work studies the performance of two Mixed Integer Linear Programming (MILP) models to solve scheduling problems in a flexible job shop environment with recirculation and assembly using a due-date-based objective function. The models convey different approaches both in the modelling of time (discrete and continuous approaches) as well as in the assignment of jobs to machines. The comparison is carried out for a job shop system considered closer to the industrial reality than the classical job shop problem of a single machine per operation that has been extensively studied in the literature, with the mould making industry providing the motivating