The paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines and release dates. Each job must be first processed on the single machine of stage 1, and then, the job is processed on one of the two dedicated machines of stage 2, depending on its type. Moreover, the jobs are available for processing at their respective release dates. Our goal is to obtain a schedule that minimizes the makespan. This problem is strongly NP-hard. In this paper, two mathematical models are developed for the problem: a mixed-integer programming model and a constraint programming model. The performance of these two models is compared on different problem configurations. And the results show that the constraint programming outperforms the mixed-integer programming in finding optimal solutions for large problem sizes (450 jobs) with very reasonable computing times.