This paper addresses a hybrid job shop problem with identical machines, where several blocking constraints can be taken into account in a same problem. A mathematical linear integer model is proposed to be able to solve optimally the problem with commercial software. Since this problem is NP-hard, we developed an evaluation function in order to be able to solve bigger problems with classical meta-heuristics, thanks to a blocking matrix, containing the blocking constraints encountered after each operation of each job. The benchmark problems are proposed at the end of this paper, and the obtained results validate as much the proposed method as the evaluation function quality and suitability.