The berth allocation problem (BAP) is one of the key decision problems at port terminals. It has been widely studied by many of research works. In this paper, the dynamic and discrete case of the BAP in a bulk port was studied, a mathematical model was proposed and solved using Cplex whose the objective is to minimize the total service time of berthed vessels. The proposed model was tested and validated through numerical experiments based on instances inspired from data of the bulk port of Sidi Youssef Sfax, Tunisia. It succeeded in finding good solutions compared to the results achieved by the port planning team.