The Berth Allocation Problem (BAP) is the problem of allocating berthing spaces and scheduling container vessels on these spaces so as to minimize total weighted time. We study a version of BAP in which containers are moved between vessels and berth space is abundant. Thus, the problem reduces to optimally assign vessels to berths. We call it the Berth Assignment Problem (BASP). We formulate it as a non standard Quadratic Assignment Problem, and we show that BASP is NP-Hard. The formulation is simplified, linearized, and valid inequalities are found. Numerical results are shown.