—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). (BASP) is an NP-Complete problem. We formulate it as a non standard Quadratic Assignment Problem, from which a 0-1 linear formulation is derived. Some valid inequalities of the resulting integer programming model are found. Numerical results are shown. Index Terms—Integer Linear Programming, Valid Inequalities, Quadratic Assignment Problem