We investigate the problem of minimising power consumption in dense Wireless Local Area Networks (WLANs), by optimally establishing the association of User Terminals (UTs) to Access Points (APs). This management allows to switch off some APs, granting important power savings, while at the same time guaranteeing to satisfy the data rate requirements of all UTs. The considered WLAN power minimization problem can be formulated as an Integer Linear Programming (ILP) model and can be in principle solved by any commercial optimization solver. However, the problem is NP-hard and, as we show through thorough computational tests, even a last generation state-of-the-art solver like IBM ILOG CPLEX can have difficulties in finding solutions of good quality in short amount of time, as required in real WLAN deployments. As a consequence, we propose two new fast heuristic algorithms for WLAN power minimization. Furthermore, we show that, in some cases, also a proper setting of the parameters of CPLEX can compute solutions associated with good power savings in a reasonable time.