The service time of container vessels is the main indicator of the competitiveness of a maritime container terminal. Vessels have to be berthed along the quay, a subset of quay cranes must be assigned to them and work schedules have to be planned for unloading the import containers and loading the export containers. This work addresses the Tactical Berth Allocation Problem, in which the vessels are assigned to a given berth, and the Quay Crane Scheduling Problem, for which the work schedules of the quay cranes are determined. The nature of this environment gives rise to inaccurate knowledge about the information related to the incoming vessels. Therefore, the aforementioned optimization problems can be tackled by considering fuzzy arrival times for the vessels and fuzzy processing times for the loading/unloading operations. Two fuzzy mathematical models are provided to solve the problems at hand. The computational experiments carried out in this work corroborate the effectiveness of the proposed methodologies.This work has been partially funded by the Spanish Ministry of Economy and Competitiveness (TIN2012-32608). It has also been partially supported by FEDER founds, the DGICYT and Junta de Andalucía under the projects (TIN2011-27696-C02-01) and (P11-TIC-8001), respectively. Christopher Expósito and Eduardo Lalla thank the Canary Government for the financial support they receive through their post-graduate grants.