Liquefied natural gas (LNG) is natural gas that has been transformed to liquid form for the purpose of transportation, which is mainly done by specially built LNG vessels travelling from the production site to the consumers. We describe a real-life ship routing and scheduling problem from the LNG business, with both inventory and berth capacity constraints at the liquefaction port. We propose a solution method where the routing and scheduling decisions are decomposed. The routing decisions consist of deciding which vessels should service which cargoes and in what sequence. The scheduling decisions are then to decide when to start servicing the cargoes while satisfying inventory and berth capacity constraints. The proposed solution method has been tested on several problem instances based on the real-life problem. The results show that the proposed solution method is well suited to solve this LNG shipping problem.