We consider a maritime inventory routing problem faced by actors involved in transportation in the LNG (liquefied natural gas) supply chain. A fleet of ships transport LNG between loading and unloading terminals with inventory constraints and time varying production and consumption profiles. In addition complex contracts regulate both volumes, legal destinations and prices. The problem is modeled using a general framework for maritime inventory routing problems. A construction heuristic is combined with an adaptive large neighborhood search procedure to produce high quality solutions to real world cases, even with strict requirements on response time.