A floating or onshore structure comprising at least one tank in which is contained liquefied natural gas or a mixture of liquid methane and an alkane comprising at least two carbon atoms and being in the liquid state, at least one consumer, at least one supply system for supplying a fuel to the consumer in a first configuration, the fuel being prepared from a gas resulting from boil-off of the liquefied natural gas contained in the tank, and for supplying the fuel to the consumer in a second configuration, the fuel being prepared from a gas resulting from the boil-off of the mixture contained in the tank, the supply system comprising a conversion device configured to alternate between the first configuration and the second configuration of the supply system, the supply system comprising a heat exchange module configured to at least partially liquefy the gas resulting from the boil-off of the mixture contained in the tank and a fuel preparation system from the at least partly liquefied gas, the fuel being prepared from the at least partly liquefied gas having a methane number greater than a methane number of the mixture.