Method and apparatus for producing a cooled hydrocarbon stream (60). The method employs cooling, at at least two consecutive pressure levels, a first stream and a first mixed refrigerant stream, using portions of the first mixed refrigerant from the first mixed refrigerant stream in first and second heat exchangers (125, 145); first and second expansion devices (135, 165); and a first compressor (105) to provide the first mixed refrigerant stream. The cooling process is controlled using an advanced process controller based on model predictive control to determine simultaneously control actions for a set of manipulated variables in order to optimise at least one of a set of parameters whilst controlling at least one of a set of controlled variables. The set of manipulated variables comprises: the composition of the mixed first refrigerant, the setting of the first expansion device (135), and the setting of the second expansion device (165).