We consider a quasi-projective noetherian scheme. It is well known that for a coherent sheaf we can construct a sheaf resolution of locally free of finite rank. It is introduced in Hartshorne chapter III.6 for computing Ext and $\mathscr{Ext}$ for example.

In terms of quasi-coherent sheaves, does there always exist a locally free resolution of quasi-coherent sheaves on a quasi-projective noetherian scheme? If exists, what will happen if we do a similar cohomological argument using locally free resolution of infinite rank? If not, how do people talk about this kind of **bounded above resolutions in the category of quasi-coherent sheaves**? Will we suffer from infinite direct sums?

I know that in general if we remove the condition "quasi-coherent or coherent", we can construct flat resolutions. However, it may be useless in concrete computation for quasi-coherent sheaves.