It is well known that for an affine scheme $X$, every finitely generated locally free sheaf $\mathcal{E}$ is projective in the category Qcoh$(X)$. i.e. the functor $\text{Hom}_{\text{Qcoh}(X)}(\mathcal{E},\cdot)$ is exact. Of course this is no longer true if $X$ is a general, non-affine scheme.

Now we go beyond schemes: Let $(X,\mathcal{O}_X)$ be a ringed space. We still have a definition of quasi-coherent sheaf: A sheaf of $\mathcal{O}_X$-modules $\mathcal{F}$ is called quasi-coherent if for every point $x\in X$ there exists an open neighbourhood $x\in U\subset X$ such that $\mathcal{F}|_U$ is isomorphic to the cokernel of a map $$ \bigoplus_{j\in J} \mathcal{O}_U\rightarrow \bigoplus_{i\in I} \mathcal{O}_U. $$ See http://stacks.math.columbia.edu/download/modules.pdf Section 10.

My question is: do we have a condition on the ringed space $(X,\mathcal{O}_X)$ to guarantee it has the similar property as an affine scheme, i.e. every finitely generated locally free sheaf $\mathcal{E}$ is projective in the category Qcoh$(X)$?