Is the basic architecture of the minimalist program, with its numeration and various interfaces, meant to model how language is comprehended or how it is generated? Or is it supposed to be abstract enough to cover both? Since the numeration is unordered, I tend to think it's supposed to be generation, since comprehension involves pre-formed strings, but my fellow student disagrees.
Not exactly the most orthodox source, but I find Johnson & Lappin's (1997) synopsis concise and easy to follow for non-practitioners. As they explain,
...on the MP, a sentence is grammatical iff it is assigned a well-formed (convergent) PF and LF via some derivation D, but a derivation D is well-formed iff it satisfies all the constraints and is most highly valued by the economy metric with respect to a set of competing convergent derivations (its "reference set"). (275--6)
So derivations, subject to grammaticality constraints and global conditions, create pairs of representations. MP then models how sets of lexical items are converted to representations. If it were a model of comprehension, it would model how PF representations are converted to LF representations. If it were a model of production, it would be the other way around. Since it is neither, the answer must be "abstract enough to cover both."
The question relates to Chomsky's competence/performance distinction, which can be a little difficult to grasp. (see the discussion in Aspects of the theory of syntax). Your question seems to presuppose that MP relates to performance, i.e. actual language use. Minimalism is not intended to be an account of the generator/parser, but rather it is intended to be a competence grammar - it models an ideal speaker/hearer's knowledge of language while abstracting away from actual language use (although, naturally, evidence on which a competence grammar is based can only be inferred from actual use).
A minimalist model of the grammar can be used as the basis for a parser or generator - adapting it for a generator would be fairly straight-forward, as derivations proceed 'from the bottom up'. This is probably the basis of your intuition.