  This paper reviews compact continuous-time formulations for the multi-mode
resource-constrained project scheduling problem. Specifically, we first point
out a serious flaw in an existing start-end-event-based formulation owing to
inconsistent mode choices. We propose two options to formulate the missing
constraints and we consider an equivalent reformulation with sparser constraint
matrix. Second, we formulate an aggregate variant of an existing model that
relies on on-off-events and clarify the role of mode consistency issues in such
models. Third, we suggest two variants of an existing network flow formulation.
We enhance our models by adapting several techniques that have been used
previously, e.g., in cases with only a single mode. A large set of benchmark
instances from the literature provides the basis for an up-to-date and fair
computational study with an out-of-the-box solver package. We compare our
models against two models from the literature. Our experiments assert
confidently that network flow formulations prevail in the test bed, and they
provide a hint on why event-based models become less competitive in multi-mode
settings.
