  We propose multi-type probabilistic serial (MPS) and multi-type random
priority (MRP) as extensions of the well known PS and RP mechanisms to the
multi-type resource allocation problem (MTRA) with partial preferences. In our
setting, there are multiple types of divisible items, and a group of agents who
have partial order preferences over bundles consisting of one item of each
type. We show that for the unrestricted domain of partial order preferences, no
mechanism satisfies both sd-efficiency and sd-envy-freeness. Notwithstanding
this impossibility result, our main message is positive: When agents'
preferences are represented by acyclic CP-nets, MPS satisfies sd-efficiency,
sd-envy-freeness, ordinal fairness, and upper invariance, while MRP satisfies
ex-post-efficiency, sd-strategy-proofness, and upper invariance, recovering the
properties of PS and RP.
