  We study the problem of assigning objects to agents in the presence of
arbitrary linear constraints when agents are allowed to be indifferent between
objects. Our main contribution is the generalization of the (Extended)
Probabilistic Serial mechanism via a new mechanism called the Constrained
Serial Rule. This mechanism is computationally efficient and maintains
desirable efficiency and fairness properties namely constrained ordinal
efficiency and envy-freeness among agents of the same type. Our mechanism is
based on a linear programming approach that accounts for all constraints and
provides a re-interpretation of the bottleneck set of agents that form a
crucial part of the Extended Probabilistic Serial mechanism.
