  It is often beneficial for agents to pool their resources in order to better
accommodate fluctuations in individual demand. Many multi-round resource
allocation mechanisms operate in an online manner: in each round, the agents
specify their demands for that round, and the mechanism determines a
corresponding allocation. In this paper, we focus instead on the offline
setting in which the agents specify their demand for each round at the outset.
We formulate a specific resource allocation problem in this setting, and design
and analyze an associated mechanism based on the solution concept of
lexicographic maximin fairness. We present an efficient implementation of our
mechanism, and prove that it is envy-free, non-wasteful, resource monotonic,
population monotonic, and group strategyproof. We also prove that our mechanism
guarantees each agent at least half of the utility that they can obtain by not
sharing their resources. We complement these positive results by proving that
no maximin fair mechanism can improve on the aforementioned factor of one-half.
