Summary: Optimal Mechanisms for Scheduling
May 21, 2010
We study the design of optimal mechanisms in a setting where a service provider needs to
schedule a set of non-preemptive jobs, one job at a time. Jobs need to be compensated for
waiting, and waiting cost is private information. In this setting, an optimal mechanism is one
that induces jobs to report truthfully their waiting cost, while minimizing the total expected
compensation cost of the service provider. Here, truthful refers to Bayes-Nash implementability,
and assumes that private information is independently drawn from known distributions. We
derive closed formulae for the optimal mechanism, and show that it is a modification of Smith's
ratio rule. We also show that it can be implemented in dominant strategies. Our analysis relies
on a graph-theoretic interpretation of the incentive compatibility constraints. It parallels the
analysis known for auctions with single parameter agents, yet it exhibits some subtle differences.
We also consider the multi-dimensional case where also the service times of jobs are private
information. We show that for this problem the optimal mechanism generally does not satisfy
an independence condition known as IIA, and thus known approaches are doomed to fail.