Task allocation and on-the-job training

We study dynamic task allocation when providers' expertise evolves endogenously through training. We characterize optimal assignment protocols and compare them to discretionary procedures, where it is the clients who select their service providers. Our results indicate that welfare gains from centralization are greater when tasks arrive more rapidly, and when training technologies improve. Monitoring seniors' backlog of clients always increases welfare but may decrease training. Methodologically, we explore a matching setting with endogenous types, and illustrate useful adaptations of queueing theory techniques for such environments.