The Stochastic Sequential Assignment Problem with Arrivals

We extend the classic sequential stochastic assignment problem to include arrivals of workers. When workers are all of the same type, we show that the socially optimal policy is the same as the individually optimal policy where workers are given priority according to LCFS. This result also holds under several variants in the model assumptions. When workers have different types, we show that the socially optimal policy is determined by thresholds such that more valuable jobs are given to more valuable workers, but now the individually optimal policy is no longer socially optimal. We also show that the overall value increases when worker or job values become more variable.