Optimal Sequential Assignment

For each job n (=1, …, N) there is an associated random variable X n and for each person m (=1, …, N) there is an associated constant p m so that if job n is assigned to person m a reward p m X n is obtained. We do not assume that the X n are necessarily independent. The jobs are observed sequentially and must be assigned nonanticipatively to the persons so as to maximise the total expected reward. The optimal assignment is established for both the case when N is finite and when N is infinite.