OPTIMAL ASSIGNMENT FOR A RANDOM SEQUENCE WITH AN UNKNOWN NUMBER OF JOBS

Abstract

We will consider a sequential stochastic assignment problem where the number of jobs is not known beforehand. Unlike the well known sequential stochastic assignment problem, since the number of jobs is unknown, a policy of the decision-maker depends not only on the size of each job, but also on information about the number of remaining jobs. The optimal policy and the total expected reward under this policy are determined by a system of recursive equations which are obtained in the main theorem. In the last section, we will consider a case over an infinite horizon.