A SEQUENTIAL STOCHASTIC ASSIGNMENT PROBLEM FOR A RANDOM SEQUENCE WITH UNKNOWN NUMBER OF VALUES PER PERIOD

In this paper, we treat a sequential stochastic assignment problem for the random number of jobs per period. In Section 2, we consider several preliminary results about an optimal selection problem as in Nakai [10]. We treat this problem for two cases, i.e., a case with known number of arriving jobs and a one with unknown number. In Section 3, we treat a case with a previously known about the total number of arriving jobs. In Section 4, we consider a case not knowing about the number of jobs but only knowing the probability distribution of this number at each period. For these problems, there exists threshold values depending only on the distribution function of the arriving jobs. We obtain the optimal policy and the expected value obtainable by this policy by using these threshold values.