The distribution free job control problem

The job control problem is to determine an optimal release time where the flow time is a random variable with a known probability distribution. There is a trade-off between the penalty cost for late delivery and the holding cost for early finish. C. Liao [Computers Industrial Engineering, 22, 163-169 (1992)] formulated this problem and provided a practical decision procedure. This paper addresses the job control problem where only the mean and the variance of the flow time are known. The motivation of this paper comes from the fact that the distributional information on the flow time is usually limited for some job shops. We provide a simple line search algorithm to find a job release time which can be used in the absence of the distributional information