Bicriterion stochastic scheduling on one or more machines

This paper is concerned with two types of bicriterion stochastic scheduling problems, the first involving a single machine, and the second involving the m-machine flow shop. In both problem types, a set of n jobs is to be processed on one or more machines, and the objective is to find a job sequence which minimizes the sum of the expected total weighted tardiness and the expected total weighted flowtime. The job processing times are independent random variables and the jobs have a common, random due date. For both problem types, an optimal job sequence is obtained by processing the jobs in increasing stochastic order of their processing times.