Stochastic group scheduling problems on single and multiple machines

Abstract

This paper considers two types of stochastic group scheduling problems, one involves a single machine, and the other involves an m -machine flow shop. In both problems, jobs are classified into groups. The jobs of the same group are to be processed one after another, and a sequence independent setup time is incurred between each two consecutively scheduled groups. The job processing times are independent random variables and group setup times are functions of the job processing times. The objective is to find both a group sequence and a job sequence that minimizes the expected total flow time. An optimal group sequence and an optimal job sequence are obtained by processing jobs in increasing stochastic order of their mean processing times and group setup times for a single machine problem. A precedence relationship is derived for the m -machine flow shop problem.