Algorithms for single-machine scheduling with stochastic outtree precedence relations to minimize expected weighted flow time or maximum expected lateness

Abstract

Stochastic single-machine scheduling problems with special tree-like GERT precedence constraints and expected weighted flow time or maximum expected lateness as objective functions are considered. To obtain polynomial algorithms for these problems, Smith's ratio rule and Lawler's rule for the deterministic problems 1¦outtree¦Σw v C v and 1¦prec¦f max , respectively, are generalized.