Stochastic Single-Machine Scheduling to Minimize the Sum of Expected Weighted Completion Times Subject to OR Precedence Constraints

Summary

OR networks are cyclic GERT project networks all of whose nodes have an OR entrance and a deterministic or stochastic exit. The assumption that, figuratively speaking, different walks emanating from a deterministic node of an OR network do not meet beyond that node ensures that an OR network has some (generalized) tree structure. The tree-structure property can be exploited to generalize Smith’s ratio rule from deterministic scheduling to solve the stochastic single-machine scheduling problem for minimizing the sum of expected weighted completion times subject to precedence constraints given by an OR network. We consider two different cases: First, activities in cycles are counted for the objective function as often as they are carried out, and second, a passage through a strong component is viewed as a whole and taken into account only once.