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.
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© 1987 Springer-Verlag Berlin Heidelberg
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Morlock, M., Neumann, K. (1987). Stochastic Single-Machine Scheduling to Minimize the Sum of Expected Weighted Completion Times Subject to OR Precedence Constraints. In: Opitz, O., Rauhut, B. (eds) Ökonomie und Mathematik. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72672-9_22
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DOI: https://doi.org/10.1007/978-3-642-72672-9_22
Publisher Name: Springer, Berlin, Heidelberg
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