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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bruno FL (1976) Scheduling algorithms for minimizing the mean weighted flow-time criterion. In Coffman EG Jr (ed) Computer and Job-Shop Scheduling Theory. John Wiley & Sons New York 101–137
Bücker M (1990) Ein-Maschinen-Scheduling-Probleme mit stochastischen Reihenfolgebeziehungen unter besonderer Berücksichtigung polynomialer Algorithmen. Doctoral Dissertation, University of Karlsruhe
Bücker M (1992) Time complexity of single-machine scheduling with stochastic precedence constraints. Zeitschrift für Operations Research 36:211–226
Bücker M, Neumann K (1989) Stochastic single-machine scheduling to minimize the weighted expected flow-time and maximum expected lateness subject to precedence constraints given by an OR Network. Report WIOR-361, Institut für Wirtschaftstheorie und Operations Research, University of Karlsruhe
Cinlar E (1975) Introduction to stochastic processes. Prentice-Hall, Englewood Cliffs
Elmaghraby SE (1977) Activity networks: Project planning and control by network models. John Wiley & Sons New York
Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: A Survey. Annals of Discrete Mathematics 5:287–326
Horn WA (1972) Single-machine job sequencing with treelike precedence ordering and linear delay penalties. SIAM Journal of Applied Mathematics 23:189–202
Lawler EL (1973) Optimal sequencing of a single machine subject to precedence constraints. Management Science 19:544–546
Lawler EL (1976) Combinatorial optimization: Networks and matroids. Holt, Rinehart and Winston New York
Lenstra JK, Rinnooy Kan AHG (1978) Complexity of scheduling under precedence constraints. Operations Research 26:22–35
Lenstra JK, Rinnooy Kan AHG, Brucker P (1977) Complexity of machine scheduling problems. Annals of Discrete Mathematics 1:343–362
Neumann K (1984) Recent developments in stochastic activity networks. Canadian Journal of Operational Research and Information Processing 22:219–248
Neumann K (1985) EOR project networks. Computing 34:1–15
Neumann K (1990) Stochastic project networks. Lecture Notes in Economics and Mathematical Systems Vol 344. Springer Berlin
Neumann K, Steinhardt U (1979) GERT networks and the time-oriented evaluation of projects. Lecture Notes in Economics and Mathematical Systems Vol 172 Springer Berlin
Nicolai W (1980) On the temporal analysis of special GERT networks using a modified Markov renewal process. Zeitschrift für Operations Research 24:263–272
Pritsker AAB (1977) Modeling and analysis usingQ-GERT networks. John Wiley & Sons New York
Pritsker AAB, Sigal CE (1983) Management decision making — A network simulation approach. Prentice Hall, Englewood Cliffs
Rubach T (1984) Stochastische Reihenfolgeplanung mit Hilfe von GERT-Netzplänen. Doctoral Dissertation. University of Karlsruhe
Smith WE (1956) Various optimizers for single-stage production. Naval Research Logistics Quarterly 3:59–66
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bücker, M., Neumann, K. & Rubach, T. Algorithms for single-machine scheduling with stochastic outtree precedence relations to minimize expected weighted flow time or maximum expected lateness. ZOR - Methods and Models of Operations Research 39, 321–348 (1994). https://doi.org/10.1007/BF01435461
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01435461