Abstract
The so-called classical project networks used by the network techniques CPM, PERT, and MPM, only allow for modelling projects whose evolution in time is uniquely specified in advance (cf. Elmaghraby 1977 and Moder et al. 1983). Here, each project activity is carried out exactly once during a single project execution and it is not possible to return to activities previously performed (that is, no feedback is permitted). Many practical projects, however, do not meet those conditions, for example, R&D projects and projects in production management where quality control is included and thus some feedback may occur.
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References
Adams, J., E. Balas, and D. Zawack. 1988. The Shifting Bottleneck Procedure for Job Shop Scheduling. Management Science 34, 391–401.
Blazewicz, J., K.H. Ecker, E. Pesch, G. Schmidt, and J. Weglarz. 1996. Scheduling Computer and Manufacturing Processes. Springer, Berlin.
Brucker, P. 1995. Scheduling Algorithms. Springer, Berlin.
Bücker, M. 1992. Time Complexity of Single Machine Scheduling with Stochastic Precedence Constraints. ZOR-Mathematical Methods of Operations Research 36, 211–225.
BÜcker, M., K. Neumann, and T. Rubach. 1994. Algorithms for Single-Machine Scheduling with Stochastic Outtree Precedence Relations to Minimize Expected Weighted Flowtime or Maximum Expected Lateness. ZOR-Mathematical Methods of Operations Research 39, 321–348.
Carlier, J. and E. Pinson. 1989. An Algorithm for Solving the Job Shop Problem. Management Science 35, 164–176.
Elmaghraby, S.E. 1977. Activity Networks: Project Planning and Control by Network Models. John Wiley and Sons, New York.
Fujii, M., T. Kasami, and K. Nonomiya. 1969, 1971. Optimal Sequencing of Two Equivalent Processors. SIAM Journal of Applied Mathematics 17, 784–789, Erratum 20, 141.
Giffler, B. and G.L. Thompson. 1960. Algorithms for Solving Production-Scheduling Problems. Operations Research 8, 487–503.
Gittins, J.C. 1989. Multi-Armed Bandit Allocation Indices. John Wiley and Sons, New York.
Horn, W.A. 1972. Single-Machine Job Sequencing with Treelike Precedence Ordering and Linear Delay Penalties. SIAM Journal of Applied Mathematics 23, 189–202.
Hu, T.C. 1961. Parallel Sequencing and Assembly Line Problems. Operations Research 9, 841–848.
Lawler, E.L. 1973. Optimal Sequencing of a Single Machine Subject to Precedence Constraints. Management Science 19, 544–546.
Lenstra, J.K. and A.H.G. Rinnooy Kan. 1978. Complexity of Scheduling under Precedence Constraints. Operations Research 26, 22–35.
Lenstra, J.K., A.H.G. Rinnooy Kan, and P. Brucker. 1977. Complexity of Machine Scheduling Problems. Annals of Discrete Mathematics 1, 343–362.
Moder, J.J., C.R. Phillips, and E.W. Davis. 1983. Project Management with CPM, PERT and Project Diagramming. Van Nostrand Reinhold, New York.
Neumann, K. 1984. Recent Developments in Stochastic Activity Networks. Canadian Journal of Operational Research and Information Processing 22, 219–248.
Neumann, K. 1990. Stochastic Project Networks. Lecture Notes in Economics and Mathematical Systems, Vol. 344. Springer, Berlin.
Neumann, K. and W.G. Schneider. 1997. Job-Shop and Flow-Shop Scheduling with OR Network Precedence Constraints: Structural Questions and Heuristic Procedures. Technical Report WIOR-498, Institut für Wirtschaftstheorie und Operations Research, University of Karlsruhe.
Neumann, K. and W.G. Schneider. 1998. Heuristic Algorithms for Job-Shop Scheduling Problems with Stochastic Precedence Constraints. Submitted to Annals of Operations Research.
Neumann, K. and U. Steinhardt. 1979. GERT Networks and the Time-Oriented Evaluation of Projects. Lecture Notes in Economics and Mathematical Systems, Vol. 172. Springer, Berlin.
Neumann, K. and J. Zimmermann. 1998. Heuristic Procedures for Parallel-Machine Scheduling Problems with Stochastic Precedence Constraints. Annals of Operations Research, to appear.
Pinedo, M. 1995. Scheduling: Theory, Algorithms, and Systems. Prentice Hall, Englewood Cliffs.
Schneider, W.G. 1997. Job Shop Scheduling with Stochastic Precedence Constraints. Shaker, Aachen.
Zimmermann, J. 1995. Mehrmaschinen-Schedulingprobleme mit GERT-Anordnungsbeziehungen. Ph.D. Dissertation, University of Karlsruhe.
Zimmermann, J. 1999. Time Complexity of Single-and Identical Parallel-Machine Scheduling with GERT Network Precedence Constraints. Mathematical Methods of Operations Research, to appear.
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Neumann, K. (1999). Scheduling of Projects with Stochastic Evolution Structure. In: Węglarz, J. (eds) Project Scheduling. International Series in Operations Research & Management Science, vol 14. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5533-9_14
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DOI: https://doi.org/10.1007/978-1-4615-5533-9_14
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