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Schedule network node time distributions and arrow criticalities
| Content Provider | Semantic Scholar |
|---|---|
| Author | Singleton, Scott |
| Copyright Year | 1996 |
| Abstract | This research develops exact methods to calculate project duration distributions and to calculate Van Slyke's (1963) criticallly for arrows, the probability that an arrow is on a critical path, assuming nonnegatlve integer duration distributions. These calculations for project duration distributions correct estimates made by the Program Evaluation and Review Technique (PERT), and the Van Slyke critlcality calculations extend the arrow critlcality ansdysls by the Critical Path Method (CPM) Into the probabilistic realm. Exact methods for calculating project duration distributions and Van Slyke's criticallly sire demonstrated on series networks, parallel networks, parallel-series networks, and the Wheatstone network. The Van Slyke criticallly equation for parallel networks is in a form that appears to Improve upon one proposed by Dodln & Elmaghraby (1985). The present form Is generalized to, In principle. Include sill networks. The exact methods are enhanced by developing a procedure to limit the number of calculations needed to analyze large networks. The procedure identifies paths through a large network, calculates the minimum and maximum path durations, and ranks the paths by duration. A smaller skeletal network is constructed from the arrows of the longest paths and is analyzed by exact methods. The procedure emphasizes accuracy for the longer project durations, of greatest concern to project managers and schedulers, while limiting the number of necessary calculations. The procedure for large networks is iUustrated on the 40-arrow Klelndorfer (1971) network. Of the 51 Klelndorfer paths, the procedure selected 6 paths to construct a skeletal network. Analysis of the skeletal network yields a project duration distribution that is correct in Its range and in the duration probabilities for the upper 5% of the distribution. Analysis results are compared with SLAM II and FORTRAN simulations. No arrow critlcality appears to be seriously miscalculated. The project duration distribution is calculated to be bimodal. In keeping with the simulation. Conditions under which the Just mentioned blmodality can occur are determined for parallel, normally-distributed paths. The large-network procedure warns when these oddly shaped distributions are possible. |
| File Format | PDF HTM / HTML |
| DOI | 10.31274/rtd-180813-10386 |
| Alternate Webpage(s) | https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=12339&context=rtd |
| Alternate Webpage(s) | http://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=12339&context=rtd |
| Alternate Webpage(s) | https://doi.org/10.31274/rtd-180813-10386 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
