Calculating the theoretical project completion time of large networks in polynomial time
Bibliographic record
Abstract
One of the most important theoretical problems in project management is to obtain the distribution of the total completion time in PERT networks. For practical and managerial purposes what matters is the criticality of each activity within a PERT network, which can be assessed using a sound approach to calculate the completion time. Critical activities are activities that if delayed would delay the entire project. A sequence of critical activities throughout the network is called a critical path. The critical path is the longest path in the network and it is possible to have more than one critical path at once. But unlike CPM, in stochastic activity networks the duration time of individual activities varies and so activities are critical for some combinations of duration times and may not be critical for other combinations. Therefore, activities have a given probability of being critical (i.e. being part of the longest path). We call this probability criticality. The focus of this paper is to describe an analytical method for calculating the theoretical expectation of the project completion time as well as the criticality index of each activity.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".