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# Critical Path Method

## The critical path method, or critical path analysis, is an algorithm for scheduling a set of project activities. It is commonly used in conjunction with the program evaluation and review technique.

This is a python program that

- takes an activity table with each activity's predecessors and duration and stores it into a graph
- using a modified Breadth First Search algorithm to traverse the graph and determine the correct path
- calculates number of attributes for each activity following the selected path, these attributes are :
  - DU = Activity Duration
  - ES = Early Start Time
  - EF = Early Finish Time
  - LS = Late Start Time
  - LF = Late Finish Time
  - SK = Slack Value
- draws a plot showing the the graph, attributes for each node and critical path (green nodes),

---

## Here is Some Sample Tests And It's Output

| Activity | Predecessors | Duration |
| -------- | ------------ | -------- |
| A        | -            | 7        |
| B        | A            | 9        |
| C        | A            | 3        |
| D        | B            | 8        |
| E        | C            | 5        |
| F        | C            | 4        |
| G        | D E F        | 2        |
| H        | G            | 1        |

## ![fig1](https://raw.githubusercontent.com/cppcoders/cpm-python/master/images/fig1.png)

| Activity | Predecessors | Duration |
| -------- | ------------ | -------- |
| A        | -            | 5        |
| B        | -            | 4        |
| C        | A            | 7        |
| D        | A            | 3        |
| E        | B            | 2        |
| F        | D            | 9        |
| G        | B C          | 8        |

## ![fig2](https://raw.githubusercontent.com/cppcoders/cpm-python/master/images/fig2.png)

| Activity | Predecessors | Duration |
| -------- | ------------ | -------- |
| A        | -            | 3        |
| B        | A            | 4        |
| C        | A            | 2        |
| D        | B            | 5        |
| E        | C            | 1        |
| F        | C            | 2        |
| G        | D E          | 4        |
| H        | F G          | 3        |

## ![fig3](https://raw.githubusercontent.com/cppcoders/cpm-python/master/images/fig3.png)

| Activity | Predecessors | Duration |
| -------- | ------------ | -------- |
| A        | -            | 3        |
| B        | A            | 60       |
| C        | A            | 5        |
| D        | A            | 15       |
| E        | B            | 6        |
| F        | D            | 40       |
| G        | C E          | 10       |
| H        | F            | 7        |
| I        | G            | 6        |
| J        | H I          | 12       |

## ![fig4](https://raw.githubusercontent.com/cppcoders/cpm-python/master/images/fig4.png)

| Activity | Predecessors | Duration |
| -------- | ------------ | -------- |
| A        | -            | 7        |
| B        | A            | 7        |
| C        | B            | 14       |
| D        | A            | 14       |
| E        | D            | 14       |
| F        | D            | 14       |
| G        | E            | 21       |
| H        | F            | 7        |
| I        | G            | 7        |
| J        | C H          | 1        |
| K        | E            | 7        |
| L        | E            | 7        |
| M        | L            | 7        |
| N        | I J K M      | 7        |

## ![fig5](https://raw.githubusercontent.com/cppcoders/cpm-python/master/images/fig5.png)

| Activity | Predecessors | Duration |
| -------- | ------------ | -------- |
| A        | -            | 2        |
| B        | A            | 4        |
| C        | B            | 3        |
| D        | B            | 2        |
| E        | C D          | 10       |
| F        | B            | 4        |

## ![fig6](https://raw.githubusercontent.com/cppcoders/cpm-python/master/images/fig6.png)

| Activity | Predecessors | Duration |
| -------- | ------------ | -------- |
| A        | -            | 16       |
| B        | -            | 20       |
| C        | -            | 30       |
| D        | B            | 15       |
| E        | B            | 10       |
| F        | D            | 3        |
| G        | D            | 16       |
| H        | A            | 15       |
| I        | E F          | 12       |

## ![fig6](https://raw.githubusercontent.com/cppcoders/cpm-python/master/images/fig7.png)

| Activity | Predecessors | Duration |
| -------- | ------------ | -------- |
| A        | -            | 8        |
| B        | -            | 2        |
| C        | A            | 5        |
| D        | B            | 4        |
| E        | C D          | 6        |
| F        | E            | 7        |
| G        | D            | 7        |
| H        | G            | 5        |
| I        | E            | 6        |

## ![fig6](https://raw.githubusercontent.com/cppcoders/cpm-python/master/images/fig8.png)

# Calculating Duration From Optimistic, Most probable and Pessimistic Time

| Activity | Predecessors | Optimistic Time | Most probable Time | Pessimistic Time |
| -------- | ------------ | --------------- | ------------------ | ---------------- |
| A        | -            | 6               | 9                  | 12               |
| B        | A            | 3               | 4                  | 11               |
| C        | A            | 2               | 5                  | 14               |
| D        | B C          | 4               | 6                  | 8                |
| E        | C            | 1               | 1.5                | 5                |
| F        | E            | 5               | 6                  | 7                |
| G        | D            | 7               | 8                  | 15               |
| H        | B            | 1               | 2                  | 3                |

## ![fig6](https://raw.githubusercontent.com/cppcoders/cpm-python/master/images/fig9.png)

| Variance | 7.22222222 |
| Standard Deviation | 2.68741925 |
| Propability on 26 day | 4.9% |

Used Tools:

- Python -obviously-
- Pandas: to import the data from csv files and store it in adjacency list for the graph
- Networkx: to make the graph, nodes, edges, colors, arrows and everything
- Graphviz: to calculate the positions for the graph nodes by "dot" engine
- Matplotlib: to draw all these stuff

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