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Pert.py
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Pert.py
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import math
import pandas as pd
from graphviz import Digraph
def pert(tasks, dependencies):
task_data={}
#Calculate the expected time, variance and standard deviation of each task
for task, times in tasks.items():
O, P, M = times
expected_time = (O + M*4 + P)/6
variance = ((P-O)**2)/36
standard_deviation = math.sqrt(variance)
# Convert to float and round to two
float(expected_time)
float(variance)
float(standard_deviation)
expected_time = round(expected_time, 2)
variance = round(variance, 2)
standard_deviation = round(standard_deviation, 2)
# Add the task data to the currently empty dictionary
task_data[task] = {
"expected_time": float(expected_time),
"variance": float(variance),
"standard_deviation": float(standard_deviation),
"earliest_start": 0,
"latest_start": None,
"earliest_finish": float(expected_time),
"latest_finish": None,
"slack": 0
}
dependencies = {key: [dep] if isinstance(dep, str) else dep for key, dep in dependencies.items()}
#Calculate the earliest start and earliest finish of each task
for _ in range(len(task_data)):
for task in task_data:
if task in dependencies:
earliest_start = max([task_data[dep]["earliest_finish"] for dep in dependencies[task]], default=0)
task_data[task]["earliest_start"] = earliest_start
task_data[task]["earliest_finish"] = earliest_start + task_data[task]["expected_time"]
project_duration = max(task_data[task]["earliest_finish"] for task in task_data)
for task in task_data:
task_data[task]["latest_finish"] = project_duration
# Calculate the latest start, finish and slack of each task
for _ in range(len(task_data)):
for task in task_data:
if task not in dependencies or not dependencies[task]:
continue
for dep in dependencies[task]:
task_data[dep]["latest_finish"] = min(task_data[dep]["latest_finish"], task_data[task]["earliest_start"])
task_data[dep]["latest_start"] = task_data[dep]["latest_finish"] - task_data[dep]["expected_time"]
task_data[dep]["slack"] = task_data[dep]["latest_start"] - task_data[dep]["earliest_start"]
task_data[dep]["slack"] = round(task_data[dep]["slack"], 2)
return task_data
def create_pert_graph(task_data):
dot = Digraph()
for task, data in task_data.items():
dot.node(task, label=f"{task}\nExpected time: {data['expected_time']} (SD: {data['standard_deviation']})")
for task, deps in dependencies.items():
for dep in deps:
label = str(task_data[dep]['expected_time'])
dot.edge(dep, task, label=label)
return dot
#Define the tasks
tasks = {
"A": (2, 8, 5),
"B": (3, 10, 4),
"C": (5, 10, 6),
"D": (1, 10, 4),
"E": (2, 9, 5),
"F": (3, 8, 4),
"G": (4, 10, 6),
}
# Define the dependencies
dependencies = {
"A": [],
"B": [],
"C": "A",
"D": "B",
"E": ["C"],
"F": ["D"],
"G": ["E", "F"],
}
results = pert(tasks, dependencies)
pert_graph = create_pert_graph(results)
pert_graph.render("pert_graph.png")
#Print the results
results_df = pd.DataFrame.from_dict(results, orient='index')
print(results_df)
#save to csv file
results_df.to_csv('results.csv')