Project Management (PERT/CPM)

Planning, scheduling, and controlling projects to ensure they are completed on time and within budget.

Introduction

Project management involves managing complex projects with many interconnected tasks. Two common quantitative techniques used are:

  • PERT (Program Evaluation and Review Technique): Used when task times are uncertain (probabilistic).
  • CPM (Critical Path Method): Used when task times are known (deterministic).

PERT (Program Evaluation and Review Technique)

PERT uses three time estimates for each activity to calculate an expected time and variance.

Time Estimates

  • Optimistic time ($a$): Minimum time if everything goes perfectly.
  • Most likely time ($m$): The normal time required.
  • Pessimistic time ($b$): Maximum time if things go wrong.

Expected Time ($t_e$): $$ t_e = \frac{a + 4m + b}{6} $$

Variance ($v$): $$ v = \left(\frac{b - a}{6}\right)^2 $$

CPM (Critical Path Method)

CPM assumes activity times are known with certainty. It focuses on the trade-off between the cost of the project and its completion time.

The Critical Path

The Critical Path is the longest path through the project network. It determines the shortest possible time to complete the project.

Key Concept: Any delay in a task on the critical path will delay the entire project. Tasks not on the critical path have "slack" or "float" time.