Network analysis psm university exam
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Here is a complete theory write-up for Network Analysis (PSM - Project & Systems Management / Production & Systems Management) for university exams.
Network Analysis - Complete Theory Notes
1. Introduction to Network Analysis
Network analysis is a project management technique used to plan, schedule, and control complex projects. It helps in:
- Determining the minimum time to complete a project
- Identifying activities that are critical (cannot be delayed)
- Allocating resources efficiently
- Monitoring progress
The two main techniques are CPM (Critical Path Method) and PERT (Programme Evaluation and Review Technique).
2. Basic Terminology
| Term | Definition |
|---|---|
| Activity | A task or job that consumes time and resources. Represented by an arrow (→). |
| Event / Node | A point in time marking the start or end of an activity. Represented by a circle. |
| Network / Arrow Diagram | A graphical representation of all activities and their inter-relationships. |
| Predecessor Activity | An activity that must be completed before another can begin. |
| Successor Activity | An activity that follows another. |
| Dummy Activity | A fictitious activity with zero time and zero resources, used to show logical dependency. Shown as a dashed arrow. |
| Path | A sequence of connected activities from the start node to the end node. |
| Critical Path | The longest path through the network. It determines the minimum project duration. |
| Critical Activity | An activity on the critical path. Any delay in it delays the entire project. |
3. Rules for Drawing a Network
- Each activity is represented by a single arrow.
- Each activity must have a unique pair of head and tail events (i-j rule).
- No two activities should have the same head and tail events - use dummy activities if needed.
- The network must flow from left to right (no loops).
- There should be only one start node and one end node.
- Dummy activities are used to:
- Maintain logical sequence
- Avoid duplication of activity numbers
4. CPM - Critical Path Method
Origin
Developed by DuPont and Remington Rand in 1957 for industrial projects.
Nature
- Deterministic - activity times are known with certainty (single time estimate).
- Best suited for repetitive, well-understood projects (construction, maintenance).
Steps in CPM:
- List all activities.
- Determine sequence/precedence relationships.
- Draw the network diagram.
- Assign time durations to each activity.
- Calculate Earliest Event Time (E) and Latest Event Time (L) for each node.
- Calculate floats for each activity.
- Identify the critical path (where Total Float = 0).
5. Forward Pass and Backward Pass
Forward Pass (Earliest Times)
- Move left to right through the network.
- E(j) = max [ E(i) + duration of activity i→j ]
- E for start node = 0.
Backward Pass (Latest Times)
- Move right to left through the network.
- L(i) = min [ L(j) - duration of activity i→j ]
- L for end node = E for end node (no slack at end).
6. Types of Float / Slack
Float measures the flexibility or leeway available for an activity.
(a) Total Float (TF)
TF = L(j) - E(i) - Duration (t)
- Maximum time an activity can be delayed without delaying the project completion.
- Critical activities have TF = 0.
(b) Free Float (FF)
FF = E(j) - E(i) - Duration (t)
- Time an activity can be delayed without delaying the Earliest Start of its successor.
(c) Independent Float (IF)
IF = E(j) - L(i) - Duration (t)
- Time an activity can be delayed without affecting any other activity (predecessor or successor).
- IF can never be negative; if negative, treat as 0.
(d) Interfering Float
Interfering Float = Total Float - Free Float
- The portion of float that, if used, will affect successor activities.
7. PERT - Programme Evaluation and Review Technique
Origin
Developed by the US Navy in 1958 for the Polaris Missile Program.
Nature
- Probabilistic - three time estimates are used.
- Best suited for new, R&D, or uncertain projects.
Three Time Estimates in PERT:
| Estimate | Symbol | Meaning |
|---|---|---|
| Optimistic Time | a (or t₀) | Minimum possible time if everything goes perfectly |
| Most Likely Time | m (or tₘ) | Time under normal conditions |
| Pessimistic Time | b (or tₚ) | Maximum time if everything goes wrong |
Expected Time (tₑ):
$$t_e = \frac{a + 4m + b}{6}$$
Variance (σ²):
$$\sigma^2 = \left(\frac{b - a}{6}\right)^2$$
Standard Deviation (σ):
$$\sigma = \frac{b - a}{6}$$
8. Probability in PERT
The project duration follows a normal distribution.
- Project Variance = Sum of variances of all critical activities
- Project Standard Deviation = √(Project Variance)
Z-score formula:
$$Z = \frac{T_s - T_e}{\sigma}$$
Where:
- Tₛ = Scheduled (target) completion time
- Tₑ = Expected project completion time
- σ = Standard deviation of critical path
Use the normal distribution table to find the probability of completing the project by Tₛ.
9. Difference Between CPM and PERT
| Basis | CPM | PERT |
|---|---|---|
| Developed by | DuPont (1957) | US Navy (1958) |
| Nature | Deterministic | Probabilistic |
| Time estimates | Single estimate | Three estimates (a, m, b) |
| Best for | Repetitive, known projects | New, uncertain, R&D projects |
| Focus | Time-cost trade-off | Time uncertainty |
| Activity orientation | Activity-on-Arrow | Activity-on-Arrow |
| Cost data | Considered | Not considered |
| Crashing | Possible | Not usually applied |
10. Crashing (Time-Cost Trade-off)
Crashing means reducing the project duration by adding extra resources (money, labor) to critical activities.
Key Concepts:
| Term | Meaning |
|---|---|
| Normal Time (Tₙ) | Time taken under normal conditions |
| Normal Cost (Cₙ) | Cost at normal time |
| Crash Time (Tᶜ) | Minimum possible time after crashing |
| Crash Cost (Cᶜ) | Cost at crash time |
Cost Slope:
$$\text{Cost Slope} = \frac{C_c - C_n}{T_n - T_c}$$
- Cost slope = extra cost per unit time saved.
- Crash activities with the lowest cost slope first (most economical to crash).
Steps in Crashing:
- Draw the network and find the critical path.
- Calculate cost slope for all activities.
- Crash the critical activity with the lowest cost slope by 1 unit.
- Check if a new critical path has emerged.
- If multiple critical paths exist, crash activities on all paths simultaneously.
- Continue until desired duration or minimum duration is reached.
11. Resource Leveling vs Resource Allocation
| Basis | Resource Leveling | Resource Allocation |
|---|---|---|
| Aim | Smooth out resource usage over time | Assign limited resources to activities |
| Project duration | May be extended | Fixed or extended |
| Constraint | Resource availability fluctuates | Resource limit is fixed |
| Method | Shift non-critical activities | Prioritize critical activities |
12. Advantages of Network Analysis
- Provides a clear visual picture of the entire project.
- Helps identify the critical path and critical activities.
- Enables better time and cost planning.
- Useful for monitoring and controlling project progress.
- Helps in resource allocation and scheduling.
- Identifies float/slack to allow flexible scheduling.
- Facilitates communication among project stakeholders.
13. Limitations of Network Analysis
- Drawing and updating large networks is time-consuming.
- Time estimates (especially in PERT) may be subjective.
- Does not automatically account for resource constraints.
- Changes in project scope require complete rework of the network.
- Requires skilled personnel to apply correctly.
14. Applications of Network Analysis
- Construction projects (buildings, roads, bridges)
- Defense and aerospace projects (missiles, satellites)
- Research and development projects
- Software development (system launches)
- Maintenance shutdowns in plants
- Event management and product launches
Quick Exam Tips
- CPM = deterministic, cost-focused, repetitive projects
- PERT = probabilistic, time-uncertain, new projects
- Critical path = longest path = zero total float
- Dummy activity = dashed arrow, zero time, zero cost
- tₑ = (a + 4m + b) / 6 - always memorize this
- Cost slope = (Crash cost - Normal cost) / (Normal time - Crash time)
- For probability questions, always compute Z and use the normal table
- Float hierarchy: Total Float ≥ Free Float ≥ Independent Float
This covers all major theory topics asked in university PSM/Operations Research exams. Let me know if you want solved numerical examples for CPM, PERT, or Crashing!
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