Simulation of PERT networks

Simulation of PERT Networks

PERT (Program Evaluation and Review Technique)

PERT is a network-based project management technique used to:

• Plan
• Schedule
• Control
• Analyze uncertain project activities

PERT is especially useful when activity durations are uncertain.

Applications of PERT

• Software development projects
• Construction projects
• Research and development
• Defense and aerospace projects

Simulation of PERT Networks

Simulation of PERT networks involves repeatedly simulating project activity durations to:

• Estimate project completion time
• Identify risk in schedule
• Analyze variability

Basic PERT Network Diagram

Start → A → B → D → End
          ↓
          C

Why Simulation is Needed in PERT

• Activity times are uncertain
• Deterministic CPM is insufficient
• Real projects involve risk

Critical Path Computation

Critical Path

The critical path is the longest path in the network and determines the minimum project completion time.

Steps to Compute Critical Path

• Draw PERT network
• Calculate expected time for each activity
• Perform forward pass (earliest times)
• Perform backward pass (latest times)
• Identify zero-slack activities

Forward Pass Formula

$$ES=\max (EF\text{ of predecessor})$$$$EF=ES+t$$

Backward Pass Formula

$$LF=\min (LS\text{ of successor})$$$$LS=LF-t$$

Slack (Float)

$$Slack=LS-ES$$

Critical Path Diagram

A* → B* → D*

(* = Critical activity)

Uncertainties in Activity Duration

PERT considers three time estimates:

Time Type	Symbol	Meaning
Optimistic	a	Best case
Most likely	m	Normal case
Pessimistic	b	Worst case

Expected Time Formula

$$t=\frac{a+4m+b}{\mathrm{6}}$$

Variance

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

Why Uncertainty Matters

• Delays increase cost
• Risk of missing deadlines
• Helps in contingency planning

Resource Allocation and Consideration

Resource allocation refers to assigning limited resources such as:

• Manpower
• Machines
• Money
• Materials

Problems in Resource Allocation

• Resource conflicts
• Over-allocation
• Under-utilization

Resource Leveling

A technique to smooth resource usage without changing project duration.

Resource Allocation Table

Activity	Time	Workers
A	3 days	2
B	4 days	3
C	2 days	1

Role of Simulation

• Tests different resource scenarios
• Minimizes idle time
• Improves utilization

Simulation Languages

Simulation languages are specialized programming languages used to build and analyze simulation models.

Types of Simulation Languages

Type	Example
General purpose	C, Python
Special purpose	GPSS, SIMULA
Hybrid	Arena, AnyLogic

Features

• Event scheduling
• Random number generation
• Statistical reporting
• Modeling flexibility

Object-Oriented Simulation

Object-Oriented Simulation (OOS) models a system using objects, classes, and inheritance.

Key Concepts

Concept	Description
Object	Real-world entity
Class	Blueprint of object
Inheritance	Reuse of code
Polymorphism	Multiple behaviors

Object-Oriented Simulation Diagram

Class: Activity
 ├─ Duration
 ├─ Resources
 └─ Execute()

Advantages

• Modularity
• Reusability
• Easy maintenance
• Realistic modeling

Examples of OOS Tools

• SIMULA
• AnyLogic
• Java-based simulators

Comparison Table

Traditional vs Object-Oriented Simulation

Basis	Traditional	Object-Oriented
Structure	Procedural	Object-based
Flexibility	Low	High
Reusability	Low	High
Maintenance	Difficult	Easy

Summary Table

Topic	Key Point
PERT simulation	Handles uncertainty
Critical path	Longest path
Activity uncertainty	Three-time estimates
Resource allocation	Limited resources
Simulation languages	Modeling tools
Object-oriented simulation	Modular design

Exam Writing Tips 

• Start with definition
• Draw PERT network
• Write formulas clearly
• Use tables
• Mention real-life examples