Artificial Intelligence Techniques (ME-703 (B)) - Unit 5 Short Notes

V. Project Management

PERT vs CPM: Similarities and Differences

Both are network-based project management tools for planning, scheduling, and controlling projects.

[!TIP]

• CPM is activity-oriented (precise times).

• PERT is event-oriented (probabilistic times).

• Both use network diagrams and identify the critical path.

Network Diagrams: AOA vs AON

Activity-on-Arrow (AOA)

• Activities represented by arrows, events (milestones) by nodes (circles).

• Dummy activities (dashed arrows) used to show dependencies without time/cost.

• Less common due to complexity with multiple relationships.

Activity-on-Node (AON)

• Activities represented by nodes (boxes), arrows show dependencies.

• More intuitive; widely used in software (e.g., MS Project).

• Logical relationships directly on arrows:

  • FS (Finish-to-Start): Most common. B starts after A finishes.

  • SS (Start-to-Start): B starts when A starts.

  • FF (Finish-to-Finish): B finishes when A finishes.

  • SF (Start-to-Finish): Rare. B finishes when A starts.

[!TIP]

• Dummy activity (zero duration) resolves ambiguity in AOA when two activities share same start/end nodes.

• AON preferred for complex projects; easier to update.

Critical Path Method (CPM)

Key Steps:

1. Forward Pass (compute earliest times):

   • $$\displaystyle ES_i $$ = Earliest Start of activity $i$.

   • $$\displaystyle EF_i = ES_i + \text{duration}_i $$.

   • For successor $j$: $$\displaystyle ES_j = \max(EF_i) $$ over all predecessors $i$.

2. Backward Pass (compute latest times):

   • $$\displaystyle LF_i $$ = Latest Finish of activity $i$.

   • $$\displaystyle LS_i = LF_i - \text{duration}_i $$.

   • For predecessor $i$: $$\displaystyle LF_i = \min(LS_j) $$ over all successors $j$.

3. Float/Slack Calculation:

   • Total Float: $$\displaystyle TF_i = LS_i - ES_i = LF_i - EF_i $$.

   • Free Float: $$\displaystyle FF_i = \min(ES_j) - EF_i $$ (slack without delaying successors).

   • Independent Float: $$\displaystyle IF_i = FF_i - \text{total slack of predecessor} $$.

4. Critical Path: Path with zero total float (longest path, determines project duration).

[!CAUTION]

• Degeneracy: Multiple critical paths possible if several paths have same length.

• Dummy activities have zero duration and zero float.

Program Evaluation and Review Technique (PERT)

Three Time Estimates per Activity:

• Optimistic ($a$): Minimum time if everything goes perfectly.

• Most Likely ($m$): Realistic estimate under normal conditions.

• Pessimistic ($b$): Maximum time if significant delays occur.

Expected Time and Variance:

• Expected duration:

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

• Variance of activity duration:

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

Project Length and Probability:

• Expected project length ($$\displaystyle T_E $$): Sum of $$\displaystyle t_e $$ along the critical path.

• Project variance ($V$): Sum of variances along the critical path (assuming independence):

$$V = \sum_{i \in \text{critical path}} \sigma_i^2$$

• Probability of completion by due date $D$:

  Compute standard normal variable:

$$Z = \frac{D - T_E}{\sqrt{V}}$$

Use standard normal table to find $P(Z \leq z)$.

[!EXAMPLE]

If $$\displaystyle T_E = 60 $$ weeks, $$\displaystyle V = 9 $$ (std dev = 3), for $$\displaystyle D = 66 $$ weeks:

$$\displaystyle Z = \frac{66-60}{3} = 2 $$ → $P \approx 0.9772$ (97.72% chance).

Project Management Phases (PMBOK Guide)

1. Initiation: Define project, feasibility, stakeholder identification.

2. Planning: Scope, schedule (WBS, network), cost, quality, resources, risk.

3. Execution: Coordinate resources, implement plan, manage teams.

4. Monitoring & Controlling: Track performance (EV, PV, AC), control changes, manage risks.

5. Closing: Formal acceptance, handover, documentation, lessons learned.

[!TIP]

• Critical path is central to Planning and Monitoring & Controlling.

• PERT used in Planning for uncertain durations; CPM for Monitoring with deterministic times.

Heuristic and Metaheuristic Algorithms

Heuristics: Problem-specific rules of thumb for quick, good (not optimal) solutions.
Examples: Nearest neighbor (TSP), dispatching rules (Johnson’s for 2-machine flow shop).

Metaheuristics: High-level frameworks exploring large search spaces; less problem-dependent.
Examples:

• Genetic Algorithms (GA): Evolution-inspired (selection, crossover, mutation).

  Application: Resource-constrained scheduling.

• Simulated Annealing (SA): Mimics annealing process; accepts worse moves to escape local optima.

  Application: Facility layout, project crashing.

Key Properties:

• Intensification vs Diversification balance.

• Stochastic nature; multiple runs may yield different results.

[!CAUTION]

• No guarantee of optimality; used for NP-hard problems (e.g., project scheduling with resource constraints).

• Parameter tuning (e.g., cooling rate in SA) crucial for performance.

Common Pitfalls & Exam Tips

• Simplex vs Transportation: Simplex handles general LPs; transportation exploits grid structure for faster solutions.

• Degeneracy in LP/Transportation: Occurs when basic variable = 0; may cause cycling. Use Bland’s rule or lexicographic method to resolve.

• PERT Probability: Always use critical path’s variance; non-critical paths irrelevant.

• Network Diagrams: In AOA, dummy activities only for logic, not time. In AON, FS is default if no lag specified.

• Float Interpretation:

  • Total float = allowable delay without delaying project.

  • Free float = delay without delaying early start of successor.

  • Critical activities have zero total float.

[!TIP]

For probability questions: Convert to standard normal, use $Z$-table, and remember $$\displaystyle Z = \frac{\text{Target} - \text{Mean}}{\text{Std Dev}} $$.

For network diagrams: Draw clearly, label ES/EF/ LS/LF on nodes (AON) or arrows (AOA).