Unit 4: Network analysis & inventory control
Operation Research notes · PTU syllabus (BBA501-18)
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Unit summary
Projects and inventories both need careful planning. This unit covers network analysis with PERT and CPM — background, stages and time calculations — and inventory control with its classification, the EOQ model and ABC analysis.
After this unit you can
- Draw a project network and find earliest and latest times
- Identify the critical path and floats
- Compute PERT expected times and variances
- Explain inventory classification, EOQ and ABC analysis
PTU syllabus topics
- PERT/CPM background and development
- stages in application
- determination of earliest and latest allowable times
- classification of inventory control
- EOQ model
- ABC analysis
Time estimates
Three: optimistic, likely, pessimistic
One, deterministic
Focus
Time
Time and cost trade-off
Suits
Research, new projects
Construction, repetitive projects
Expected time
(a + 4m + b) / 6
Single estimate
Topic 1
PERT and CPM: background and stages
- CPM (Critical Path Method) was developed by DuPont (1957) for projects with known activity times.
- PERT (Programme Evaluation and Review Technique) was developed for the US Navy's Polaris missile project (1958) for projects with uncertain times.
- 1
Planning
List activities and dependencies
- 2
Draw the network
Nodes (events) and arrows (activities)
- 3
Estimate times
- 4
Compute earliest and latest times
- 5
Identify the critical path
- 6
Schedule, monitor and control
Topic 2
Earliest and latest times, critical path and float
- Forward pass: Earliest Start (ES) and Earliest Finish (EF = ES + duration); take the maximum EF at merging nodes.
- Backward pass: Latest Finish (LF) and Latest Start (LS = LF − duration); take the minimum LS at bursting nodes.
- Total float = LS − ES = LF − EF. Activities with zero float lie on the critical path — the longest path, which sets the project duration.
Time estimates
Three (optimistic, most likely, pessimistic)
One (deterministic)
Orientation
Event-oriented
Activity-oriented
Focus
Time
Time and cost (crashing)
Use
Research and new projects
Construction and repetitive projects
Expected time
te = (a + 4m + b) / 6
Variance
σ² = [(b − a) / 6]²
Project SD
√(sum of variances on the critical path)
Probability of completion
Z = (target − expected) / σ
Topic 3
Inventory control
Inventory classes: raw materials, work-in-progress, finished goods and spares. Inventory control balances ordering costs against carrying costs and avoids stock-outs.
EOQ
√(2DS / H)
Reorder level
Lead time × usage (+ safety stock)
Total cost
(D/Q)S + (Q/2)H
Example
D = 4,800 units, S = ₹100, H = ₹6. EOQ = √(2 × 4,800 × 100 / 6) = √1,60,000 = 400 units.
ABC analysis classifies items by annual consumption value: A (about 10% of items, 70% of value — tight control), B (20%, 20%), C (70%, 10% — simple control).
Key terms
- Critical path
- The longest path with zero float
- Float
- Time an activity can be delayed without delaying the project
- Expected time
- PERT weighted average time estimate
- EOQ
- Order size minimising total inventory cost
- ABC analysis
- Classification of inventory by value
Quick revision
- Forward pass → ES, EF; backward pass → LS, LF.
- Total float = LS − ES; critical activities have zero float.
- te = (a + 4m + b)/6; σ² = [(b − a)/6]².
- EOQ = √(2DS/H); ABC: 10-20-70 items, 70-20-10 value.
Important exam questions
Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).
Short-answer questions
- Q1.Differentiate between PERT and CPM.
- Q2.What is the critical path?
- Q3.Define total float.
- Q4.Write the PERT formula for expected time.
- Q5.What is ABC analysis?
Long-answer questions
- Q1.Draw a network, find the critical path and the floats of all activities.
- Q2.Solve a PERT problem and find the probability of completing the project by a target date.
- Q3.Explain inventory control with EOQ and ABC analysis.
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