Unit 2: Inventory control models
Inventory Management notes · PTU syllabus (MBA 956-26)
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Unit summary
Inventory control models answer two questions — how much to order and when. This unit covers the order point and reorder level, maximum and minimum levels, safety stock, deterministic EOQ models under various conditions, lead time analysis, and probabilistic models — the continuous review Q-system and the periodic review P-system.
After this unit you can
- Compute reorder, maximum, minimum and danger levels
- Determine safety stock
- Apply EOQ models under various conditions
- Apply Q-system and P-system models
PTU syllabus topics
- Order point
- re-order level
- maximum/minimum level
- safety stocks
- deterministic EOQ models under various conditions
- lead time analysis
- probabilistic models — continuous review (Q-System) and periodic review (P-System)
Reorder level
Maximum usage × maximum lead time
Minimum level
Reorder level − (normal usage × normal lead time)
Maximum level
Reorder level + reorder quantity − (minimum usage × minimum lead time)
Safety stock
Z × σ demand during lead time
Topic 1
Stock levels
Reorder level
Maximum usage × maximum lead time
Minimum level
Reorder level − (normal usage × normal lead time)
Maximum level
Reorder level + reorder quantity − (minimum usage × minimum lead time)
Average stock
(Minimum level + maximum level) ÷ 2
Danger level
Average usage × emergency lead time
Example
Usage 100–300 units a week (normal 200), lead time 4–8 weeks (normal 6), reorder quantity 2,000. Reorder level = 300 × 8 = 2,400; minimum = 2,400 − 1,200 = 1,200; maximum = 2,400 + 2,000 − 400 = 4,000.
Topic 2
Safety stock
- Safety stock: buffer against variation in demand and lead time.
Simple
(Maximum lead time − normal lead time) × average usage
Statistical (demand variation)
z × σ(daily demand) × √(lead time)
Reorder point
Average demand during lead time + safety stock
Example
Average daily demand 50, standard deviation 10, lead time 9 days, service level 95% (z = 1.65): safety stock = 1.65 × 10 × 3 = 49.5 ≈ 50 units; reorder point = 450 + 50 = 500.
Topic 3
The basic EOQ model
Economic Order Quantity
EOQ = √(2DS / H)
D annual demand, S ordering cost per order, H holding cost per unit per year
Reorder level
Lead time demand + safety stock
Number of orders
D / EOQ
Example
D = 10,000 units, S = ₹50, H = ₹4. EOQ = √(2 × 10,000 × 50 / 4) = √2,50,000 = 500 units, so 20 orders a year.
A items
About 10%
About 70% — tight control
B items
About 20%
About 20% — moderate control
C items
About 70%
About 10% — simple control
- Other selective controls: VED (vital, essential, desirable — spares), FSN (fast, slow, non-moving), HML (high, medium, low unit price).
Topic 4
EOQ models under various conditions
Basic EOQ
Instantaneous receipt, no shortages
Production order quantity (EPQ)
Gradual receipt — Q = √(2DS ÷ H(1 − d ÷ p))
Quantity discount model
Compare total cost at EOQ and at discount break points
EOQ with planned shortages
Backorders allowed at a shortage cost
Total annual cost
Purchase cost (D × price) + ordering cost (D ÷ Q × S) + holding cost (Q ÷ 2 × H)
Example
D = 4,000 units, S = ₹100, H = 20% of price. At ₹50 (no discount) EOQ = √(2 × 4,000 × 100 ÷ 10) ≈ 283; total cost ≈ ₹2,02,828. A 2% discount for 1,000+ units (₹49): total = 1,96,000 + 400 + 4,900 = ₹2,01,300 — take the discount.
Topic 5
Lead time analysis
- Analyse the distribution of past lead times (mean, variability) for each supplier.
- Combined uncertainty: σ during lead time = √(L × σd² + d² × σL²) when both demand and lead time vary.
- Use the analysis to set safety stock, choose suppliers and negotiate delivery terms.
Topic 6
Probabilistic models: Q-system and P-system
Order quantity
Fixed (EOQ)
Variable — up to a target level
Timing
When stock falls to reorder point
At fixed intervals
Safety stock
Covers lead time
Covers review period plus lead time — higher
Monitoring
Continuous records
Periodic counts
Suits
Expensive, critical items (A class)
Many low-value items from one supplier
Target level
Demand over (review period + lead time) + safety stock
Order quantity
Target level − inventory position
Key terms
- Reorder level
- Stock level at which a new order is placed
- Danger level
- Level requiring emergency purchase
- Safety stock
- Buffer against demand and lead time uncertainty
- EPQ
- Economic production quantity with gradual receipt
- Inventory position
- On-hand plus on-order minus backorders
Quick revision
- Reorder, minimum, maximum, average, danger levels.
- Safety stock: simple and statistical; reorder point.
- Basic EOQ; EPQ; quantity discounts; shortages.
- Lead time analysis; combined uncertainty.
- Q-system (fixed quantity) vs P-system (fixed interval).
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.State the formula for reorder level.
- Q2.What is the danger level?
- Q3.How is statistical safety stock calculated?
- Q4.State the EOQ formula.
- Q5.When should a quantity discount be accepted?
- Q6.Distinguish Q-system and P-system.
Long-answer questions
- Q1.Compute stock levels from given data (numerical).
- Q2.Explain the determination of safety stock.
- Q3.Explain EOQ models including quantity discounts (numerical).
- Q4.Explain probabilistic inventory models — Q-system and P-system.
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