Store & Materials Mgmt Numericals: EOQ, Stock Levels & ABC-VED

UPSC DRDO SAO • UPSC Store Officer • SEBI Grade A • PFRDA Grade A

⚡ Quick Answer & AI Exam Snapshot (TL;DR)

While CrackTarget’s general Materials Management guide covers qualitative procurement concepts, UPSC DRDO SAO, UPSC Store Officer, and SEBI/PFRDA Paper-2 exams test quantitative inventory formulas: Ford W. Harris / R.H. Wilson’s Economic Order Quantity (EOQ = √[2AO / C], where Annual Ordering Cost equals Annual Carrying Cost), Stock Control Levels (Reorder Level, Minimum/Safety Stock, Maximum Level, Danger Level), selective inventory matrices (ABC, VED, FSN, SDE, HML), and the impact of FIFO vs LIFO on Closing Stock and Profit during periods of rising prices (inflation).

1. Economic Order Quantity (EOQ) & The 5 Stock Control Level Formulas

1. Wilson’s Economic Order Quantity (EOQ) Formula:
EOQ = √[ (2 × A × O) / C ]
• A = Annual Demand / Consumption in units
• O (or B) = Ordering / Buying Cost per order (₹)
• C (or H) = Carrying / Holding Cost per unit per annum (₹) = Unit Cost × Carrying Cost %
Golden Condition at EOQ: At the Economic Order Quantity point, Total Annual Ordering Cost = Total Annual Carrying Cost = (1/2) × EOQ × C, and Total Inventory Cost is MINIMUM!

2. Stock Control Level Formulas (Memorize All 5!):
• Re-Order Level (ROL) = Maximum Consumption × Maximum Re-order Period (Lead Time)
(Alternative with Safety Stock: ROL = Safety Stock + [Normal Consumption × Normal Lead Time])
• Minimum Stock Level (Buffer / Safety Stock) = ROL − (Normal/Average Consumption × Normal/Average Lead Time)
• Maximum Stock Level = ROL + Re-Order Quantity (EOQ) − (Minimum Consumption × Minimum Lead Time)
• Average Stock Level = (Minimum Level + Maximum Level) / 2 OR Minimum Level + (1/2 of Re-Order Quantity)
• Danger Level = Average (or Minimum) Consumption × Maximum Re-Order Period for Emergency Purchases

Solved UPSC Store Officer Numerical: Annual demand (A) = 16,000 units; Ordering cost per order (O) = ₹100; Cost per unit = ₹40; Carrying cost = 20% per annum.
C = 20% of ₹40 = ₹8 per unit per year.
EOQ = √[ (2 × 16,000 × 100) / 8 ] = √[ 32,00,000 / 8 ] = √4,00,000 = 632.45 (or 632 units).
If Ordering Cost had been ₹90 and Carrying Cost ₹8: EOQ = √[ (2 × 16,000 × 90) / 8 ] = √3,60,000 = 600 units; Number of orders per year = 16,000 / 600 = 26.67 orders.

2. Selective Inventory Control Techniques (ABC, VED, FSN, HML, SDE, SOS, GOLF)

UPSC matches each acronym with its exact basis of classification (this table is tested in DRDO SAO, Store Officer, EPFO, and SEBI Grade A):

Technique	Full Form	Basis of Classification (The Exam Keyword!)	Detailed Breakdown
1. ABC Analysis (Always Better Control / Pareto 80-20 Rule)	Category A, B, and C Items	Annual Consumption Value `(Annual Usage Units × Unit Cost)`	• Class A (Tightest Control by Top Mgmt): ~10% of items accounting for ~70% of total annual consumption value. • Class B (Moderate Control): ~20% of items accounting for ~20% of value. • Class C (Two-Bin / Loose Control): ~70% of items accounting for only ~10% of value!
2. VED Analysis	Vital, Essential, Desirable	Criticality of Item to Production / Spare Parts	Used primarily for Maintenance & Engineering Spare Parts (where even a ₹10 fuse whose absence halts a ₹100 Cr plant is Vital!).
3. HML Analysis	High, Medium, Low	Unit Price (Cost per Single Unit) of the item (regardless of annual usage volume!).	Distinguish carefully: ABC = Annual Consumption Value vs HML = Unit Price!
4. FSN Analysis	Fast-Moving, Slow-Moving, Non-Moving	Rate of Consumption / Frequency of Issue (Turnover / Obsolescence)	Identifies dead stock and obsolete stores for disposal under GFR Rule 217.
5. SDE Analysis	Scarce, Difficult, Easy	Availability in Market & Lead Time required for procurement.	Scarce: Imported/monopoly items with lead time > 6 months.
6. GOLF & SOS	Govt, Ordinary, Local, Foreign & Seasonal vs Off-Seasonal	Source of Supply (GOLF) & Seasonality of Agricultural Raw Material (SOS).	Used in PSU & agro-processing procurement.

3. Effect of FIFO vs LIFO vs Weighted Average During INFLATION (Rising Prices)

This is a classic conceptual trap in UPSC EPFO, DRDO SAO, and SEBI Grade A—examine what happens when raw material prices are continuously rising (Inflation):

Financial Metric During INFLATION (Rising Prices)	FIFO (First-In, First-Out)	LIFO (Last-In, First-Out)
1. Cost of Goods Sold (COGS / Issue to Production)	LOWEST (Old, cheaper lots are issued to production first).	HIGHEST (Latest, most expensive lots are issued to production first—matches current cost with current revenue).
2. Value of Closing Inventory (Balance Sheet)	HIGHEST (Closing stock consists of the latest, highest-priced purchases—reflects current market prices!).	LOWEST (Closing stock consists of the oldest, lowest-priced historical lots).
3. Reported Gross Profit & Income Tax Liability	HIGHEST Profit & HIGHEST Tax (Overstates profit via ‘Inventory Profit’ during inflation).	LOWEST Profit & LOWEST Tax (Prohibited under AS-2, Ind AS 2, and Indian Income Tax Act!).

Note: During Deflation (Falling Prices), all three relationships above reverse completely! Also remember: Inventory Turnover Ratio (ITR) = Cost of Goods Sold (COGS) / Average Inventory; and Inventory Holding Period (Days) = 365 / Inventory Turnover Ratio.

🎯 High-Yield Exam One-Liners (Last-Minute Revision Box)

The Economic Order Quantity (EOQ) formula was developed by Ford W. Harris (1913) and popularized by R.H. Wilson.
At the EOQ level, Total Annual Ordering Cost is EXACTLY EQUAL to Total Annual Carrying (Holding) Cost.
If Annual Demand increases 4 times, EOQ increases 2 times (since EOQ is proportional to √A).
Re-Order Level (ROL) = Maximum Consumption × Maximum Re-Order Period (Lead Time).
Minimum Stock Level (Safety Stock) = ROL − (Normal Consumption × Normal Lead Time).
Maximum Stock Level = ROL + Re-Order Quantity (EOQ) − (Minimum Consumption × Minimum Lead Time).
ABC Analysis classifies inventory on the basis of ‘Annual Consumption Value’ (Pareto’s 80/20 Law)—NOT unit price.
Class ‘A’ items represent ~10% of total item count but ~70% of total annual consumption value.
HML (High, Medium, Low) Analysis classifies inventory strictly on the basis of ‘Unit Price’ of an item.
VED (Vital, Essential, Desirable) Analysis classifies spare parts based on their ‘Criticality to Production’.
FSN (Fast, Slow, Non-moving) Analysis classifies inventory based on ‘Consumption Rate / Frequency of Issue’ to detect obsolete stock.
SDE (Scarce, Difficult, Easy) Analysis is based on ‘Lead Time and Availability of Supply’.
In a Two-Bin System (used for low-value Class ‘C’ items like nuts and bolts), when the first bin becomes empty, a new order is placed and the second bin serves as Reserve/Safety Stock during lead time.
During a period of Inflation (rising prices), FIFO results in the HIGHEST Closing Stock value, LOWEST Cost of Goods Sold, and HIGHEST reported Net Profit.
During Inflation, LIFO results in the LOWEST Closing Stock value, HIGHEST Cost of Goods Sold, and LOWEST reported Net Profit.
AS-2 and Ind AS 2 permit FIFO and Weighted Average Cost for inventory valuation, and explicitly prohibit LIFO.
Perpetual Inventory System maintains a continuous real-time record of stock balances after every receipt and issue (Bin Card + Stores Ledger).
A ‘Bin Card’ is maintained by the Storekeeper and records ONLY quantities (no monetary values); a ‘Stores Ledger’ is maintained by the Cost Accounting department and records BOTH quantities and monetary values.

📝 UPSC & Regulatory Level Practice MCQs (With Detailed Solutions)

Q1. A defence laboratory uses 10,000 units of an electronic component annually. The cost of placing one order is ₹80, the purchase price per unit is ₹50, and the annual inventory carrying cost is 16% of the unit price. What is the Economic Order Quantity (EOQ)?

A. 200 units
B. 400 units
C. 447 units
D. 500 units

Correct Answer: (C) — Here A = 10,000, O = ₹80, C = 16% of ₹50 = ₹8. EOQ = √[(2 × A × O) / C] = √[(2 × 10,000 × 80) / 8] = √[16,00,000 / 8] = √2,00,000 ≈ 447.2 units. (Note: If annual usage is 8,000 units, EOQ = √[(2 × 8,000 × 80) / 8] = √1,60,000 = 400 units).

Q2. For a manufacturing store item, Normal Usage is 100 units per day, Minimum Usage is 60 units per day, Maximum Usage is 130 units per day, Re-Order Quantity (EOQ) is 5,000 units, and Lead Time (Re-Order Period) is 25 to 30 days (Average 27.5 days). What are the ‘Re-Order Level’ (ROL) and ‘Minimum Stock Level’ respectively?

A. ROL = 3,900 units; Minimum Stock Level = 1,150 units
B. ROL = 3,000 units; Minimum Stock Level = 1,500 units
C. ROL = 3,900 units; Minimum Stock Level = 2,400 units
D. ROL = 3,250 units; Minimum Stock Level = 1,150 units

Correct Answer: (A) — Re-Order Level (ROL) = Maximum Usage × Maximum Lead Time = 130 × 30 = 3,900 units. Minimum Stock Level = ROL − (Normal Usage × Normal Lead Time) = 3,900 − (100 × 27.5) = 3,900 − 2,750 = 1,150 units.

Q3. During a period of continuous INFLATION (rising raw material prices), how does the use of the FIFO (First-In, First-Out) method compare with the LIFO (Last-In, First-Out) method?

A. FIFO gives lower Closing Stock value and lower Net Profit than LIFO
B. FIFO gives higher Closing Stock value, lower Cost of Goods Sold, and higher reported Profit than LIFO
C. FIFO gives higher Cost of Goods Sold and lower Income Tax liability than LIFO
D. Both FIFO and LIFO yield identical Closing Stock values during inflation

Correct Answer: (B) — During inflation, FIFO issues the oldest (cheapest) units to production first (giving lower COGS and higher profit) and leaves the latest (most expensive) units in Closing Stock (giving higher Closing Stock value).

Q4. Match List-I (Inventory Control Technique) with List-II (Basis of Classification):
List-I: (a) ABC Analysis, (b) HML Analysis, (c) VED Analysis, (d) FSN Analysis
List-II: (1) Unit Price of Item, (2) Annual Consumption Value, (3) Rate of Consumption / Movement, (4) Criticality of Spare Parts

A. a-2, b-1, c-4, d-3
B. a-1, b-2, c-4, d-3
C. a-2, b-4, c-1, d-3
D. a-3, b-1, c-2, d-4

Correct Answer: (A) — ABC Analysis is based on Annual Consumption Value (2); HML is based on Unit Price (1); VED is based on Criticality of Spare Parts (4); and FSN is based on Rate of Consumption/Movement (3).

Q5. What is the key difference between a ‘Bin Card’ and a ‘Stores Ledger’ in Materials Accounting?

A. A Bin Card records both quantities and values, whereas a Stores Ledger records only quantities
B. A Bin Card is kept inside the Store by the Storekeeper and records ONLY quantities, whereas a Stores Ledger is kept by the Cost Accounting department and records BOTH quantities and monetary values
C. A Bin Card is updated annually, whereas a Stores Ledger is updated decade-wise
D. There is no difference between the two documents

Correct Answer: (B) — A Bin Card is a quantitative record attached to the storage bin maintained by the Storekeeper (quantities only), while the Stores Ledger is an accounting record maintained by the Costing department showing both quantities and monetary rates/values.

❓ Frequently Asked Questions (Exam FAQs)

Q: What is the difference between ABC Analysis and HML Analysis?

ABC Analysis classifies items based on their Total Annual Consumption Value (Annual Usage Quantity × Unit Price), whereas HML (High, Medium, Low) Analysis classifies items solely based on their individual Unit Price regardless of how many units are consumed.

Q: Why does Annual Ordering Cost equal Annual Carrying Cost at the EOQ point?

Because Total Ordering Cost (A/Q × O) decreases hyperbolically with order size Q while Total Carrying Cost (Q/2 × C) increases linearly with Q. By calculus (setting the first derivative of Total Cost with respect to Q to zero), the minimum point occurs precisely where the two curves intersect: (A/Q)O = (Q/2)C, giving Q = √(2AO/C).

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