## Stock Levels & EOQ

### Economic Order Quantity (EOQ)

Meaning: The order size at which total of ordering cost and carrying cost is minimised.

#### Two Costs That Trade Off

Cost	Behaviour	What Drives It
Ordering Cost	Falls as order size rises (fewer orders needed)	Cost of placing order, inspection, receiving
Carrying Cost	Rises as order size rises (more stock held on average)	Capital tied up, storage, insurance

#### Formula

$$EOQ = \sqrt{\frac{2AO}{C}}$$

Where:

#### Assumptions

1. Ordering cost per order and carrying cost per unit per annum are constant.

2. Annual usage is known.

3. Cost per unit of material is constant and known.

4. Lead time is zero (ordered quantity received immediately).

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### Stock Level Formulas

Level	Meaning	Formula
Reorder Level (ROL)	Level at which fresh order should be placed	Max Usage × Max Lead Time (or) Min Level + (Avg Usage × Avg Lead Time)
Minimum Level	Stock must not fall below this	ROL − (Normal Usage × Normal Lead Time)
Maximum Level	Stock must not exceed this	ROL + ROQ − (Min Usage × Min Lead Time)
Average Stock Level	Average stock held	Min Level + ROQ/2 (or) (Max Level + Min Level) / 2
Danger Level	Normal issues stopped; only emergency issues made	Normal Usage × Max Lead Time for emergency purchases
Buffer Stock	Safety stock for sudden large orders	Separately determined

#### Memory Hook for Formula Logic

Reorder Level: Worst-case demand before new stock arrives → Max Usage × Max Lead Time.
Minimum Level: Buffer you still have when new stock just arrives.
Maximum Level: Most stock after a new order lands at the best possible time.
Danger Level: Uses emergency lead time (shorter than normal lead time).

Worked example

### Example 1

EOQ Example:

Annual usage (A) = 10,000 units; Ordering cost (O) = ₹50 per order; Carrying cost (C) = ₹2 per unit per annum.

EOQ = √(2 × 10,000 × 50 / 2) = √(5,00,000) = 707 units (approx.)

Number of orders per year = 10,000 / 707 ≈ 14 orders.

### Example 2

Stock Level Example:

Max usage = 500 units/week; Min usage = 200 units/week; Normal usage = 350 units/week;

Max lead time = 4 weeks; Min lead time = 2 weeks; Normal lead time = 3 weeks; ROQ = 1,500 units.

ROL = Max Usage × Max Lead Time = 500 × 4 = 2,000 units
Min Level = ROL − (Normal Usage × Normal Lead Time) = 2,000 − (350 × 3) = 2,000 − 1,050 = 950 units
Max Level = ROL + ROQ − (Min Usage × Min Lead Time) = 2,000 + 1,500 − (200 × 2) = 3,500 − 400 = 3,100 units
Avg Stock Level = Min Level + ROQ/2 = 950 + 750 = 1,700 units

⚠️ Common exam mistakes

Using the wrong lead time in the Reorder Level formula — always use MAXIMUM usage and MAXIMUM lead time for ROL (worst case).
Using the wrong lead time in the Minimum Level formula — use NORMAL usage and NORMAL lead time.
Forgetting EOQ assumptions: if the question says 'lead time is not zero', EOQ formula still applies but assumptions are violated (note it).
Confusing Danger Level with Minimum Level: Danger Level uses Emergency lead time (shorter); Minimum Level uses Normal lead time.
Not squaring the result under the square root — a very common arithmetic error in EOQ calculations.

Reference:

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Stock Levels and Economic Order Quantity (EOQ)

Worked example