Worked Solution
✓ VerifiedStep 1 – Determine Annual Requirement of Raw Material D
Production required for the year = Sales – Opening stock of finished goods = 20,000 – 1,800 = 18,200 units of X.
Annual consumption of D = 18,200 × 4 kg = 72,800 kg.
Step 2 – Daily Consumption Rates
Assuming 364 working days (52 weeks): Average daily consumption = 72,800 ÷ 364 = 200 kg/day. Maximum daily consumption = 200 + 40 = 240 kg/day. Minimum daily consumption (assumed symmetric) = 200 – 40 = 160 kg/day. Lead time: Minimum = 4 days, Maximum = 8 days, Average = 6 days.
Step 3 – Carrying Cost per kg per year = 14% × ₹250 = ₹35 per kg per year.
Step 4 – Economic Order Quantity (EOQ)
EOQ = √(2 × Annual Demand × Ordering Cost ÷ Carrying Cost per unit)
= √(2 × 72,800 × 1,340 ÷ 35) = √5,574,400 ≈ 2,361 kg.
(a) Re-order Quantity (ROQ)
ROQ = EOQ – 400 = 2,361 – 400 = 1,961 kg.
Re-order Level (required for parts b and c) = Maximum consumption × Maximum lead time = 240 × 8 = 1,920 kg.
(b) Maximum Stock Level
Maximum Stock Level = Re-order Level + Re-order Quantity – (Minimum consumption × Minimum lead time)
= 1,920 + 1,961 – (160 × 4) = 1,920 + 1,961 – 640 = 3,241 kg.
(c) Minimum Stock Level
Minimum Stock Level = Re-order Level – (Average consumption × Average lead time)
= 1,920 – (200 × 6) = 1,920 – 1,200 = 720 kg.
(d) Impact on Profitability by Not Ordering EOQ
Ordering ROQ (1,961 kg) instead of EOQ (2,361 kg) results in a higher total inventory cost. The difference represents the reduction in profitability of approximately ₹1,428 per annum. The company incurs excess ordering costs (more frequent orders due to smaller lot size) that outweigh the savings in carrying costs — net adverse impact ≈ ₹1,428.
Write it like this
1The skeleton
- Nail the annual requirement first — subtract opening finished goods stock (1,800 units) from sales (20,000) to get production, THEN multiply by 4 kg; examiners give a dedicated step mark here and skipping it loses you the foundation.
- Derive all consumption rates in one block — state average, maximum, and minimum daily consumption together with lead time min/max/average before touching any formula; examiners reward systematic data organisation and it prevents carry-forward errors.
- Write the EOQ formula symbolically before plugging numbers — √(2 × A × O / C) on its own line, THEN substitute; this earns method marks even if your arithmetic slips.
- Always state ROL before Max/Min Stock — Re-order Level = Max consumption × Max lead time is the anchor formula; Max and Min Stock formulas both reference ROL, so present it as a named interim result, not buried inside a bigger calc.
- For part (d), build a cost comparison table — compute Total Cost at EOQ and Total Cost at ROQ side by side (ordering cost + carrying cost each), then state the difference as 'reduction in profitability of ₹___'; a narrative-only answer without numbers gets zero here.
- Label every answer with units (kg) — examiner checklists tick unit alongside value; writing just '720' instead of '720 kg' is a silent half-mark leak across all four parts.
2Examiner-rewarded phrases
3Common trap
Heads up — almost everyone uses 20,000 units directly as the production figure and skips deducting the 1,800-unit opening stock of finished goods, which inflates annual raw material requirement to 80,000 kg instead of 72,800 kg; every subsequent answer (EOQ, ROQ, stock levels) then carries that error and you bleed marks across all four parts from one missed line.