Worked Solution
✓ VerifiedEconomic Batch Quantity (EBQ) Analysis for XYZ Ltd.
Given Data:
Annual demand (D) = 48,000 bearings; Holding cost (h) = ₹0.20 per bearing per month = ₹2.40 per bearing per year; Set-up cost per run (S) = ₹384.
(i) Optimum Run Size and Number of Runs
The Optimum Run Size (EBQ) is calculated using the Economic Batch Quantity formula:
EBQ = √(2DS/h) = √(2 × 48,000 × 384 / 2.40) = √15,360,000 = 3,920 bearings (approx.)
Number of Runs = Annual Demand / EBQ = 48,000 / 3,920 = 12.24 ≈ 12 runs per year
(ii) Interval Between Two Consecutive Runs
Interval = (EBQ / Annual Demand) × 365 days
= (3,920 / 48,000) × 365
= 29.8 days ≈ 30 days
Alternatively: 365 days / 12 runs = 30.42 ≈ 30 days between consecutive runs
(iii) Extra Cost if Run Size = 8,000 Bearings
Total Cost at Optimum Run Size (EBQ = 3,920):
Minimum Total Cost = √(2 × D × S × h) = √(2 × 48,000 × 384 × 2.40) = √88,473,600 = ₹9,406
Total Cost at Run Size of 8,000 bearings:
Set-up Cost = (48,000 / 8,000) × 384 = 6 × 384 = ₹2,304
Holding Cost = (8,000 / 2) × 2.40 = 4,000 × 2.40 = ₹9,600
Total Cost = 2,304 + 9,600 = ₹11,904
Extra Cost = ₹11,904 − ₹9,406 = ₹2,498 per annum
(iv) Opinion on Run Size
The company should adopt the optimum run size of 3,920 bearings per run (approximately 12 runs per year, with each run every 30 days). A policy of 8,000 bearings per run significantly inflates the holding cost due to excess inventory, resulting in an avoidable additional expenditure of ₹2,498 per year compared to the optimum. While larger runs reduce set-up costs, they increase carrying costs disproportionately. The EBQ balances both costs at their lowest combined level and is the recommended policy.
Write it like this
1The skeleton
- Convert holding cost to annual FIRST, in line 1 — write '₹0.20/month × 12 = ₹2.40 per bearing per year' as your very first step; examiners award a dedicated step mark here and missing it signals a sloppy read of the data.
- State the EBQ formula before plugging numbers — write 'EBQ = √(2DS/h)' explicitly, then substitute; examiners award a formula mark separately from the computation mark, so you lose free marks if you jump straight to the square root.
- Box or bold every final answer — 'EBQ = 3,920 bearings', 'Number of runs = 12', 'Interval = 30 days'; examiners scanning under time pressure tick the boxed figure, not a number buried mid-sentence.
- Show the two-cost split clearly in part (iii) — present Set-up Cost and Holding Cost on separate labelled lines before adding them; the marking scheme awards one mark each for the two components, so a single lump sum loses you both even if the total is right.
- Write the opinion in part (iv) as a two-line verdict, not an essay — state the recommended run size, name the extra cost (₹2,498), and give one reason (holding cost rises disproportionately); examiners reward a crisp conclusion, not a paragraph rehashing your calculations.
2Examiner-rewarded phrases
3Common trap
Most students forget to annualise the holding cost and plug ₹0.20 (monthly) straight into the EBQ formula — your EBQ comes out wildly wrong and every subsequent part collapses with it. Double-check the unit of h matches the unit of D before you touch the formula.