Godown capacity, loading limit and the cost of holding buffer stock
Godown A of a Food Corporation depot has a sanctioned capacity of 8,000 metric tonnes (MT) and holds 6,500 MT of wheat at the start of July. Every month the depot receives 2,100 MT from the state agency and issues wheat to three Public Distribution System districts - X, Y and Z - in the ratio 5 : 3 : 2. The total issue for the quarter (three months) is fixed at 4,800 MT and is released evenly month by month. The manager has been told that stock must not cross the sanctioned capacity during the next six months, because the spill-over godown is under repair until then. Each truck carries 9 MT; the depot can load at most six trucks a day for six working days a week, and a month is treated as 26 working days. The depot also holds 2,000 MT of buffer stock valued at ₹2,400 per quintal, financed by working capital borrowed at 8.5% per annum simple interest.
1. Work out the monthly quota for districts X, Y and Z, and decide whether the loading arrangement can physically despatch that quantity each month. If it cannot, state the minimum loading needed.
Read the worked answer
Monthly quantity. Quarterly issue = 4,800 MT, so monthly issue = 4,800 ÷ 3 = 1,600 MT.
District split. Ratio 5 : 3 : 2, total parts = 10, one part = 1,600 ÷ 10 = 160 MT.
- X = 5 × 160 = 800 MT
- Y = 3 × 160 = 480 MT
- Z = 2 × 160 = 320 MT
Loading feasibility. Six trucks × 9 MT = 54 MT per day; over 26 working days = 54 × 26 = 1,404 MT per month. This is short of the 1,600 MT requirement by 196 MT (about 12%). So the schedule cannot be met with six trucks.
Minimum requirement. 1,600 ÷ 26 = 61.5 MT per day. Six trucks give 54 MT, seven trucks give 63 MT - so seven trucks a day is the minimum. The 196 MT gap must also be watched in the weighment register, because despatch shortfalls of this size are exactly what later show up as unexplained stock build-up.
2. By how much does stock grow each month, in which month does it cross the sanctioned capacity, and what is the least extra monthly despatch that keeps stock within capacity for the full six months? Check that figure against the loading limit.
Read the worked answer
Net monthly build-up. Receipts minus issues = 2,100 − 1,600 = 500 MT per month.
Headroom available. 8,000 − 6,500 = 1,500 MT. The stock reaches 7,000 (end of month 1), 7,500 (month 2) and exactly 8,000 (month 3). It does not exceed capacity until month 4, when it would stand at 8,500 MT. So the breach occurs in the fourth month, not the third - a distinction that matters if the manager is relying on the third month as a safe deadline.
Despatch needed for six safe months. Permitted net build-up = 1,500 ÷ 6 = 250 MT per month, so despatch must be at least 2,100 − 250 = 1,850 MT per month, i.e. 250 MT extra.
Loading check. 1,850 ÷ 26 = 71.2 MT per day, which needs 8 trucks of 9 MT (72 MT). This is higher than the 7 trucks the base plan required, so the transport contract must be revised before the plan can be claimed as feasible; alternatively, part of the 2,100 MT intake can be deferred to the next quarter.
3. The manager proposes to release 500 MT of buffer stock so that space is freed and interest is saved, since the spill-over godown would cost ₹15 lakh a quarter in rent. Evaluate the proposal.
Read the worked answer
Interest saved on 500 MT for one quarter. 500 MT = 5,000 quintals. Value = 5,000 × ₹2,400 = ₹1,20,00,000. Interest = 1,20,00,000 × 8.5% × 3/12 = ₹2,55,000.
(For context, the full 2,000 MT buffer costs 20,000 × ₹2,400 × 8.5% × 3/12 = ₹10,20,000 a quarter.)
Comparison. The rent is ₹15,00,000 against a saving of ₹2,55,000, so the proposal is not justified on cost alone - it would spend about ₹12.45 lakh to save ₹2.55 lakh.
Judgement beyond arithmetic. Buffer stock is held to maintain prescribed buffer norms and cannot be dipped merely to create space; any release needs sanction and a fresh stock position. The correct response is to raise despatch to 1,850 MT a month, hire the spill-over space only if the arithmetic still favours it, or seek a temporary storage waiver - not to break the buffer.