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EOQ and reorder point for rebar

Short answer

EOQ minimizes total ordering and carrying costs. Carrying cost =15% of Rs 90,000 = Rs 13,500/tonne/year. EOQ = sqrt(2*1000*10000/13500) ≈ 38.5 tonnes. Reorder point = lead time consumption (4*50 t) + safety stock (50 t) = 250 tonnes.

Define economic order quantity. Calculate EOQ and reorder point if rebar required is 1000 tonnes; Ordering Cost is Rs. 10,000; Carrying Cost is 15%, rebar rate is Rs. 90,000 per tonne; Safety Stock is 50 tonnes; lead time is 4 day and consumption per day is 50 tonnes.

Economic order quantity

EOQ is the order size that makes the total of ordering cost and carrying cost a minimum:

EOQ=2DCoChEOQ = \sqrt{\frac{2 D C_o}{C_h}}

where DD is the annual requirement, CoC_o the ordering cost per order and ChC_h the carrying cost per unit per year.

Calculation

D=1000D = 1000 t, Co=C_o = Rs 10,000, carrying cost = 15% of Rs 90,000 = Rs 13,500 per tonne per year.

EOQ=2×1000×1000013500=38.49 tonnesEOQ = \sqrt{\frac{2 \times 1000 \times 10000}{13500}} = 38.49\ \text{tonnes}

Number of orders = 1000/38.49 = 26.0 per year.

Re-order point

Lead-time consumption = 4 days x 50 t/day = 200 t. Safety stock = 50 t.

ROP=200+50=250 tonnesROP = 200 + 50 = 250\ \text{tonnes}

Answer: EOQ = 38.49 tonnes (about 38.5 t); re-order point = 250 tonnes.

✓ Answer checked by Claude Opus 5.5 (high effort)

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