EOQ, stock levels and ROL for cement

Data

$D = 20{,}000$ bags/year, $C_o =$ Rs 10,000/order, $P =$ Rs 900/bag, carrying cost = 5% of price, so $C_h = 0.05 \times 900 =$ Rs 45 per bag per year. A working year of 365 days is assumed, so daily use = 20,000/365 = 54.79 bags/day. Safety stock = 10 days, lead time = 5 days.

EOQ

$$EOQ = \sqrt{\frac{2 \times 20000 \times 10000}{45}} = 2981.4\ \text{bags} \approx 2{,}981\ \text{bags}$$

Stock levels

• Safety (minimum) stock = 10 x 54.79 = 547.9 bags $\approx$ 548 bags
• Lead-time consumption = 5 x 54.79 = 274.0 bags
• Re-order level (ROP/ROL) = 274.0 + 547.9 = 821.9 bags $\approx$ 822 bags
• Maximum stock level = safety stock + EOQ = 547.9 + 2,981.4 = 3,529.3 bags $\approx$ 3,529 bags
• Minimum stock level = safety stock $\approx$ 548 bags
• Average stock level = (3,529.3 + 547.9)/2 = 2,038.6 bags $\approx$ 2,039 bags

Total inventory cost

• Number of orders = 20,000/2,981.4 = 6.71 per year
• Ordering cost = 6.71 x 10,000 = Rs 67,082
• Carrying cost = (EOQ/2) x 45 = 1,490.7 x 45 = Rs 67,082
• Total ordering + carrying cost = Rs 1,34,164
• Purchase cost = 20,000 x 900 = Rs 1,80,00,000

(If the carrying cost of the safety stock is also included, add 547.9 x 45 = Rs 24,658, giving Rs 1,58,822 before purchase cost.)

Answer: EOQ = 2,981 bags; ROL = 822 bags; maximum = 3,529 bags; minimum = 548 bags; average = 2,039 bags. Total inventory cost (ordering + carrying) = Rs 1,34,164; including the purchase cost, Rs 1,81,34,164.