Narayani Garden Centers (NGC) sells 580,000 bags of lawn fertilizer annually. NGC requires safety stock of 2,000 bags. Cost of fertilizer is Rs 16 per bag, inventory carrying cost is 10 percent and…

a. Optimal Order Quantity (EOQ)

The Economic Order Quantity (EOQ) model determines the optimal order quantity that minimizes total inventory costs. The formula is:

$$EOQ=\sqrt{\frac{2DS}{H}}$$

Where:

• $D$ = Annual demand = 580,000 bags
• $S$ = Ordering cost per order = Rs 50
• $H$ = Holding cost per unit per year = 10% of Rs 16 = Rs 1.6

Calculation: $$EOQ=\sqrt{\frac{2\times 580,000\times 50}{1.6}}=\sqrt{\frac{58,000,000}{1.6}}=\sqrt{36,250,000}=\ast \ast 19,039bags\ast \ast$$

Answer: The optimal order quantity is 19,039 bags.

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b. Total Inventory Costs

Total inventory costs consist of ordering costs and holding costs.

1. Ordering Cost

$$\text{Number of orders}=\frac{D}{EOQ}=\frac{580,000}{19,039}\approx 30.47\approx 31\text{ orders}$$ $$\text{Total ordering cost}=31\times 50=\ast \ast Rs1,550\ast \ast$$

2. Holding Cost

$$\text{Average inventory}=\frac{EOQ}{2}+\text{Safety Stock}=\frac{19,039}{2}+2,000=9,519.5+2,000=11,519.5\text{ bags}$$ $$\text{Total holding cost}=11,519.5\times 1.6=\ast \ast Rs18,431\ast \ast$$

3. Total Inventory Cost

$$\text{Total cost}=\text{Ordering cost}+\text{Holding cost}=1,550+18,431=\ast \ast Rs19,981\ast \ast$$

Answer: The total inventory cost is Rs 19,981.

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c. Order Frequency

$$\text{Order frequency}=\frac{\text{Annual demand}}{\text{EOQ}}=\frac{580,000}{19,039}\approx 30.47\text{ orders/year}$$ $$\text{Orders per month}=\frac{30.47}{12}\approx 2.54\text{ orders/month}$$

Answer: NGC must place an order approximately every 1.2 months (or 37 days).

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Note: The slight discrepancy in ordering cost (Rs 1,550 vs. Rs 1,483 in the figure) arises from rounding EOQ to 19,039. For precise calculations, use exact EOQ values.