Compute from the above (1) EOQ and Total inventory cost (2) if the supplier is willing to supply quarterly 1,500 units at a discount of 5%, is it worth accepting?

Steps to Solve

1. Calculate Annual Demand

To estimate the annual demand, multiply the average monthly market demand by 12 months: $$ \text{Annual Demand} = 2000 , \text{tubes/month} \times 12 , \text{months} = 24000 , \text{tubes/year} $$

2. Identify Carrying Cost Per Tube

The carrying cost per tube is calculated as a percentage of the cost of each tube: $$ \text{Carrying Cost per Tube} = 0.20 \times 500 = 100 , \text{per tube per year} $$

3. Calculate Economic Order Quantity (EOQ)

Utilize the EOQ formula: $$ EOQ = \sqrt{\frac{2DS}{H}} $$ Where:

• (D) = Annual demand (24000 tubes)
• (S) = Ordering cost (100 per order)
• (H) = Carrying cost per tube (100)

Plugging in the values: $$ EOQ = \sqrt{\frac{2 \times 24000 \times 100}{100}} = \sqrt{48000} = 219.09 \approx 219 , \text{tubes} $$

4. Evaluate Supplier's Discount

Calculate the new cost per tube with a 5% discount: $$ \text{Discounted Cost} = 500 \times (1 - 0.05) = 500 \times 0.95 = 475 , \text{per tube} $$

5. Compare Annual Costs

First, calculate the total annual cost without discount: $$ \text{Total Cost without Discount} = D \times \text{Cost per Tube} + \frac{D}{EOQ} \times S + \frac{EOQ}{2} \times H $$ Substituting the relevant values:

• Total Cost without Discount: $$ \text{Total Cost} = 24000 \times 500 + \frac{24000}{219} \times 100 + \frac{219}{2} \times 100 $$

Now calculate with the discounted cost: $$ \text{Total Cost with Discount} = D \times \text{Discounted Cost} + \frac{D}{EOQ} \times S + \frac{EOQ}{2} \times H $$