Calculate the economic order quantity of raw materials. Advise how frequently should order for procurement be placed.

Understand the Problem

The question is asking to calculate the economic order quantity of raw materials and how frequently orders should be placed based on the provided costs and annual production data.

Answer

EOQ is approximately $1386.67$ kg and orders should be placed approximately $29$ times per year.

Steps to Solve

Identify the relevant costs
Calculate the total cost components needed for the EOQ formula:

Cost per order = Rs 360
Carrying cost per kg per month = Rs 0.50
Annual carrying cost = $0.50 \times 12 = Rs 6.00$ per kg
Total carrying cost per kg, including finance = $6 + 9 = Rs 15$ per kg

Calculate the annual demand
Determine the total amount of raw material needed for production:

Annual production = 100,000 units
Units per kg of raw material = 2.5 units/kg
Annual demand in kg = $100,000 \div 2.5 = 40,000$ kg

Apply the EOQ formula
Use the Economic Order Quantity (EOQ) formula: $$ EOQ = \sqrt{\frac{2 \times \text{Demand} \times \text{Cost per Order}}{\text{Carrying Cost per unit}}} $$ Substituting in the values:

Demand = 40,000 kg
Cost per order = Rs 360
Carrying cost per unit = Rs 15
The formula becomes: $$ EOQ = \sqrt{\frac{2 \times 40,000 \times 360}{15}} $$

Calculate EOQ value
Calculate the EOQ: $$ EOQ = \sqrt{\frac{28,800,000}{15}} $$ Calculate further: $$ EOQ = \sqrt{1,920,000} \approx 1386.67 \text{ kg} $$
Determine order frequency
Calculate how often orders should be placed annually:

Annual demand = 40,000 kg
EOQ = 1386.67 kg
Order frequency = $ \frac{\text{Annual Demand}}{EOQ} = \frac{40,000}{1386.67} \approx 28.87 \text{ orders} $
So, approximately 29 orders per year.

Economic Order Quantity (EOQ) is approximately $1386.67$ kg.
Orders should be placed approximately $29$ times per year.

More Information

The Economic Order Quantity (EOQ) helps firms minimize inventory costs by determining the optimal order size. By managing inventory effectively, companies can reduce storage costs and improve cash flow. The frequency of placement can inform management strategy around raw material procurement.

Tips

Ignoring carrying costs: It's essential to include both carrying and financing costs in the EOQ formula.
Incorrect unit conversions: Ensure all costs and units are consistent when performing calculations.
Rounding too soon: Keep more decimal places during calculations and round only in the final answer for accuracy.

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