Question
Ace Ltd. manufactures a product and the following particulars are collected for the year ended March, 2013:
• Monthly demand (units) 25000
• Cost of placing an order (`) 10000
• Annual carrying cost (`per unit) 1500
• Normal usage (units per week) 5000
• Minimum usage (units per week) 2500
• Maximum usage (units per week) 7500
• Re-order period (weeks) 4-6
Practice question cont...
You are required to calculate:
(i) Re-order quantity
(ii) Re-order level
(iii) Minimum level
(iv) Maximum level
(v) Average stock level
• Monthly demand (units) 25000
• Cost of placing an order (`) 10000
• Annual carrying cost (`per unit) 1500
• Normal usage (units per week) 5000
• Minimum usage (units per week) 2500
• Maximum usage (units per week) 7500
• Re-order period (weeks) 4-6
Practice question cont...
You are required to calculate:
(i) Re-order quantity
(ii) Re-order level
(iii) Minimum level
(iv) Maximum level
(v) Average stock level
Answers
GPT-4o
To calculate each of the required inventory management metrics for Ace Ltd., we need to use the formulas based on the provided data.
### (i) Re-order Quantity
The Economic Order Quantity (EOQ) formula is often used to find the re-order quantity. The EOQ formula is:
\[
EOQ = \sqrt{\frac{2DS}{H}}
\]
Where:
- \( D \) = Annual demand (units)
- \( S \) = Cost of placing an order
- \( H \) = Annual carrying cost per unit
Given:
- Monthly demand = 25000 units
- Annual demand (\(D\)) = 25000 units * 12 months = 300000 units
- Cost of placing an order (\(S\)) = ₹10000
- Annual carrying cost per unit (\(H\)) = ₹1500
Now we can calculate the EOQ:
\[
EOQ = \sqrt{\frac{2 \times 300000 \times 10000}{1500}}
\]
\[
EOQ = \sqrt{\frac{6000000000}{1500}}
\]
\[
EOQ = \sqrt{4000000}
\]
\[
EOQ = 2000 \text{ units}
\]
So, the re-order quantity is 2000 units.
### (ii) Re-order Level
The reorder level is calculated as:
\[
Reorder \, Level = Maximum \, Usage \times Maximum \, Reorder \, Period
\]
Given:
- Maximum usage per week = 7500 units
- Maximum reorder period = 6 weeks
\[
Reorder \, Level = 7500 \times 6 = 45000 \text{ units}
\]
### (iii) Minimum Level
The minimum level of stock can be calculated as:
\[
Minimum \, Level = Reorder \, Level - (Normal \, Usage \times Average \, Reorder \, Period)
\]
Given:
- Normal usage per week = 5000 units
- Average reorder period = \(\frac{4+6}{2} = 5\) weeks
\[
Minimum \, Level = 45000 - (5000 \times 5)
\]
\[
Minimum \, Level = 45000 - 25000 = 20000 \text{ units}
\]
### (iv) Maximum Level
The maximum level of stock can be calculated as:
\[
Maximum \, Level = Reorder \, Level + Reorder \, Quantity - (Minimum \, Usage \times Minimum \, Reorder \, Period)
\]
Given:
- Minimum usage per week = 2500 units
- Minimum reorder period = 4 weeks
- Reorder Quantity (from (i)) = 2000 units
\[
Maximum \, Level = 45000 + 2000 - (2500 \times 4)
\]
\[
Maximum \, Level = 45000 + 2000 - 10000
\]
\[
Maximum \, Level = 37000 \text{ units}
\]
### (v) Average Stock Level
The average stock level can be calculated as:
\[
Average \, Stock \, Level = \frac{Minimum \, Level + Maximum \, Level}{2}
\]
\[
Average \, Stock \, Level = \frac{20000 + 37000}{2}
\]
\[
Average \, Stock \, Level = 28500 \text{ units}
\]
### Summary of Calculations:
- Re-order quantity: 2000 units
- Re-order level: 45000 units
- Minimum level: 20000 units
- Maximum level: 37000 units
- Average stock level: 28500 units
### (i) Re-order Quantity
The Economic Order Quantity (EOQ) formula is often used to find the re-order quantity. The EOQ formula is:
\[
EOQ = \sqrt{\frac{2DS}{H}}
\]
Where:
- \( D \) = Annual demand (units)
- \( S \) = Cost of placing an order
- \( H \) = Annual carrying cost per unit
Given:
- Monthly demand = 25000 units
- Annual demand (\(D\)) = 25000 units * 12 months = 300000 units
- Cost of placing an order (\(S\)) = ₹10000
- Annual carrying cost per unit (\(H\)) = ₹1500
Now we can calculate the EOQ:
\[
EOQ = \sqrt{\frac{2 \times 300000 \times 10000}{1500}}
\]
\[
EOQ = \sqrt{\frac{6000000000}{1500}}
\]
\[
EOQ = \sqrt{4000000}
\]
\[
EOQ = 2000 \text{ units}
\]
So, the re-order quantity is 2000 units.
### (ii) Re-order Level
The reorder level is calculated as:
\[
Reorder \, Level = Maximum \, Usage \times Maximum \, Reorder \, Period
\]
Given:
- Maximum usage per week = 7500 units
- Maximum reorder period = 6 weeks
\[
Reorder \, Level = 7500 \times 6 = 45000 \text{ units}
\]
### (iii) Minimum Level
The minimum level of stock can be calculated as:
\[
Minimum \, Level = Reorder \, Level - (Normal \, Usage \times Average \, Reorder \, Period)
\]
Given:
- Normal usage per week = 5000 units
- Average reorder period = \(\frac{4+6}{2} = 5\) weeks
\[
Minimum \, Level = 45000 - (5000 \times 5)
\]
\[
Minimum \, Level = 45000 - 25000 = 20000 \text{ units}
\]
### (iv) Maximum Level
The maximum level of stock can be calculated as:
\[
Maximum \, Level = Reorder \, Level + Reorder \, Quantity - (Minimum \, Usage \times Minimum \, Reorder \, Period)
\]
Given:
- Minimum usage per week = 2500 units
- Minimum reorder period = 4 weeks
- Reorder Quantity (from (i)) = 2000 units
\[
Maximum \, Level = 45000 + 2000 - (2500 \times 4)
\]
\[
Maximum \, Level = 45000 + 2000 - 10000
\]
\[
Maximum \, Level = 37000 \text{ units}
\]
### (v) Average Stock Level
The average stock level can be calculated as:
\[
Average \, Stock \, Level = \frac{Minimum \, Level + Maximum \, Level}{2}
\]
\[
Average \, Stock \, Level = \frac{20000 + 37000}{2}
\]
\[
Average \, Stock \, Level = 28500 \text{ units}
\]
### Summary of Calculations:
- Re-order quantity: 2000 units
- Re-order level: 45000 units
- Minimum level: 20000 units
- Maximum level: 37000 units
- Average stock level: 28500 units