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A company has an annual demand of 1000 units, ordering cost of Rs. 100/ order and carrying cost of Rs. 100/unit-year. If the stockout costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, the safety stock justified by the carrying cost will be
[2004]
- a)4
- b)20
- c)40
- d)1 : 8
Correct answer is option 'C'. Can you explain this answer?
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A company has an annual demand of 1000 units, ordering cost of Rs. 100...
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The safety stock is the extra stock that a company holds to mitigate the risk of stockouts. It serves as a buffer to cover unexpected fluctuations in demand or lead time. To calculate the safety stock justified by the carrying cost, we need to consider the trade-off between carrying cost and stockout cost.
Given data:
- Annual demand: 1000 units
- Ordering cost: Rs. 100/order
- Carrying cost: Rs. 100/unit-year
- Stockout cost: Rs. 400
To calculate the safety stock, we need to determine the reorder point. The reorder point is the inventory level at which a new order should be placed to replenish the stock. It is calculated as the lead time demand plus the safety stock.
1. Calculate the lead time demand:
The lead time demand is the average demand during the lead time (time between placing the order and receiving it). Let's assume the lead time is L and the average daily demand is D.
Lead time demand = L * D
2. Calculate the economic order quantity (EOQ):
EOQ is the order quantity that minimizes the total cost of inventory management. It can be calculated using the EOQ formula:
EOQ = sqrt((2 * Annual demand * Ordering cost) / Carrying cost)
3. Calculate the reorder point:
Reorder point = Lead time demand + Safety stock
To determine the safety stock justified by the carrying cost, we need to find the reorder point that minimizes the sum of carrying cost and stockout cost.
4. Calculate the total cost for different reorder points:
- For each potential reorder point, calculate the carrying cost and stockout cost.
- Carrying cost = (Reorder point / 2) * Carrying cost per unit per year
- Stockout cost = (Annual demand - Reorder point) * Stockout cost per unit
5. Identify the reorder point that minimizes the total cost:
- Determine the reorder point that results in the lowest total cost (carrying cost + stockout cost).
- This reorder point will be the safety stock justified by the carrying cost.
In the given options, option C (40) is the correct answer as it represents the safety stock justified by the carrying cost.
Given data:
- Annual demand: 1000 units
- Ordering cost: Rs. 100/order
- Carrying cost: Rs. 100/unit-year
- Stockout cost: Rs. 400
To calculate the safety stock, we need to determine the reorder point. The reorder point is the inventory level at which a new order should be placed to replenish the stock. It is calculated as the lead time demand plus the safety stock.
1. Calculate the lead time demand:
The lead time demand is the average demand during the lead time (time between placing the order and receiving it). Let's assume the lead time is L and the average daily demand is D.
Lead time demand = L * D
2. Calculate the economic order quantity (EOQ):
EOQ is the order quantity that minimizes the total cost of inventory management. It can be calculated using the EOQ formula:
EOQ = sqrt((2 * Annual demand * Ordering cost) / Carrying cost)
3. Calculate the reorder point:
Reorder point = Lead time demand + Safety stock
To determine the safety stock justified by the carrying cost, we need to find the reorder point that minimizes the sum of carrying cost and stockout cost.
4. Calculate the total cost for different reorder points:
- For each potential reorder point, calculate the carrying cost and stockout cost.
- Carrying cost = (Reorder point / 2) * Carrying cost per unit per year
- Stockout cost = (Annual demand - Reorder point) * Stockout cost per unit
5. Identify the reorder point that minimizes the total cost:
- Determine the reorder point that results in the lowest total cost (carrying cost + stockout cost).
- This reorder point will be the safety stock justified by the carrying cost.
In the given options, option C (40) is the correct answer as it represents the safety stock justified by the carrying cost.
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A company has an annual demand of 1000 units, ordering cost of Rs. 100/ order and carrying cost of Rs. 100/unit-year. If the stockout costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, the safety stock justified by the carrying cost will be[2004]a)4b)20c)40d)1 : 8Correct answer is option 'C'. Can you explain this answer?
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