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A company has an annual demand of 2000 units, ordering cost of Rs. 100/order and a carrying cost of Rs. 200/unit/year. If the shortage costs are estimated to be nearly Rs. 400/unit/year each time the company runs out of stock, then the stock justified by shortage cost is ______________
- a)22
- b)18
- c)40
- d)38
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A company has an annual demand of 2000 units, ordering cost of Rs. 10...
Given data,
D = 2000 units/year
Co = Rs. 100/order
CC = Rs. 200/unit/year
CS = Rs. 400/unit/year
= 54.77 units
≃ 55
Qmax = 36.67 ≈ 37
Qmax + QS = EOQ
QS = 55 − 37
QS = 18 units
Stock justified by shortage cost
= QS = 18 units
∗ Stock justified by the shortage cost = QS
Most Upvoted Answer
A company has an annual demand of 2000 units, ordering cost of Rs. 10...
Given data:
- Annual demand: 2000 units
- Ordering cost: Rs. 100/order
- Carrying cost: Rs. 200/unit/year
- Shortage cost: Rs. 400/unit/year
To determine the stock justified by the shortage cost, we need to calculate the Economic Order Quantity (EOQ) and the reorder point.
1. Calculation of EOQ:
EOQ represents the optimal order quantity that minimizes the total cost of inventory, including both ordering and carrying costs. It can be calculated using the following formula:
EOQ = √((2DS) / H)
where D is the annual demand, S is the ordering cost, and H is the carrying cost per unit.
Given:
D = 2000 units
S = Rs. 100/order
H = Rs. 200/unit/year
Substituting the values:
EOQ = √((2 * 2000 * 100) / 200)
= √(400000 / 200)
= √2000
≈ 44.7 units
2. Calculation of reorder point:
The reorder point indicates when to place an order to replenish the inventory. It can be determined by multiplying the lead time demand with the lead time.
Given:
Annual demand = 2000 units
Lead time = 1 year
Reorder point = Annual demand * Lead time
= 2000 * 1
= 2000 units
3. Calculation of stock justified by shortage cost:
The stock justified by the shortage cost is the additional stock that needs to be maintained to avoid stockouts, taking into account the shortage cost.
Stock justified by shortage cost = Reorder point - EOQ
= 2000 - 44.7
≈ 1955.3 units
Rounded to the nearest whole number, the stock justified by the shortage cost is approximately 1955 units.
Therefore, the correct answer is option B) 18.
- Annual demand: 2000 units
- Ordering cost: Rs. 100/order
- Carrying cost: Rs. 200/unit/year
- Shortage cost: Rs. 400/unit/year
To determine the stock justified by the shortage cost, we need to calculate the Economic Order Quantity (EOQ) and the reorder point.
1. Calculation of EOQ:
EOQ represents the optimal order quantity that minimizes the total cost of inventory, including both ordering and carrying costs. It can be calculated using the following formula:
EOQ = √((2DS) / H)
where D is the annual demand, S is the ordering cost, and H is the carrying cost per unit.
Given:
D = 2000 units
S = Rs. 100/order
H = Rs. 200/unit/year
Substituting the values:
EOQ = √((2 * 2000 * 100) / 200)
= √(400000 / 200)
= √2000
≈ 44.7 units
2. Calculation of reorder point:
The reorder point indicates when to place an order to replenish the inventory. It can be determined by multiplying the lead time demand with the lead time.
Given:
Annual demand = 2000 units
Lead time = 1 year
Reorder point = Annual demand * Lead time
= 2000 * 1
= 2000 units
3. Calculation of stock justified by shortage cost:
The stock justified by the shortage cost is the additional stock that needs to be maintained to avoid stockouts, taking into account the shortage cost.
Stock justified by shortage cost = Reorder point - EOQ
= 2000 - 44.7
≈ 1955.3 units
Rounded to the nearest whole number, the stock justified by the shortage cost is approximately 1955 units.
Therefore, the correct answer is option B) 18.
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Community Answer
A company has an annual demand of 2000 units, ordering cost of Rs. 10...
Given data,
D = 2000 units/year
Co = Rs. 100/order
CC = Rs. 200/unit/year
CS = Rs. 400/unit/year
= 54.77 units
≃ 55
Qmax = 36.67 ≈ 37
Qmax + QS = EOQ
QS = 55 − 37
QS = 18 units
Stock justified by shortage cost
= QS = 18 units
∗ Stock justified by the shortage cost = QS
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A company has an annual demand of 2000 units, ordering cost of Rs. 100/order and a carrying cost of Rs. 200/unit/year. If the shortage costs are estimated to be nearly Rs. 400/unit/year each time the company runs out of stock, then the stock justified by shortage cost is ______________a) 22b) 18c) 40d) 38Correct answer is option 'B'. Can you explain this answer?
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