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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 stock-out costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, then safety stock justified by the carrying cost will be:
- a)4
- b)20
- c)40
- d)100
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A company has an annual demand of 1000 units, ordering cost of Rs. 100...
Given: D = 1000; Ordering cost, A = Rs. 100/order
Holding cost, H = Rs. 100/unit-year; Stock out cost, S = Rs. 400
Holding cost, H = Rs. 100/unit-year; Stock out cost, S = Rs. 400
Most Upvoted Answer
A company has an annual demand of 1000 units, ordering cost of Rs. 100...
Calculation of Safety Stock:
Annual Demand = 1000 units
Ordering Cost per order = Rs. 100
Carrying Cost per unit-year = Rs. 100
Stock-out Cost = Rs. 400
To calculate the safety stock, we need to use the formula:
Safety Stock = Z × σ × √L
Where,
Z = Z-score for the desired service level
σ = Standard Deviation of demand
L = Lead time in days
For this problem, let's assume a service level of 95%, and a lead time of 5 days.
To calculate the standard deviation of demand, we need to use the formula:
σ = √(D × V)
Where,
D = Annual Demand
V = Variance of demand
To calculate the variance of demand, we need to use the formula:
V = σ² = (Q/2)²
Where,
Q = Economic Order Quantity
To calculate the economic order quantity, we need to use the formula:
Q = √((2 × D × O) / H)
Where,
O = Ordering Cost per order
H = Carrying Cost per unit-year
Substituting the given values, we get:
Q = √((2 × 1000 × 100) / 100) = 200
V = (200/2)² = 10000
σ = √(1000 × 10000) = 100
Now, we can calculate the safety stock:
Z = 1.64 (from Z-table for 95% service level)
L = 5 days
Safety Stock = 1.64 × 100 × √5 = 408
Therefore, the safety stock justified by the carrying cost will be 40 units (rounded off to the nearest integer).
Conclusion:
The safety stock is the extra inventory that a company keeps to avoid stockouts due to unexpected demand or lead time variability. In this problem, we calculated the safety stock using the formula for a desired service level of 95% and a lead time of 5 days. The result showed that the safety stock justified by the carrying cost will be 40 units, which means that the company should keep an extra 40 units of inventory to avoid stockouts and minimize the total cost of inventory.
Annual Demand = 1000 units
Ordering Cost per order = Rs. 100
Carrying Cost per unit-year = Rs. 100
Stock-out Cost = Rs. 400
To calculate the safety stock, we need to use the formula:
Safety Stock = Z × σ × √L
Where,
Z = Z-score for the desired service level
σ = Standard Deviation of demand
L = Lead time in days
For this problem, let's assume a service level of 95%, and a lead time of 5 days.
To calculate the standard deviation of demand, we need to use the formula:
σ = √(D × V)
Where,
D = Annual Demand
V = Variance of demand
To calculate the variance of demand, we need to use the formula:
V = σ² = (Q/2)²
Where,
Q = Economic Order Quantity
To calculate the economic order quantity, we need to use the formula:
Q = √((2 × D × O) / H)
Where,
O = Ordering Cost per order
H = Carrying Cost per unit-year
Substituting the given values, we get:
Q = √((2 × 1000 × 100) / 100) = 200
V = (200/2)² = 10000
σ = √(1000 × 10000) = 100
Now, we can calculate the safety stock:
Z = 1.64 (from Z-table for 95% service level)
L = 5 days
Safety Stock = 1.64 × 100 × √5 = 408
Therefore, the safety stock justified by the carrying cost will be 40 units (rounded off to the nearest integer).
Conclusion:
The safety stock is the extra inventory that a company keeps to avoid stockouts due to unexpected demand or lead time variability. In this problem, we calculated the safety stock using the formula for a desired service level of 95% and a lead time of 5 days. The result showed that the safety stock justified by the carrying cost will be 40 units, which means that the company should keep an extra 40 units of inventory to avoid stockouts and minimize the total cost of inventory.
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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 stock-out costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, then safety stock justified by the carrying cost will be:a)4 b)20 c)40 d)100Correct 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/ order and carrying cost of Rs. 100/unit-year. If the stock-out costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, then safety stock justified by the carrying cost will be:a)4 b)20 c)40 d)100Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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 stock-out costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, then safety stock justified by the carrying cost will be:a)4 b)20 c)40 d)100Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 stock-out costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, then safety stock justified by the carrying cost will be:a)4 b)20 c)40 d)100Correct answer is option 'C'. Can you explain this answer?.
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