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The annual demand of the company is 10000 units per year. The ordering cost per order is Rs 100 per year and the carrying cost is Rs10 per unit per year and the shortage is allowed. The shortage cost is Rs 5 per unit per year. Maximum inventory is_______.
- a)193
- b)259
- c)421
- d)111
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The annual demand of the company is 10000 units per year. The orderin...
Here we will use shortage model of inventory control,
View all questions of this test
The EOQ in shortage model is given by
Q* = EQQ QUANTITY
D = DEMAND PER YEAR
C0 = ORDERING COST PER YEAR
CC = CARRYING COST PER UNIT PER YEAR
CS = SHORTAGE COST PER UNIT PER YEAR
= 516.39
= MAXIMUM INVENTORY = Q*- S* = 258.193
Most Upvoted Answer
The annual demand of the company is 10000 units per year. The orderin...
Given data:
Annual demand: 10000 units per year
Ordering cost per order: Rs 100 per year
Carrying cost: Rs 10 per unit per year
Shortage cost: Rs 5 per unit per year
To find:
Maximum inventory
Explanation:
The Economic Order Quantity (EOQ) model can be used to determine the optimal order quantity that minimizes the total cost of inventory.
1. Calculating the EOQ:
EOQ formula:
EOQ = sqrt((2 * D * S) / H)
Where,
D = annual demand (in units)
S = ordering cost per order (in Rs)
H = carrying cost per unit per year (in Rs)
Plugging in the given values:
EOQ = sqrt((2 * 10000 * 100) / 10)
= sqrt(2000000)
= 1414.21 (approx.)
2. Calculating the optimal number of orders:
Number of orders = D / EOQ
= 10000 / 1414.21
= 7.07 (approx.)
Since we cannot have a fractional number of orders, we round up to the nearest whole number. Therefore, the optimal number of orders is 8.
3. Calculating the optimal order quantity:
Optimal order quantity = D / Number of orders
= 10000 / 8
= 1250
4. Calculating the maximum inventory:
Maximum inventory = EOQ / 2 + (D / Number of orders) / 2
= 1414.21 / 2 + 1250 / 2
= 707.11 + 625
= 1332.11 (approx.)
Therefore, the maximum inventory is approximately 1332 units.
Conclusion:
The maximum inventory is 1332 units.
Annual demand: 10000 units per year
Ordering cost per order: Rs 100 per year
Carrying cost: Rs 10 per unit per year
Shortage cost: Rs 5 per unit per year
To find:
Maximum inventory
Explanation:
The Economic Order Quantity (EOQ) model can be used to determine the optimal order quantity that minimizes the total cost of inventory.
1. Calculating the EOQ:
EOQ formula:
EOQ = sqrt((2 * D * S) / H)
Where,
D = annual demand (in units)
S = ordering cost per order (in Rs)
H = carrying cost per unit per year (in Rs)
Plugging in the given values:
EOQ = sqrt((2 * 10000 * 100) / 10)
= sqrt(2000000)
= 1414.21 (approx.)
2. Calculating the optimal number of orders:
Number of orders = D / EOQ
= 10000 / 1414.21
= 7.07 (approx.)
Since we cannot have a fractional number of orders, we round up to the nearest whole number. Therefore, the optimal number of orders is 8.
3. Calculating the optimal order quantity:
Optimal order quantity = D / Number of orders
= 10000 / 8
= 1250
4. Calculating the maximum inventory:
Maximum inventory = EOQ / 2 + (D / Number of orders) / 2
= 1414.21 / 2 + 1250 / 2
= 707.11 + 625
= 1332.11 (approx.)
Therefore, the maximum inventory is approximately 1332 units.
Conclusion:
The maximum inventory is 1332 units.
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