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For a single item inventory system, the demand is continuous, which is 10000 per year.
The replacement is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.
As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year.
Based on the total cost minimization criteria, the maximum inventory reached in the system is ________ (round off to nearest integer).
The replacement is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.
As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year.
Based on the total cost minimization criteria, the maximum inventory reached in the system is ________ (round off to nearest integer).
Correct answer is '1137.147'. Can you explain this answer?
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Verified Answer
For a single item inventory system, the demand is continuous, which is...
Given data: D = 10000 items/year, Co = Rs. 300/order,
Ch = Rs. 4/unit/year, Cb = Rs. 25/unit/year,
For minimum tool cost,
Quantity ordered, Q =
Q = 1319.09 unit
Now, for minimum cost, optimum units backordered
(Q – S) × Ch =(S) × Cb
S (Cb + Ch)= Q × Ch
Maximum inventory in the system, Qmax = Q – S
= 1319.09 – 181.94
= 1137.15 unit
≈ 1137 units
Alternate:
Maximum inventory in system =
Ch = Rs. 4/unit/year, Cb = Rs. 25/unit/year,
For minimum tool cost,
Quantity ordered, Q =
Q = 1319.09 unit
Now, for minimum cost, optimum units backordered
(Q – S) × Ch =(S) × Cb
S (Cb + Ch)= Q × Ch
Maximum inventory in the system, Qmax = Q – S
= 1319.09 – 181.94
= 1137.15 unit
≈ 1137 units
Alternate:
Maximum inventory in system =
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For a single item inventory system, the demand is continuous, which is 10000 per year.The replacement is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year.Based on the total cost minimization criteria, the maximum inventory reached in the system is ________ (round off to nearest integer).Correct answer is '1137.147'. Can you explain this answer?
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For a single item inventory system, the demand is continuous, which is 10000 per year.The replacement is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year.Based on the total cost minimization criteria, the maximum inventory reached in the system is ________ (round off to nearest integer).Correct answer is '1137.147'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about For a single item inventory system, the demand is continuous, which is 10000 per year.The replacement is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year.Based on the total cost minimization criteria, the maximum inventory reached in the system is ________ (round off to nearest integer).Correct answer is '1137.147'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a single item inventory system, the demand is continuous, which is 10000 per year.The replacement is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year.Based on the total cost minimization criteria, the maximum inventory reached in the system is ________ (round off to nearest integer).Correct answer is '1137.147'. Can you explain this answer?.
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