Economic Order Quantity
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EOQ Model
Equations (part - 1)
Equations (part – 2)
EOQ Model
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Total Inventory cost is the
minimum.
Annual demand of the item is
constant and known.
Annual demand of the item is
uniformly distributed through out
the year.
Lead time is zero.
Total OC (P) = Total CC (R)
Equations
For EOQ, Total OC (P) = Total CC (R)
Total OC (p) = AO/Q
Total CC (R) = QC/2
AO/Q = QC/2
Where, A = Annual Demand
O = Ordering Cost ( Rs) / Order
Q = EOQ
C = Carrying Cost ( Rs )/ Year
Equations (part - 1)
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2.
3.
4.
Average Inventory =
(Max. Inventory + Min. Inventory) / 2
Also, Average Inventory = Q / 2
Total Inventory Cost (T) = P + R
Number of Orders per year = A/Q
Duration of one inventory cycle = Q/A
Problem Solution
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5.
Zen Bicycles Ltd sources 3,000 seat covers for its
bicycles from an outside supplier. The OC is Rs 10
per order and the CC is Rs 6 per unit per year. The
company has 300 working days per year. Find
EOQ
Number of orders/year
Total Inventory Cost
Number of Inventory Cycles in a Year
Duration of an Inventory Cycle
Problem Solution
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5.
The demand of small electric motor used in a fan
is 20,000 per year. The price of the motor is
Rs.100 per motor. The carrying cost is 8 percent
of the purchase price. The ordering cost is Rs.200
per order. The number of working days is 320.
EOQ
Number of orders/year
Total Inventory Cost
Number of Inventory Cycles in a Year
Duration of an Inventory Cycle
Equation (Part – 2)
EOQ model with shortages
2
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Q
= (2AO/C)(C+K)/K
Where Q = EOQ
A = Annual Demand
O = Order Cost
C = Carrying Cost
K = Cost of Shortage
Equation (Part – 2)
Maximum inventory with shortages
2
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Q
1
Where
= (2AO/C)(K/(C+K) ) or
=Q-S
Q = EOQ
A = Annual Demand
O = Order Cost
C = Carrying Cost
K = Cost of Shortage
S = Maximum Shortage
Equation (Part – 2)
Shortage,
S = CQ/(C+K)
Where S = Maximum shortage
Q = EOQ
C = Carrying Cost
K = Cost of Shortage
Equation (Part – 2)
Maximum inventory = Q – S
Reorder level = DDLT - S
Where S = Maximum shortage
Q = EOQ
DDLT = Demand During lead time
Problem
Vishal Computer sales (P) Ltd is a leading dealer of
computer servers and net working devices at Raipur.
Servers are expensive machines and therefore, Vishal
follows a back ordering policy. The CC is Rs. 50,000 per
servers per year and the OC is Rs 1,200 per order. The
cost of shortage per server is estimated at Rs. 20,000.
The annual demand of servers is 300 units. Find
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4.
The optimal order quantity (EOQ with intentional
shortages)
Maximum shortage level
Maximum Inventory level
Reorder level, considering lead time 7 days and DDLT is 3
units.
Problem
The annual demand for an automobile component is
24,000 units. The carrying cost is Rs 0.40/unit/year, the
ordering cost is Rs.20,00 per order and the shortage
cost is Rs.10./unit/year. Find
1.
2.
3.
4.
5.
The optimal order quantity (EOQ with intentional
shortages)
Maximum shortage level
Cycle Time
Maximum Inventory level
Reorder level, considering lead time 7 days and DDLT is 5
units.