1. Economic Order Quantity
EOQ Model
Equations (part - 1)
Equations (part – 2)

2. EOQ Model 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)

3. 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

4. Equations (part - 1) 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

5. Problem Solution
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

6. Problem Solution
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

7. Equation (Part – 2) EOQ model with shortages 2 Q = (2AO/C)(C+K)/K
Where Q = EOQ
A = Annual Demand
O = Order Cost
C = Carrying Cost
K = Cost of Shortage

8. Equation (Part – 2) Maximum inventory with shortages 2
Q1 = (2AO/C)(K/(C+K) ) or
= Q - S
Where Q = EOQ
A = Annual Demand
O = Order Cost
C = Carrying Cost
K = Cost of Shortage
S = Maximum Shortage

9. Equation (Part – 2) Shortage, S = CQ/(C+K) Where S = Maximum shortage
Q = EOQ
C = Carrying Cost
K = Cost of Shortage

10. Equation (Part – 2) Maximum inventory = Q – S Reorder level = DDLT - S
Where S = Maximum shortage
Q = EOQ
DDLT = Demand During lead time

11. 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
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.

12. 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
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.