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How to calculate Economic Order Quantity (EOQ)?

Economic Order Quantity: It is an amount of stock ordered which minimises the total cost of production or we can say minimise the ordering cost and carrying cost.

Assumptions:
·         The lead time is constant.
·         The demand rate remains constant and evenly spread throughout the year.
·         The ordering cost and carrying cost remain constant and it doesn’t change with change in ordered quantity.
·         There is only two cost involved in inventory that is ordering cost and carrying cost.

Formula:
Q = √ ((2*D*S)/ H)
N= D/ Q
Annual holding cost = H * (Q / 2)
Annual Ordering cost = S * (D / Q)
∆π = D * d + [(D / Q EOQ) – (D / Q DO)] S – [((Q DO – (P-d) H)/ 2) – ((Q EOQ * P*H)/ 2)]
Where,
Q = Economic order quantity
D = Annual demand or sales
S = Order cost
P = Price per unit
∆π = Change in profit
d= Discount amount
Q EOQ = economic order quantity
Q DO = Discount offered in that quantity
H = holding cost per unit or carrying cost
N = Number of expected order

The two costs involved in this equation that is ordering cost and carrying cost. In which the carrying cost include other cost also like transportation cost for carrying goods from supplier place to ordering company. The handing cost for unloading the goods and storage cost for keeping the goods in warehouse until it sold out to customers. The carrying cost also includes the insurance cost for protecting the goods from theft, fire and flood etc.

Example: Find out the economic order quantity (EOQ) and number of quantity order with the help of given information:

Particulars
Amount (in Rs.)
Annual Cost per order
7
Annual sales
10, 000
Carrying cost%
30
Price per unit
5

Solution:
Q = √ ((2*D*S)/H)
= √ (2*10, 000*7)/0.30*5
= √ (1, 40,000 / 1.5)
= √93, 333.33
= 305.50
= 306 units
Number of Order placed (N) = D / Q
= 10, 000 / 306
= 32.67 or 33
Quantity ordered = 10, 000 / 33
= 303
The total annual costs of placing 33 orders are:
Annual carrying cost =1.5 *(303 / 2)
= Rs. 227.25
Annual ordering cost = 7 * (10,000 / 303)
= 7 * 32.67
= 231
Total cost = 227 + 231
= Rs. 458
The total cost is same in 32 orders or 33 orders that is Rs.458.

Example: Find out the optimum order quantity from the given information:

Particulars
Amount (in Rs.)
Annual usage or demand
8, 000
Carrying cost per unit
12%
Ordering cost per unit
20
Discount rate per unit
10
Price per unit
32
 Discount available in given quantity: 200 and 400 units.

Solution:
Q = √ ((2*D*S)/H)
= √ ((2*8, 000*20)/32 * 0.12)
= √ (3, 20,000/3.84)
= √ 83, 333.33
= 288.67 or 289 units
The discount available in 200 units is < economic order quantity 289 units. So, the optimum order quantity is equal to economic order quantity i.e. 289.
∆π = D * d + [(D / Q EOQ) – (D / Q DO)] S – [((Q DO – (P-d) H)/ 2) – ((Q EOQ * P*H)/ 2)]
= 8, 000 *10 + [(8, 000 / 289) – (8, 000 / 400)] 20 – [((400 – (32-10) 0.12)/ 2) – (289 * 32*0.12/ 2)]
= 80, 000 + [27.68 – 20] 20 – [198.68 – 554.88]
= 80, 000 + 160 +356
=Rs. 80, 516

The profit amount shows that the optimum order quantity is 400 units in place of 289 units. But if there is a negative amount then the EOQ will be 289 units because it shows loss for the company.



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