Question

The following table gives the annual demand and unit price of 3 items.

Items	Annual Demand (units)	Unit Price
A	800	0.02
B	400	1.00
C	13,800	0.20

Ordering cost is ₹ 5 per order and holding cost is 10% of unit price. Determine the following:

1. EOQ in units
2. Minimum average cost
3. EOQ in rupees
4. EOQ in years of supply
5. Number of orders per year

Answer 1

• Item A:

Demand rate, R = 800

Ordering cost, C₃ = ₹ 5

Carrying cost C₁ = 10% of unit price = `10/100 xx 0.02`

(i) EOQ in units

EOQ = `sqrt((2"RC"_3)/"C"_1)`

`= sqrt((2 xx 800 xx 5 xx 100)/(10 xx 0.02))`

`= sqrt((800 xx 100 xx 100)/(0.02 xx 100))`

`= sqrt((800 xx 100 xx 100)/2)`

`= sqrt(400 xx 100 xx 100)`

= 20 × 10 × 10

= 2000 units

(ii) Minimum Average Cost = C₀ = `sqrt(2"RC"_3"C"_1)`

`= sqrt(2 xx 800 xx 5 xx 10/100 xx 0.02)`

`= sqrt(800 xx 0.02)`

`= sqrt16.00`

= ₹ 4

(iii) EOQ in rupees = EOQ × Unit price

= 2000 × 0.02

`= 2000 xx 2/100`

= ₹ 40

(iv) `"EOQ"/"Demand" = 2000/800 = 2.5`

(v) `"Demand"/"EOQ" = 800/2000 = 0.4`

• Item B:

Demand rate, R = 400

Ordering cost, C₃ = ₹ 5

Carrying cost C₁ = 10% of 1.00

(i) EOQ in units

EOQ = `sqrt((2"RC"_3)/"C"_1)`

`= sqrt((2 xx 400 xx 5)/(10/100 xx 1))`

`= sqrt ((2 xx 400 xx 5 xx 100)/10)`

= 20 × 10

= 200 units

(ii) Minimum Average Cost = C₀ = `sqrt(2"RC"_3"C"_1)`

`= sqrt(2 xx 400 xx 5 xx 10/100 xx 1)`

`= sqrt400`

= ₹ 20

(iii) EOQ in rupees = EOQ × unit price

= 200 × 1

= ₹ 200

(iv) `"EOQ"/"Demand" = 200/400 = 0.5`

(v) `"Demand"/"EOQ" = 400/200 = 2`

• Item C:

Annual Demand, R = 800

Ordering cost, C₃ = ₹ 5

Carrying cost, C₁ = 10% of unit price `= 10/100 xx0.20`

`= 2/100`

(i) EOQ in units

EOQ = `sqrt((2"RC"_3)/"C"_1)`

= `sqrt((2xx13800xx5)/(2/100))`

= `sqrt((2xx13800 xx5xx100)/2)`

`= sqrt (138 xx100xx5xx100)`

`= 10 xx 10 sqrt(138 xx 5)`

`= 100sqrt690`

= 100 × 26.2678

= 100 × 26.27

= 2627

(ii) Minimum Average Cost = C₀ = `sqrt(2"RC"_3"C"_1)`

`= sqrt(2 xx 13800 xx 5 xx 10/100 xx 0.2)`

`= sqrt (2 xx 138 xx 5 xx 2)`

`= sqrt2760`

= 52.535

= ₹ 52.54

(iii) EOQ in rupees = 2627 × 0.20 = ₹ 25.40 [∵ Unit price = 0.20]

(iv) `"EOQ"/"Demand" = 2627/13800 = 0.19036 = 0.19`

(v) `"Demand"/"EOQ" = 13800/2627 = 5.2531 = 5.25`