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Eoq

Illustration 2.1

Calculate the economic order quantity for material M. The following details are furnished:

  • Annual usage = 90,000 units
  • Buying cost per order = Rs 10
  • Cost of carrying inventory = 10% of cost
  • Cost per unit = Rs 50

Solution:

The formula for EOQ is:

$$ EOQ = \sqrt{\frac{2AB}{CS}} $$

Where:

  • ( A ) = Annual consumption
  • ( B ) = Buying Cost
  • ( C ) = Cost per unit
  • ( S ) = Storage/Carrying Cost

Calculating EOQ:

$$ EOQ = \sqrt{\frac{2 \times 90,000 \times 10}{50 \times 10%}} $$

$$ EOQ = \sqrt{\frac{2 \times 90,000 \times 10}{5}} $$

$$ EOQ = \sqrt{360,000} $$

$$ EOQ = 600 \text{ units} $$

Illustration 2.13

Given,

  • Cost of placing order or Buying Cost (B) = Rs 100
  • Purchase price of raw material (C) = Rs 10
  • Re-order period = 4-8 weeks
  • Consumption of Raw materials = 100-450 Kg per week
  • Annual consumption (A) = 275 x 52 = 14,300 Kg
  • Avg consumption of RM = 275 Kg
  • Carrying cost (S) = 20% p.a.

Calculate:

i) Re-order quantity or EOQ

$$ \text{EOQ} = \sqrt{\frac{2AB}{CS}} $$

$$ \text{EOQ} = \sqrt{\frac{2 \times 14,300 \times 100}{10 \times 20%}} $$

$$ \text{EOQ} = \sqrt{\frac{2 \times 14,300 \times 100}{2}} $$

$$ \text{EOQ} = \sqrt{1,430,000} $$

$$ \text{EOQ} = 1195.82 \text{ or } 1196 \text{ Kgs (approx.)} $$

ii) Re-order Level

$$ \text{Re-order Level} = \text{Maximum consumption} \times \text{Maximum re-order period} $$

$$ \text{Re-order Level} = 450 \times 8 $$

$$ \text{Re-order Level} = 3600 \text{ Kgs} $$

Illustration 2.3

Given,

  • Monthly consumption = 2,500 units

  • Annual consumption (A) = 2,500 x 12 = 30,000 units

  • Cost of placing order or Buying cost (B) = Rs 150

  • Cost per unit (C) = Rs 20

  • Re-order period = 4-8 weeks

  • Minimum consumption of RM = 100 units

  • Avg consumption of RM = 275 units

  • Carrying cost (S) = 20% p.a.

Calculate:

i) Re-order Quantity or EOQ

$$ \text{EOQ} = \sqrt{\frac{2AB}{CS}} $$

$$ \text{EOQ} = \sqrt{\frac{2 \times 30,000 \times 150}{20 \times 20%}} $$

$$ \text{EOQ} = \sqrt{\frac{2 \times 30,000 \times 150}{4}} $$

$$ \text{EOQ} = \sqrt{2,250,000} $$

$$ \text{EOQ} = 1500 \text{ units} $$

ii) Re-order level

$$ \text{Re-order Level} = \text{Maximum consumption} \times \text{Maximum level} $$

Calculate the average consumption to find the maximum level:

$$ \text{Avg Consumption} = \frac{\text{Minimum level} + \text{Maximum level}}{2} $$

$$ 275 = 100 + \frac{\text{Maximum level}}{2} $$

$$ 550 - 100 = \text{Maximum level} $$

$$ \text{Maximum level} = 450 \text{ Kgs} $$

Now calculate the Re-order Level:

$$ \text{Re-order Level} = 450 \times 8 $$

$$ \text{Re-order Level} = 3600 \text{ Kgs} $$

Illustration 2.5

Given,

  • Monthly consumption = 1500 units
  • Annual consumption (A) = 1500 x 12 = 18,000 units
  • Cost per order or Buying cost (B) = Rs 150
  • Cost per unit (C) = Rs 27
  • Carrying cost (S) = 20%

Calculate EOQ:

$$ \text{EOQ} = \sqrt{\frac{2AB}{CS}} $$

$$ \text{EOQ} = \sqrt{\frac{2 \times 18,000 \times 150}{27 \times 20%}} $$

$$ \text{EOQ} = \sqrt{\frac{2 \times 18

,000 \times 150}{5.4}} $$

$$ \text{EOQ} = \sqrt{1,000,000} $$

$$ \text{EOQ} = 1000 \text{ units} $$

Calculate the number of orders per year:

$$ \text{Number of Orders} = \frac{\text{Annual consumption}}{\text{EOQ}} $$

$$ \text{Number of Orders} = \frac{18,000}{1000} $$

$$ \text{Number of Orders} = 18 $$

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