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Economic Order Quantity (EOQ) Calculation

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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