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Economic Order Quantity (EOQ) Calculation

The Economic Order Quantity (EOQ) model is a fundamental tool in inventory management and operations research. It helps businesses minimize the total costs associated with ordering and holding inventory. These costs typically include ordering costs (such as purchase orders, shipping, and handling) and holding costs (such as storage, insurance, and obsolescence). The EOQ model finds the optimal order quantity that minimizes the total of these costs.

The formula for EOQ is:

\[ EOQ = \sqrt{\frac{2AB}{CS}} \]

Where: - \( A \) = Annual consumption in units - \( B \) = Buying cost per order - \( C \) = Cost per unit - \( S \) = Storage or carrying cost as a percentage of the unit cost

Below are detailed illustrations of EOQ calculations for different scenarios:

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 2.2

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 2.4

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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