# Economic Batch Quantity (EBQ)

## Definitions

Economic Batch Quantity (EBQ), also known as the optimum production quantity (EPQ), is the order size of a production batch that minimizes the total cost.

## Explanation

Batch production is a technique which is commonly used today for distributing the total production in a series of small batches rather than mass producing in one go.

Sometimes the production of goods in batches is necessary because, for example, certain equipment used in manufacturing (e.g. dyes) may wear out and need replacement before the production can run again.

Batch production may be desirable in other cases as well. For example, where the objects being produced are perishable, the entire production requirement for say a year can’t be manufactured in a week as it might cause the goods to expire after some time. Batch production also reduces the risk of obsolescence as any minor changes required in the specification of goods (e.g. size, color, etc.) can be made in future batches according to the feedback received from customers or retailers instead of producing everything in one go and hoping for the best.

Whereas EOQ is suitable for determining the order size when the parts, materials or finished goods are ready to be delivered by external suppliers when the order is placed, EBQ is used to determine the size of a production run (i.e. batch size) when the manufacturing takes place internally and any raw materials or parts required for production are either acquired internally or are supplied incrementally by other companies according to the production requirement.

## Formula

 Economic Batch Quantity = √ 2 x Cs x D Ch(1 - D/P)

Where:

• Cs is the setup cost of a batch
• D is the annual demand
• P is the annual production capacity
• Ch is the annual cost of holding one unit of finished inventory

The formula for calculating EBQ is very similar to EOQ with one notable difference in the denominator. The cost of holding in EBQ formula is decreased by the amount of inventory that will be produced and sold on the same day therefore not contributing to the annual cost of holding the inventory.

### Example

Sarah owns and operates a small factory that manufactures plastic bottles which she sells to bottling companies.

• Annual demand is 1 million bottles spread evenly over the year
• Setup cost is \$5000 per batch
• Holding cost is \$3 per annum for each bottle
• Maximum production capacity is 2 million bottles per annum
• Currently, bottles are manufactured in 10 batches
• A. Find the optimum production quantity that Sarah should produce to minimize her costs
• B. Calculate the current annual holding cost and setup cost
• C. Calculate the savings to Sarah if she adopts the EBQ

Solution A: Optimum Production Quantity

Economic Batch Quantity

 = √ 2 x Cs x D Ch(1 - D/P)

 = √ 2 × 5000× 1,000,000 3 x (1-(1,000,000/2,000,000))

 = √ 10,000,000,000 1.5

 = 6,666,666,666

 = 81,650

Sarah should manufacture bottles in batches of 81,650 units.

Solution B: Current Costs

Batch Quantity = Annual Demand ÷ Number of batches

= 1,000,000 ÷ 10

= 100,000 units

Annual Holding Cost = (Batch Quantity/2) × Ch × (1- D/P)

= (100,000/2) × 3 × (1-(1,000,000/2,000,000))

= \$75,000

Setup Cost = Number of setups × setup cost

= 10 × 5000

= \$50,000

Total Current Cost = (\$75,000 + \$50,000) = \$125,000

Solution C: Savings from EBQ

Annual Holding Cost:

= (Batch Quantity/2) × Ch × (1- D/P)

= (81,650/2) × 3 × (1-(1,000,000/2,000,000))

= \$61,238 (A)

Setup Cost

Number of batches = 1,000,000 ÷ 81,650 = 12.2475

Setup Cost = Number of batches × Cost of setup

= 12.2475 × \$5000 = \$61,23 (B)

Total Cost (EBQ) = (A) + (B) = \$122,476 (C)

Total Current Cost = 125,000 (D)

Savings = (D) - (C) = 2,524