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ECONOMIC ORDER QUANTITY

ECONOMIC ORDER QUANTITY

Definition

The economic order quantity (EOQ) is a model that is used to calculate the optimal quantity that can be purchased or produced to minimize the cost of both the carrying inventory and the processing of purchase orders or production set-ups.

Formula

Following is the formula for the economic order quantity (EOQ) model:

EOQ = √(2AO/C)

Where Q = optimal order quantity

A = units of annual demand

O = cost incurred to place a single order or setup

C = carrying cost per unit

This formula is derived from the following cost function:

Total cost = purchase cost + ordering cost + holding cost

Limitations of the economic order quantity model:

It is necessary for the application of EOQ order that the demands remain constant throughout the year. It is also necessary that the inventory be delivered in full when the inventory levels reach zero.

Underlying assumption of the EOQ model

Without these assumptions, the EOQ model cannot work to its optimal potential.

  • The cost of the ordering remains constant.
  • The demand rate for the year is known and evenly spread throughout the year.
  • The lead time is not fluctuating (lead time is the latency time it takes a process to initiate and complete).
  • No cash or settlement discounts are available, and the purchase price is constant for every item.
  • The optimal plan is calculated for only one product.
  • There is no delay in the replenishment of the stock, and the order is delivered in the quantity that was demanded, i.e. in whole batch.

 

Example

ABC Ltd. is engaged in sale of Metal Toy Cars. Its cost per order is 400 and its carrying cost unit is 10 per unit per annum. The company has a demand for 20,000 units per year. Calculate the order size, total orders required during a year, total carrying cost and total ordering cost for the year.

Solution

EOQ = √(2 × 20,000 × 400/10) = 1,265 units

Annual demand is 20,000 units so the company will have to place 16 orders (= annual demand of 20,000 divided by order size of 1,265). Total ordering cost is hence 64,000 (400 multiplied by 16).

Average inventory held is 632.5 ((0+1,265)/2) which means total carrying costs of 6,325 (i.e. 632.5 × 10).

ECONOMIC ORDER QUANTITY

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ECONOMIC ORDER QUANTITY

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