Economic order quantity (EOQ)

Definition and Meanings

Economic order quantity (EOQ) is the order quantity of inventory that minimizes the total cost of inventory management.

EOQ refers to the size of the order which gives the maximum economy in purchasing any material. It is the optimum of standard ordering quantity.

Explanation

This concept relates to the quantity of materials to be purchased by the purchasing department. Economic order quantity is that size of the order which gives maximum economy in purchasing any item of material. In order to determine the economic or optimum order quantity, an analysis of the various costs associated with the ordering quantity is made. These costs may be divided into two parts:

(a) Material acquisition costs, and
(b) Material carrying costs.

Material acquisition costs arise on account of having to process an order. A part of the wages and operating expenses for departments like production control, purchasing, receiving and stores is incurred for purchasing and possessing the materials. Materials carrying costs include interest charges on investment in materials, insurance costs, storage costs etc. These two types of costs behave quite differently.

The material acquisition costs are related to the number of orders placed during a given period. On the other hand, carrying costs, which are variable or semi-variable in nature, tend to change nearly in direct proportion to the level of stock carried in the manufacturing concern.

Purchasing or buying in large quantities implies low acquisition or purchasing costs (number of purchase orders placed with the suppliers being small) and high carrying costs on account of the amount of stock carried during this period being more. On the other hand, purchasing in small quantities implies high purchasing or acquisition costs and low carrying costs.

The most advantageous or economic quantity will be at a point where the acquisition costs and the costs of carrying stock are equal i.e., where total costs to order and to carry material are minimum. The other terms used for Economic Order Quantity are ‘Economic Lot Quantity‘ and, ‘Economic Buying Quantity.

Two important categories of inventory costs are ordering costs and carrying costs. Ordering costs are costs that are incurred on obtaining additional inventories. Carrying costs represents the costs incurred on holding inventory in hand. Total inventory costs are ordering costs plus carrying costs. We need to minimize total inventory costs and the economic order quantity (EOQ) model helps us to find out the point where the total inventory costs will be at the minimum. For this purpose, the following formula is devised:

EOQ Formula

The common formula used for computing Economic Order Quantity (EOQ) is:

Economic order quantity (EOQ) Formula

Where

AR =  Annual requirements
OC = Per unit cost
CC = Carrying cost per unit per year of materials inventory

Factors Governing the fixation of Economic Order Quantity (EOQ)

The following factors govern the fixation of EOQ:

1. Procurement cost. Cost of obtaining quotations, preparation of order and its placement, follow-up action, receiving and Inspection, payment of bills, etc., are included in the procurement cost, which can be also called as the cost of acquisition salary of the men involved in all the processes is the main item to be considered while calculating the procurement cost.

For a single order procurement cost is the total cost, obtained by adding up all the above costs, divided by the number of orders placed during that period; For obtaining the procurement cost of multi-item orders the total cost is divided by the number of items ordered during the given period of time.

2. Carrying cost. This is calculated by taking into consideration the insurance premium, depreciation, obsolescence, storage, preservation costs and interest on value of stock held including that of handling and other allied costs. This cost is also known as possession cost. These costs vary from item to item and plant to plant. Average carrying cost is taken as 15% to 25% of the value of average working cost which comes to usually 50% of the order quantity.

Example

The XYZ Equipment Company estimates its carrying cost at 15% and its ordering cost at $9 per order. The estimated annual requirement is 48,000 units at a price of $4 per unit.

Required 

(i). What is the most economical no. or units to order?
(ii). No. of orders to be placed in a year
(iii). About how often will an order need to be placed?
(iv). Ordering Cost
(v). Carrying Cost
(vi). Combined ordering and holding cost at economic order quantity (EOQ)

Solution

(i). No. of units to order:

Economic order quantity (EOQ) Formula

Economic order quantity (EOQ) example

Economic order quantity (EOQ) solution

Economic order quantity (EOQ) explanation

(ii). No. of orders to be placed in a year:

No. of orders per year = Annual requirement / EOQ

= 48,000 / 1,200

= 40 orders

(iii). About how often will an order need to be placed (i.e., frequency of orders):

Frequency of orders = No. of days in one year / No. of orders

= 360 / 40

= 9 days

(iv). Ordering Cost:

= No. of orders per year x Cost per order

= 40 x 9

= $360

(v). Carrying Cost:

= Average units x Carrying cost per unit

= (1,200/ 2) x 1.35

= 600 x 1.35

= $810

(vi). Combined ordering and holding cost at economic order quantity (EOQ):

= Ordering cost + Carrying cost

= $360 + $810

= $1,170

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