# Economic Order Quantity Model (EOQ)

As the name suggests, **Economic order quantity (EOQ) model** is the method that provides the company with an order quantity. This order quantity figure is where the record holding costs and ordering costs are minimized. By using this model, the companies can minimize the costs associated with the ordering and inventory holding. In 1913, Ford W. Harris developed this formula whereas R. H. Wilson is given credit for the application and in-depth analysis on this model.

**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:

Where Q = optimal order quantity

D = units of annual demand

S = cost incurred to place a single order or setup

H = 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 **

Following are the underlying assumptions for 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.

These underlying assumptions are the key to the economic order quantity model, and these assumptions help the companies to understand the shortcomings they are incurring in the application of this model.

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Inventory Management at ABC organizationABC is an organization that procures a product PQ from another organisation. ABC requires 11,000 units of PQ every year. The cost of the product is Rs.5 per unit and its ordering cost is estimated to be Rs.100 per order. The cost of carrying inventory is 25%. The consumption rate of PQ in the organization is uniform. Therefore, ABC needs to spend a huge amount on the procurement of product PQ. The CEO of ABC called the production manager of the organization to discuss whether the manufacturing of the product PQ would be more economical for the organisation.

The production manager conducts a research and identifies equipment that can be used for producing PQ. This equipment can yield 100 units of PQ per day. The cost of producing a single unit of PQ by using the equipment is Rs.3.50 per unit. In addition, the setup cost of equipment and inventory carrying costs are Rs.50 per setup and 25%, respectively. From the preceding data, it is found that the production of product PQ would be more beneficial for ABC. Therefore, ABC has purchased the equipment and has started in - house production of PQ. This has reduced the cost of procuring PQ almost five times.

QuestionCalculate the EOQ. Analyse if EOQ has helped ABC in managing inventory.

1) Calculation of EOQ

2) Briefly describe situation that led to the use of the EOQ model.

3) Assess the pre EOQ situation to post EOQ situation

4) Summarise if EOQ has helped ABC

Very helpful clear explanation