## What is EOQ & EPQ?

Economic Order Quantity (EOQ) and Economic Production Quantity (EPQ) both are widely and successfully used models of inventory management. Economic order quantity is the optimum order size that should be placed with a vendor to minimize blockage of funds and holding and ordering costs. At the same time, it is that adequate quantity of a product or part that will ensure unstopped production or sales activity in an organization.

On the other hand, economic production quantity is the optimum lot size that is to be manufactured in a production unit to avoid unnecessary blockage of funds and excess storage costs. This production quantity is adequate to ensure uninterrupted work.

Both models aim to minimize costs in an organization by keeping control of inventory. The target is to optimize inventory utilization so that money does not block in excess inventory. Also, the company should not face a shortage of inventory due to which production and other processes get hampered. An optimum mix of major costs related to inventory, like holding costs and ordering costs, is worked out to keep costs under control.

## Assumptions EOQ and EPQ Models

A few assumptions under both the models are:

### Constant Demand and Easy Restocking

Both models assume the demand to be constant over the year. The EOQ model assumes that the product is easily available in the open market. Its replenishment will happen as soon as it reaches the minimum threshold level. Similarly, the EPQ model assumes that the production capacity aligns with the requirements. And the product can happen as the stock goes down below a minimum level. It will ensure no stock-out situation. And also successfully took care of all demand.

### Constant Price

Both models assume the price of the product to be constant all through the year. The price does not vary while making a purchase under EOQ or producing the product under EPQ; the price does not vary. Also, no discounts are on offer on quantity or value.

### Constant Quality

Both models assume that the quality of the products purchased or produced remains the same all year-round. There is no variation in it, due to which the demand also does not change.

### Holding and Ordering Costs remain Unchanged.

Holding the cost of inventory is the cost of stocking and maintaining inventory. It can be in the form of rentals for the storage area, salaries of personnel looking after the inventory, electricity bills, repairs, maintenance, etc. Ordering costs are the costs at the time of placing an order for the inventory. These can be in the form of freight, packing and forwarding charges, etc.

Both models have the assumption that these costs will remain unchanged throughout the year. Besides, the EPQ model assumes that the set-up costs of production also remain constant throughout the year. And this set-up cost will not change with the production length.

Read Economic Order Quantity(EOQ), a more detailed article.

## Calculation of Economic Order Quantity (EOQ) & Economic Production Quantity (EPQ)

### EOQ Formula

One needs to use the formula to arrive at the quantity as per this concept. The formula for EOQ is:

**EOQ**= √‾‾(2xDxO/ H) ie. square root of (2xDxO/ H).

D= Annual demand in units of a product

O= Ordering cost per order

H= Holding cost per unit of the product. The calculation for annual holding cost can be done by dividing the order quantity by two and multiplying it by the holding cost per unit of the product.

### EPQ Formula

The formula for calculation of Economic Production Quantity is:

**EPQ**= Square root of {2xDx O/ H(1-x)}

Here, x= D/ P where P= Production rate.

## Difference between the EOQ vs EPQ

Both EOQ and EPQ models are inventory-management models and have been implemented successfully across organizations. They are almost similar. The background concept and idea for both are common: to optimize the order or production quantity so that the overall cost of inventory holding remains low.

However, the key difference between the two is that the EOQ model is applied when the inventory item is ordered from a third party. The company itself is not producing the item under consideration.

On the other hand, the EPQ model comes into use when the company is the producer itself of the product or the part under consideration. Thus, the assumption of a constant lead time also arises in the EPQ model, which is not so in the EOQ model.

## Limitations of EOQ and EPQ Model

## Unrealistic Assumptions

The most significant limitation of both models is that the assumptions are unrealistic.

- Both models assume the holding cost, ordering cost, demand, price, quality, etc., of the product or part to be constant throughout the year. It is not realistic in the real world.
- Holding and ordering costs may vary due to changes in rentals, salaries of personnel, and other overhead expenses.
- Constant demand, as well as the price of a product, can hardly be constant. They fluctuate a lot in the real world.
- Consumer income, tastes, and preferences, prices of inputs and raw materials, seasonal variation in demand, etc., are key factors that will affect demand as well as price.

Similarly, the assumption of the constant quality of the product is not realistic, especially under the EPQ model. The quality of the product generally changes with every production batch. The production process also does not remain constant because of factors like an interruption in power supply, breakages, and repairs in plant and machinery, overheating, changes in the quality of inputs and raw materials, etc.

Also, the model does not consider wastages or damages in the production process due to which the product quality may go wrong, directly impacting the demand for the product.

## Differentiation Table

Basis | EOQ | EPQ |
---|---|---|

Meaning | Economic order quantity is the optimum order size that should be placed with a vendor to minimize blockage of funds and holding and ordering costs | Economic production quantity is the optimum lot size that is to be manufactured in a production unit to avoid unnecessary blockage of funds and excess storage costs |

Formula | EOQ= √‾‾(2xDxO/ H) the square root of (2xDxO/ H). | EPQ= Square root of {2xDx O/ H(1-x)} |

Production | The company itself is not producing the item under consideration | The company is the producer itself of the product or the part under consideration |

Lead Time | The presence of constant lead time is assumed | There is no such assumption |

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