# Economic Order Quantity (EOQ)

Economic Order Quantity model is the inventory management technique for determining
the optimum order quantity which is the one that minimizes the total of its ordering
and carrying costs. It also balances the fixed ordering costs against variable ordering
costs. The EOQ is the optimum amount of goods to order each time to minimize total
inventory costs. EOQ analysis should be applied to every product that represents
a significant proportion of sales.

Thus, the EOQ analysis provides answers to the following order quantity problems:

- How much of inventory should be bought in an order on each replenishment?
- Should the quantity be purchased be large or small?
- Should the requirement of materials during a given period of time be purchased in one lot or should it be purchased in instalments?

__Assumptions of EOQ model:__

- Demand is known with certainty and is constant during the period.
- Depletion of stock is linear and constant.
- The time interval between placing an order and receiving delivery (lead time), is constant.
- The orders placed to replenish inventory stocks are received at exactly that point in time when inventories reach zero.

__EOQ Formula:__

EOQ = √2SP / C

Number of orders to be placed in a period = S / EOQ

Where: | S | = | Annual usage in units |

P | = | Ordering cost per order | |

C | = | Carrying cost per unit |

Number of orders to be placed in a period = S / EOQ

*Figure showing EOQ Point:***A Company is determining its frequency of orders for Product A. Each product A costs $20. The annual carrying cost is $400 and the cost per order is $15. The company expects to sell 50 units of Product A each month. It has also decided to maintain an average inventory level of 40 units. Find the EOQ.**

*Example:*Solution:

S (Annual usage in units) => 50 units per month x 12 = 600 units annually.

P (Ordering cost per order) => $15

C => Average inventory x Carrying cost per unit. In this case, $400 is the total carrying cost annually. Therefore, carrying cost per unit = $400 / 40 = $10 per unit.

EOQ = √2SP / C => = √(2 x 600 x 15) / 10 => 42 units (after rounding)

Number of orders per year = S / EOQ => 600 units/42 = 14.29 or 14 orders (rounded)

__Limitations of EOQ Model:__

- The assumption of constant usage and the instantaneous or immediate replenishment of inventories are not always practical.
- Safety stock is always required because deliveries from suppliers may be delayed for reasons beyond control. Also because there may be an unexpected demand for stocks.
- EOQ assumes that the demand is constant and known with certainty which always is not the case. Demand may rise and fall depending upon various factors leaving a certain degree of uncertainty behind it.
- Computational problems may arise and hence the number of orders to be placed may not be always 100% accurate if fractions or decimals are involved.

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