# Economic Order Quantity (EOQ)

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Economic Order Quantity (EOQ)

In this lesson, you’re expected to understand all the costs associated with the Economic Order Quantity (EOQ) model.

The Economic Order Quantity (EOQ) deals with defining the lot size and the frequency of purchase of products that you consume regularly.

Suppose that you drink one liter of milk per day, i.e. seven per week, and you have only two options: buy milk every day or do it weekly.

How often should you run to the store?
Buying milk every day means that you will have less capital tied up in inventory and that you save storage space. However, you need to travel to the store every day, which is costly (i.e. time, transportation, etc.)

Buying milk only once a week means that you need to tie up capital in inventory and that you need to allocate a lot of storage space to holding milk. However, you save time by traveling to the store less often. EOQ Problem Overview

EOQ sets order size for repetitive ordering process with fixed order cost.

It is based on the following trade-off:
Order size too large → too much average inventory
Order size too small → too much ordering cost

EOQ Assumptions

• Demand for the product is known and inventory is depleted at a constant, uniform rate throughout.
• The replenishment lead time is constant, independent of the demand rate and of the quantity ordered.
• All demands for the product must be satisfied (i.e. stock-out is not allowed).
• The entire order quantity is delivered at the same time.
• The cost factors do not change with time (no inflation).
• Items can be inventoried indefinitely (i.e. no obsolescence or perishability).
• Price per unit of product (i.e. sum of variable procurement costs) is constant.
• Ordering or setup cost (i.e. sum of fixed procurement costs) are constant.
• Inventory holding cost is based on average inventory.

Costs involved in the EOQ model

In the EOQ model, we want to find the order quantity that minimizes the total average cost per unit.

Three types of costs contribute towards total cost:
– Acquisition Cost
– Setup / Ordering Cost
– Holding Cost 1) Acquisition Cost: represents the variable portion of the procurement costs, that varies according to the quantity ordered

2) Setup / Ordering Cost: represents the fixed portion of the procurement costs, that occur every time an order is placed, independent of the quantity.

3) Holding Cost: the cost of holding units in inventory. Average acquisition cost in the EOQ model

– Let c represent the acquisition cost per unit.
– Let Q represent the order quantity
– Let D represent the demand per year
– Since stock-outs are not allowed and we know the demand, we always buy the quantity that will satisfy the demand in a given period.
– Average acquisition cost per year is then D * c, which does not depend on Q. Average ordering cost diminishes as we increase the order quantity

– Let A represent the ordering cost
– Let Q represent the order quantity
– Let D represent the demand per year
– The total number of orders placed in a year is going to be D/Q
– Average ordering cost per year is then A * D/Q Average holding cost in the EOQ model

Average holding cost increases with the order quantity.

– Let h represent the cost of holding one dollar of inventory during a year.
– Let c represent the acquisition cost per unit
– Then hc represents the cost of holding one unit of inventory during a year
– Let Q represent the order quantity
– Since demand is constant, average inventory will always be Q/2
– Average holding cost per year is then Q/2 * hc The point Q* is the EOQ formula, which represents the order quantity that offers the optimal cost to our given setting.
If we sum everything up, then we have TC(Q) = (A * D/Q) + (hc * Q/2) + Dc as the total inventory cost per year.

We can see on the chart below that, at the beginning, the total cost diminished as we increase the order size; this is up to a certain point, on which the total cost increases because of the holding costs.

We want to find a quantity Q* that minimizes the total cost. Problem

A manufacturer uses a specific component at a steady rate of 100 units per week (assume 52 weeks per year). The company purchases this component from a supplier at a cost of \$50 each. The purchasing department estimates that it costs \$175 to process an order, and the accounting department estimates the cost of carrying inventory at 20% per year.

What is the optimal order quantity?

Solution

First, we identify the problem parameters:
A = \$175
c = \$50
I = 20% per year
hc = 20% x 50 = \$10 per year

Demand rate is given per week but carrying cost is per year (always convert the parameter to a common unit).

D = 100 units/week x 52 weeks/year = 5,200 per year

Now, we can find Q*. [Optional] How to Calculate Economic Order Quantity
Watch this 5-minute video of an EOQ example by Nick Harrison: