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.
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 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
• 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.
– Acquisition Cost
– Setup / Ordering Cost
– Holding Cost
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.
– 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.
– 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
– 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
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.
What is the optimal order quantity?
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*.
https://www.youtube.com/watch?v=A88uoWbxG2M
https://www.youtube.com/watch?v=AYpjPWmlyHM
* Notation may differ across different examples.