Module 2 - EOQ

When we want to order inventory, say raw material for use in manufacturing, or products we want to distribute or sell retail, how much should we order and have in inventory? Obviously that depends quite a bit on how much we need based on demand. But it also is based on how much it costs to order and how much it costs to hold. The basic amount of inventory to order that provides the most cost effective amount is called the Economic Order Quantity (EOQ). This Wikipedia article explains what this is:

Economic Order Quantity (2011). Wikipedia, retrieved from http://en.wikipedia.org/wiki/Economic_order_quantity

Note that the Wikipedia article also provides discussion on some additional, more complicated inventory models.

Here is another good resource on EOQ:

Piasecki, D. (n.d.). Optimizing Economic Order Quantity (EOQ), InventoryOps.com, retrieved from http://www.inventoryops.com/economic_order_quantity.htm

What if we are not buying inventory but are making it in a manufacturing process?

In this case, there is no Order Cost, but instead there is a Set-up cost – the cost to changeover or setup the machine (or process) to produce the parts. Some setups can be long and time consuming, taking up to 8 hours. Other setups can be quite short, taking only several minutes. The cost of the setup will influence what the EOQ is. For example: suppose you have an item that costs $20 to make and it costs 10% to hold it per year, or $2. Suppose further that the setup for the machine takes 7 hours at $50 per hour, or costs $350. The EOQ for this would be 1870 units. Now suppose that you can reduce the setup time to 1.5 hours which now costs $75. The EOQ using this setup cost is 866 units. Theoretically, if you drive the setup cost to $0, the EOQ also become 0, or more realistically 1 unit. This is the idea behind lean manufacturing.

What if you don't know the costs?

How can you determine the effect of reducing SET-UP COSTS? - see the example below.

Customer orders are different than shop orders. Note that in manufacturing, production orders are sent to the production floor. These production orders often are not the same amount of quantity that is being ordered by the customer. Why? Because we are producing inventory. Lean thinking and lean manufacturing are opposed to this concept. See the information on Lean Inventory.

The effects of reducing Setup time - without knowing the costs or demand.

EOQ = Q* = SQRT(2DS/H)

D = annual demand

S = fixed order cost OR the fixed SET-UP cost

H = annual holding costs

For SHOP orders, the orders that go into the manufacturing processes, the EOQ will be based on the SET-UP costs, which is the Setup Time x the hour rate.

Let S = T*R or just TR (the setup time times the rate)

Q* = SQRT(2DTR/H)

Suppose that setup time is 4 hours.

Q* = SQRT(2D4R/H)

Suppose you can reduce setup time to 1 hour.

Q** = SQRT(2DR/H)

How much smaller is Q** than Q*?

Using algebra you can determine that:

Q* / Q** = 2 SQRT(2DR/H) / SQRT(2DR/H)

Q** = ½ Q*

By reducing the setup time by a factor of ¼ you can reduced the SHOP ORDER QUANTITY (EOQ) by ½. This means that there is ½ as much WIP inventory flowing through the shop. Suppose you could reduce the Setup time to just 15 minutes.