A day ago I had a debate/discussion with a fellow lean thinker on EOQ, or Economic Order Quantity. It seems some think EOQ is incompatible with Lean and Just In Time. So lets define what we mean by EOQ. EOQ was first developed by F. W. Harris in 1915, though R. H. Wilson is credited for his in-depth analysis of the model. Calculation of the simple form of economic order quantity is not difficult if you remember:

**“The square root of two Quarter Pounders (w/) Cheese.”**

### EOQ=√(2QP/C)

where | Q = Quantity in annual units |

P = Placing an order cost | |

C = Carry costs |

EOQ is our economic order quantity, or how much we will make or buy to minimize our total costs Q is the demand rate for our product P is our ordering or set up cost, this may be the cost of delivery of raw material, changing a die in a press, setting up an assembly area, all costs that under normal accounting principals are not considered direct labor costs and in some cases are rolled up into overhead costs C is the carrying cost which is the actual product cost required to produce an item, again this can be the unit cost of raw material, the direct labor and material costs, etc. times the bank or opportunity rate of inventory. For example if our average inventory is $10,000, and we could earn about 5%, or $500 (5% of $10,000) so we are missing out on an opportunity to earn $500 from the bank for our $10,000 investment in inventory. Also, the EOQ is based on a couple of assumptions: i) the demand rate is constant, and ii) stock is replenished as soon as it is depleted. What becomes evident in looking at the EOQ is that our lot size is proportional to our set-up costs and our demand rate, and inversely proportional to your product costs and the bank rate. So as you travel along your lean journey and start making some real progress your MRP may be giving you some undesirable results. For example; when you reduce your product costs your EOQ goes up and your inventory levels will go up which is contradictory to one of the expected benefits of your lean journey, i.e. inventory reductions. Also, one of the advantages of low interest rates is that you’d be able to borrow at a good rate to build a new warehouse for all of that excess inventory. So, don’t be fooled! You need to ensure that your inventory holding costs C are reflective of all the costs of inventory. Holding costs C won’t be prime plus, it can often be two or three times prime when you include warehouse rent, depreciation, insurance, taxes, cycle counting, obsolescence. You don’t want to forget the forklift driver and the forklift to move all this material around and the scrap created by engineering change orders and damage. Don’t forget the planning department, controlling the inventory is part of the cost to hold it as well. These costs can be 40% or more of the value of the inventory and are unlikely to be less than 15%.

What then of Lean and Just-In-Time with its philosophy of (essentially) very small orders/levels of stock (i.e. EOQ=1). Is thhere a contradiction between EOQ and Lean?

In fact there need not be. This is because in JIT we notice that we *need not* take ordering and holding cost as fixed. In particular, if we can reduce the cost of ordering then the EOQ will get smaller as well. For example, if we were to reduce P by a factor of 4 we would reduce total cost by a factor of 2 (note the EOQ would change as well, being halved). This, in fact, is exactly one of the ideas behind JIT to reduce (continuously) the cost of ordering P and holding cost C so as to drive down total cost.

Hence, when we are able to build close links with our suppliers so as to reduce ordering cost dramatically it becomes, just by a straightforward application of the EOQ formula, much more attractive to have small order quantities. In the limit, if the ordering cost P is zero (or the set up cost is zero), i.e. ordering is free, then we order each and every unit as we need it, that is one-piece flow (remember here our EOQ model assumes a zero lead time, i.e. orders received as soon as they are placed).

In summary then in order to reconcile JIT and EOQ we do not take cost of ordering P and holding cost C as fixed but seek to continuously to reduce them, thereby reducing the EOQ thereby simultaneously reducing the total annual cost.

- Harris, F. W.
*Operations Cost*(Factory Management Series), Chicago: Shaw (1915). - Wilson, R. H. “A Scientific Routine for Stock Control” Harvard Business Review, 13, 116-128 (1934).
- Wikipedia
- Dave Piasecki at Inventoryops.com writes about Optimizing EOQ.
- Picture of an EOQ slide ruler from the days before calculators.

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Ponders Corp., is trying to improve its inventory control system and has installed an on-line computer at its retail stores. Fisk anticipates sales of 75,000 units per year, an ordering cost of $8 per order, and carrying costs of $12.0 per unit.

a. What is the economic ordering quantity?

b. How many orders will be placed during the year?

c. What will the average inventory be?

d. What is the total cost of ordering and carrying inventory

Alice,

Assuming your numbers are correct:

a.

EOQ = square root of (2 * 75000 * 8.00) / 12.00

EOQ = square root of 100,000

EOQ = 316

b.

# orders per year = 75000/EOQ = 237, but this could be way off. How many stores? What do you know about the demand; flat, growing, noisy or stable?

c.

Average inventory – can’t answer that without knowing how many stores, starting inventory, safety stock, supplier lead time, supplier minimum order quantity, etc. At first blush I’d say it won’t be much, could be just a few days worth.

d.

Total cost of ordering = 316 * 8 = $2528.

Total cost of inventory carrying cost (see c.)

And by the way, who is Fisk?

i am doing a report, topic called” how EOQ can be applied in the retail market nowsdays”. i just found the theory support , but i can’t find the real data support me . i wanna through ”pull and push” system to explain the degree of aopting EOQ model in retail industry. If i need to find the data, which sort of data i need to find ? My assumption, that’s found out the real EOQ of one or two of the products, and comparsion with the store actual order quantity, and find that the different. could you help me solve my foolish questions? thanks

Sharkong,

Q is the annual sales quantity. This can be history or forecast. For each item how many are you going to sell?

P is the cost to order or buy more product including shipping, salary for purchasing department. How many purchasing people? How many purchase orders do they make every year? Figure out how much it costs to make one purchase order.

C is the cost to hold the stock. What is the cost of the product? What is the cost to borrow money or interest rate. What is the cost for the warehouse and all the people who move, count, inspect the product?

Does this help?

yeah~ your answer is very useful. Thanks a lot

However, such data is a confidential information, i’m just a student,

how can i obtain such infromation in a more easy way? such as internet, library ?

Anyway, thank for your answering!!! i just guessing will you reply me!! It’s really fun 🙂

what are the limataion of eoq.

Tolani, the EOQ formula “blows up” when the cost to place an order (or set up a machine)goes to zero. In the lean world we work toward single piece flow. We take hour long machine or process changeovers and find ways to get them done in minutes. When changeovers are minutes EOQ is irrelevant. EOQ Thinking usually goes in the other direction – it helps people justify large batches.

The EOQ formula is a classical and elegant formula but it not longer fits the world of business today. First, it is only based on minimizing variable cost and the cost to order in the age of e-commerce has been drastically reduced. Furthermore, the EOQ does not factor in safety stocks etc…

That is why we developed a new model based on a better metric – economic value added (also known as economic profit). We determine the safety stock and the order quantity at the point of maximum economic value added. We utilize Lean Six Sigma Methodology by utilizing color coded kanbans to communicate inventory status and maintain optimum levels.

We make doing inventory order management right easy.

I have an assignment that asks us to explore the limitations of EOQ relating to externalities which may be more important than the model’s cost terms. Would this refer to things like environmental impacts, defective product recalls or repairs, depletion of resources, etc.?

agree with john. not all the formula will work, things are processing fast

Does anyone know why (EOQ = square root of 2 X QP/C) it is two times? Why not 3 x QP/C

Because the average inventory is half of the max-min Q. Think of a saw tooth time series graph where inventory goes up upon receipt and then declines as consumed until the next receipt. The average inventory is the area under the curve, or simplistically (max inventory – min inventory)/2

Read http://en.wikipedia.org/wiki/Economic_order_quantity

for a good write up on the total cost function.