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.”
|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).
- Dave Piasecki at Inventoryops.com writes about Optimizing EOQ.
- Picture of an EOQ slide ruler from the days before calculators.