What’s wrong with EOQ?

Economic Order Quantity (EOQ) EOQ is essentially an accounting formula that determines the point at which the combination of replenishment costs and inventory carrying costs are the least. The goal being to minimize both the ongoing costs of carrying inventory and the expenses involved with replenishing inventory.

The basic EOQ formula looks like this:

As you can see, this formula attempts to balance (simultaneously) the following factors related to the business expense linked to holding and replenishing inventory:

1. Usage rates – how many are sold or consumed over a period of time (one year in the basic formula)
2. Cost of replenishment – how much it costs the firm to replenish a single inventory item (SKU) from the point of recognizing the need for replenishment through putting the quantities back on the shelf
3. Carrying costs – all of the costs and expenses related to storing and handling of the inventory quantities held

Let us take a look at how these factors interact in a practical example:

In our example, we have an item that has a cost of $25 per unit, and the average daily demand is five (5) units. For this firm, the cost of replenishment is slightly above average—sitting at $30 per PO line processed for inventoried goods.

Observe what happens to the EOQ on this item as the cost of carrying inventory moves through the range from five percent (5%) to 40 percent.

When inventory carrying costs are very low compared to the cost of replenishment (five percent and $30, respectively), EOQ recommends big orders. In this case, each order would support more than 75 days of average demand.

On the other end of the spectrum, when carrying costs are quite high (40 percent) relative to the cost of replenishment, EOQ suggests smaller inventories (as the result of smaller orders) and the order cycle is slashed to almost one-third its former value (now, just over 26 days).

Underlying assumptions

The assumption being made in the construction of the EOQ formula is that the cost of carrying inventory is linear. That, at a five percent rate, a one dollar decrease in inventory on-hand will lead to a five cent reduction in carrying costs to the firm. Similarly, at a 40 percent carrying cost rate, a one dollar decrease in inventory on-hand will lead to a 40 cent decline in carrying costs.

Unfortunately, the linear relationship assumed by the EOQ formula simply does not exist.

When calculating the cost of carrying inventory, a large number of factors are generally considered:

1. Warehouse space rental (or equivalent)
2. Utilities expense
3. Property tax expense
4. Maintenance expenses on the warehouse and warehouse equipment
5. Inventory write-offs/write-downs
6. Other inventory shrinkage
7. Financing expenses for the warehouse, the equipment, and the inventory itself
8. Insurance expenses on the warehouse and the inventory
9. Labor expenses related to warehouse operations

When inventory is reduced $1,000 in a warehouse with a calculated 25 percent carrying cost, what are the likely real impacts on expenses for carrying inventory?

1. Warehouse space rental (or equivalent) – no change
2. Utilities expense – no change
3. Property tax expense – no change
4. Maintenance expenses -  no change
5. Inventory write-offs/write-downs – possibly some change, but not necessarily at the same “average” rate
6. Other inventory shrinkage – same as above
7. Financing expenses for the warehouse, et al -  no change
   Financing expense on the value of the inventory – some change possible
8. Insurance expenses on the warehouse, et al – no change
   Insurance expenses on inventory – some change
9. Labor expenses – no change

In short, only three of the nine items involved in calculating the cost of carrying inventory would likely change based on $1,000 reduction in inventory. That’s because increases or decreases in the volume and dollar amount of inventory held in a warehouse operations produce relatively large but non-linear changes operating expenses.

As inventory grows, changes like adding a second shift in the warehouse, acquiring additional warehouse space, or adding manpower to handle increased volumes happen incrementally. The EOQ formula has no way to account for these non-linear changes to operating expenses. Therefore, your EOQ decision-making my be entirely off the mark for success and increased profits.

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What’s the answer?

To manage your inventory quantities, I would highly recommend the application of Dynamic Buffer Management. [Click on the link and read the article there.]

To deal with non-linear changes in your enterprise—decisions that may lead to major changes in inventories (increases or decreases)—you need a broader formula that considers your system (your enterprise) as a whole. That would be this one:

Where,

• ROI = Return on Investment
• delta-T = Change in Throughput 
• delta-OE = Change in Operating Expenses
• delta-I = Change in Inventory or demand for other Investment

This formula would cover changes like adding a second shift (change in Operating Expenses) or building a new warehouse (change in Investment).

Think about. Contact me if you need further clarifications.