In previous articles I've referenced the Economic Order Quantity (EOQ). This article is going to be the first of a few articles detailing various aspects of EOQ. This first post will discuss the basics and go step-by-step through an example of how to use EOQ when trying to determine how much to order for a single good that has a known projected demand.*First of all, what is EOQ?*

EOQ is a mathematical formula designed to minimize the combination of annual holding costs and ordering costs. There is a lot of hype about just in time inventory systems (JIT), which achieve smaller inventories through very frequent orders, but frequent ordering can often result in an over-spending on ordering costs. Even though companies often miscalculate their ordering costs, which makes frequent ordering seem costly, EOQ is an important tool for determining what inventory should be. Let's move on to the example to help explain what EOQ is.

Chuck Co. is a firm that manufactures toys requiring a part that costs $12, and can be received from multiple suppliers. The firm, which recently began ordering once a week instead of twice a month, in order to reduce inventory, wants to know how much it should order at a time because it has noticed that while their holding costs have decreased, they seem to be spending more on overtime for floor managers than they used to. While Chuck Co.'s inventory manager is happy, the plant manager is not sure the reduction in holding costs is worth the overtime pay. Here's the data they've provided us with:

**Demand (variable D)**

Annually, the part for the toy is consumed at a rate of **150,000 per year**. While there is seasonality in the toy industry, this firm produces at a level rate because of union agreements.

**Ordering Costs (variable S)**

Chuck Co. has identified 2 major costs associated with ordering; floor manager overtime required and plant manager time.

The floor managers find themselves with very little time to process orders during their shift. When an order needs to be made, a floor manager from the day shift needs to work 2 hours of overtime to shop the multiple suppliers and place the order. Overtime pay is *$21/hour*.

The plant manager spends 1 hour per order to approve the order, determine the tax implications of the order and authorize payments. Earning $80,000 per year and working 2000 hours per year, *the plant manager at Chuck Co. earns $40 in the 60 minutes he requires to process the order*.

**Total, the ordering cost is $82 per order.**

**Holding Costs (variable H)**

When I wrote about Holding Costs, I mentioned the different factors that drove holding costs. For Chuck Co. the most major factor is opportunity cost. Another toy in their product line is currently earning 20% a year for every dollar invested in it. Chuck Co. would like to invest more into the product line but their credit rating and unhappy investors are currently preventing this from happening. Each dollar in inventory is another dollar that could be in the 20% gain product line.

The opportunity cost for every dollar invested in inventory is the 20% that could be invested in the other toy, plus an additional 2% from rent and other various holding costs. *Ultimately, the holding cost is 22% annually.* Multiply this by the cost of the part ($12) and the **holding cost is $2.64 annually.**

**EOQ**

Using the information presented above, the EOQ formula can be used to determine the optimal order.

The formula is:**EOQ=SQRT{(2DS)/(H))}**

Plugging in the numbers given from Chuck Co. we get:**EOQ=SQRT{(2*150,000*$82)/($2.64)}= 3053**

According to these calculations, the most efficient amount ordered is 3502 per order. Spread out over the annual demand of 150,000 per year, the part should be ordered 49 times per year (150,000/3053). Seemingly, leading the once per week reorder calculation to be roughly correct, however, this calculation has an error in it.

**Common Misconceptions Regarding Ordering Costs**

Chuck Co. identified 2 major costs associated with ordering. Only one of them however is actually driven by the amount of orders placed. When using EOQ to minimize ordering costs, only costs that can actually be minimized should be taken into consideration.

Specifically, only the overtime hours in our example are true ordering costs. The plant manager definitely spends time ordering and he is getting a salary during those hours, but this salary is a part of his overall duties as the plant manager. If ordering frequency went down by 10%, it is unlikely that his hours and salary would be scaled back. His salary is a sunk cost and must be treated accordingly.

The floor managers' hours, however, actually do go up and down in accordance with the number of orders placed. Each order they place, they receive $42 of overtime compensation for. **Thus, $42 is our true ordering cost**. Let's take a look at how this affects our calculations:

**Correct EOQ=SQRT{(2*150,000*$42)/($2.64)}= 2185**

This order size leads to 68 orders per year (150,000/2185), making the old calculation, and the once per week practice wrong.

EOQ can be a very effective tool for helping to optimize inventory. However, in order for it to be effective, it requires good and thoughtful data. This means having decent demand projections, well-evaluated holding and ordering costs. The next post will discuss how much money this correct order size actually saves Chuck Co. and will cover some derivations of the EOQ formula.

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