This post, the second in our inventory management series, introduces the EOQ inventory management model and walks through usage, decision criteria, inputs, and tradeoffs. And, of course, we dive into manufacturing nunchucks because we all know it's an untapped gold mine.

For additional resources, check out:

- The Ondema Guide to Production Scheduling
- Minimizing Makespan, Explained Using Attack Helicopters
- Level Up Production Bottleneck Hunting With These Tips
- Manage Production Queues Like a Boss
- Inventory Management Explained With Nunchucks - Part One

## Why is managing inventory a big deal?

Inventory affects almost every aspect of your business's financial position. Business revenue is driven by product availability being closely matched to demand. Just-In-Time or Continuous Flow distribution frameworks can be the largest drivers of Cost of Goods Sold (COGS) and expenses.

In short: good inventory management is critical to a business's survival, let alone profitability.

In this post, we'll touch on the EOQ inventory management model. Our previous post introduced the Newsvendor model. Next up is Q/R.

Not only are these models industry-proven, but they form the foundation for almost every inventory management software solution on the market, even the ones with seven-figure price tags.

## The EOQ model

The Economic Order Quantity (EOQ) model helps companies choose optimum stocking quantities (Q) to minimize inventory costs such as holding, shortage, and order costs.

Whereas the Newsvendor model is best for seasonal products when demand is unknown or uncertain, the EOQ model is best used for functional products (e.g., toothpaste) where demand is known and reasonably constant, order lead time is somewhat negligible (the model treats it as instantaneous), each order arrives at once, and businesses can observe inventory levels to make restocking decisions.

Note: the Q/R model, which we'll tackle in the next post, accounts for lead time and demand uncertainty.

Graphically, the EOQ process looks like this:

Credit: Taylor (2006).

Inventory is stocked at quantity *Q*. As demand whittles down inventory levels, an order is placed when inventory reaches a certain level such that the next order quantity* Q* arrives just as the first is. depleted.

Before we dive into the Economic Order Quantity formula, let's define variables:

*Q*is the order quantity that minimizes total cost per unit time. We want to minimize*C(Q)*.*K*is the fixed ordering (i.e., setup) cost per order.*c*is the purchase cost per unit of goods.*D*is the demand per unit time.*h*is the inventory holding cost per unit of goods per unit time.*i*is the interest rate per unit time such that*h*=*i***c*.

Without further ado, allow me to barf a bunch of formulas on the page so we can break them down:

So what are the tradeoffs in the equations above? Fixed ordering cost and inventory holding costs.

If you place a big inventory order *Q*, your inventory holding costs will be high since there's more stuff to stock once the order arrives. But because you're placing large orders less frequently, your fixed ordering costs are lower. Conversely, if you place smaller inventory orders, your inventory holding costs are low but the fixed ordering costs are higher because they happen at a greater frequency.

What does this all mean? Order quantities that minimize overall costs, which is what we want, happen when fixed inventory costs per unit time equals inventory holding costs per unit time. That results in the lowest overall total cost:

Credit: Boron (2014).

## So how many nunchucks should we stock?

Yeah, how many should we stock?

In the previous post, we used the Newsvendor model to figure out the stocking quantity *Q* of Dan's Luxury Nunchucks - **LuxChucks™** to maximize profits when demand is uncertain or unknown.

LuxChucks were a hit, but the market size is small. If we want to achieve global ninja weapon market domination we need a nunchuck for the masses. That's why we introduced Dan's Tough Nunchucks - **ToughChucks™** for the quality and cost-conscious ninja weapons enthusiast.

Here's the data:

- It costs $2 for me to purchase each ToughChuck from my OEM/supplier in Centralia.
- There is a US customs fee of $250 for each shipment of ToughChucks, regardless of the quantity ordered.
- Demand for ToughChucks is 400 per week.
- My annual inventory holding cost is 30% of the purchase cost.

Let's calculate some costs:

- Purchase costs:
- $2 per week * 400 per week = $800 per week

- Inventory holding costs:
- 30% annual holding costs, so it costs $2 * 30% = $0.60 to hold one ToughChuck for one year.
*h*= $0.60 annual holding cost / 52 weeks in a year = $0.01154 to hold one ToughChuck for one week.- Average inventory =
*Q*/ 2 - Average inventory per unit time =
*h***Q*/ 2

- Fixed ordering cost:
- Regardless of quantity ordered,
*K*= $250. - Time between orders =
*Q*/*D* - Setup cost per unit time =
*K*/ (*Q*/*D*)

- Regardless of quantity ordered,

Putting it all together:

My EOQ is 4,164 ToughChucks, rounding up since I can't order 0.05 units. Interval between orders and annual inventory costs are:

You thought this was the end of the post? Not so fast.

## Bulk discounts on ToughChucks?!?! Oh you know it!

Let's examine a couple different scenarios. My ToughChuck OEM/supplier in Centralia offers a 5.0% discount on purchase price for orders 10,000 units or larger. My EOQ above is well below that number. Should I consider buying in bulk at a lesser frequency to get the discount?

We'll use these scenarios to evaluate the decision:

- Original
*Q*of 4,164 units. - Finding the new
*Q*with the 5% purchase discount. - A large
*Q*of 10,000 units. - An order
*Q*with the discount that results in the same total cost per week as #1.

Credit: adapted from DeHoratius (2015).

What is the takeaway? I should order in bulk to get the discount. In fact, ordering 14,834 ToughChucks results in the same total cost per week ($848.04) as my original EOQ of 4,164!

## That's all for today, folks

In the next blog post, we'll dive into the Q/R inventory management model which does a better job of accounting for lead time and demand uncertainty. Basically, it's the uber-talented lovechild between the Newsvendor and EOQ models. I bet that's a sentence you never expected to read.

Until next time,

DB

*Ondema Intern for Life*

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