I was reminded of this while reading Mr. Koray Köse’s great piece on how our supply chains are literally drowning in wannabes who mistake theory for expertise where he accurately and astutely noted that most of today’s so called “experts” could not pass his Economic Order Quantity (EOQ) exam question. And I totally agree. Because

1) Math (where competency in many Western nations decreases every year and where the US is literally becoming math stupid, as reflected in the latest OECD ranking which puts it 25 out of 31 “developed” countries that were globally measured with countries like Croatia coming in ahead of it).

2) No real understanding of supply chain or total supply chain cost!

3) Even less understanding that your EOQ (Economic Order Quantity) is not your suppliers EPQ (Economic Production Quantity) and for high cost/complex products, this can sometimes (but not always) be much more important (and impactful) than the classic EOQ formula would dictate.

Mr. Köse illustrates this deftly when he shared one of the questions he uses to gauge whether or not his MBA students truly understand EOQ. The core variant of the problem he shared with us was this:

1. The purchasing manager for Spacely Sprockets orders mechanical gears from an industrial supplies distributor, Cogswell Cogs.
2. Spacely Sprockets uses 5,000 gears per year.
3. Annual inventory carrying costs are 20% and order costs are 3,400 per order.
4. The following order discount price schedule is provided by Cogswell.
   • 0,200-0,999 $1300 / unit
   • 1,000-2,999 $1250 / unit
   • 3,000-4,999 $1200 / unit
   • 5,000+      $1175 / unit

5. Determine the optimal order quantity, total cost, and actual per unit cost (once order costs and inventory carrying costs are taken into account).

Now, if you were a prepared student, you might have memorized the classic EOQ formula:

• EOQ = √ ( (2 x ACPO x AUU) / (UC x CCP) )

where

• ACPO = Acquisition Cost Per Order = 3,400
• AUU = Annual Usage in Units = 5,000
• UC = Unit Cost
• CCP = Carrying Cost Percentage = 0.20

and this leaves you with

• EOQ = √ ( 34,000,000 / (0.2 * UC) )

and you can work this out at each price break:

• 1,300: √ ( 34,000,000 / 260 ) = √ (130,769) = 362
• 1,250: √ ( 34,000,000 / 250 ) = √ (136,000) = 369
• 1,200: √ ( 34,000,000 / 240 ) = √ (141,666) = 376
• 1,175: √ ( 34,000,000 / 235 ) = √ (144,680) = 380

which indicates the first price bracket is the correct one for you, and you should be making 13.8, rounded to 14, orders every 26 days (and net a total volume of 5,068 units over the year) and, on average, you will carry each unit of inventory for 13 days.

• unit cost: 5,068 * 1,300 = 6,588,400
• inventory carrying cost: 13/365 * 0.2 * 6,588,400 = 46,931
• order cost: 3,400 * 14 = 47,600
• total cost: 6,682,931
• unit cost: 1,319

But this is NOT an EPQ for the supplier, which means that you might be paying more than you need to. To figure that out, you have to analyze the costs at each breakpoint that is reasonable for you.

These are:

• 362, your computed EOQ, with 14 orders per year
• 1014, the first discount tier, at 5 orders per year every 73 days, with 36.5 days of inventory on average
• 5,068, at the third discount tier, at 1 order per year every 365 days, with 183 days of inventory on average
• … because you can’t hit the 2nd tier more than once

First run the calculation at 5,068, because your greedy executives only understand unit discounts:

• unit cost: 5,068 * 1,175 = 5,954,900
• inventory carrying cost: 183/365 * 0.2 * 5,954,900 = 595,490
• order cost: 3,400 * 1 = 3,400
• total cost: 6,553,790
• unit cost: 1,293

You quickly see that you clearly want the discounts even if your inventory costs shoot up because 633.5K in savings is greater than 595.5K in expected inventory carrying costs.

But you’re not done yet. Now you have to run the calculation at 1,014 units an order over 5 orders, because it’s also a valid option and captures the suppliers first EPQ point:

• unit cost: 5,068 * 1,250 = 6,335,000
• inventory carrying cost: 36.5/365 * 0.2 * 6,335,000 = 126,700
• order cost: 3,400 * 5 = 17,000
• total cost: 6,478,700
• unit cost: 1,278

which is your actual EOQ because it not only takes advantage of the supplier’s EPQ level but does so at the breakpoint that is closest to that given by your traditional EOQ calculation!

Now we’ve now clearly demonstrated why most of today’s so called experts couldn’t calculate EOQ with a computer because it’s not always the classic EOQ formula (or whatever pseudo-random formula happens to be in the forecasting system they try to use), or the supplier’s optimal EPQ level (if that leads to a significantly high storage cost for you — JIT is a core tenet of lean for a reason, inventory is costly, and while you need a safety stock, too much not only presents too much obsolescence risk but shoots your carrying costs way up), but usually somewhere in between (where the optimal curves intersect closest to their respective minima). Good luck doing that if you can’t do math, don’t know supply chain, and think Chat-GPT holds the answer to everything.

What we didn’t demonstrate is why, in reality, you often need a computer to calculate it (and that comes down to the inventory carrying costs which are often much more involved than Finance believes) and your associated supply chain costs. The reality is that you might have to re-write your formulas, which really will require a computer to constantly calculate and recalculate your true inventory carrying costs, but the reality is that you will only be able do this AFTER you understand what the proper order volumes should be (because you need to check that you worked out the formulas and calculations right for your supply chain)! We might tackle this in another article, because the only way to get costs way down is to help Finance and Operations understand the true costs and how to tackle them (because if you’re still running on an average ICC of 20%, or even worse, 25% to 30%, someone, somewhere, is performing pretty poorly in their profession).