Inventory Management Review

A Case Study in Software Implementation

I recently had the pleasure of attending a guest lecture delivered by Optiant director of research, Ph.D. John Neale on the topic of multi-echelon inventory management software implementation.  Optiant is a supply chain software solutions provider for companies including Gillette and HP.  His discussion described how the implementation of Optiant's PowerChain® software suite helped to dramatically decrease inventory and increase service for a well-known manufacturer of consumer adhesives.  This post will give a history of the adhesive manufacturer's supply chain problems and the solution they chose.  The results of that solution will be explained with a brief lesson on multi-echelon inventory.

Supply Chain
The manufacturer being discussed operates primarily in North America.  Their supply chain has the following characteristics:

Raw Materials
First, they procure over 3000 raw materials from multiple sources and hold the raw materials at one of their two manufacturing sites until they are processed.  This is the first stage (echelon) where inventory is held.  After the raw materials are turned into finished goods, they are immediately shipped to a distribution center (DC).

Finished Goods
The firm has two DCs and over 1800 SKUs (stock keeping units.  This is basically how many different products and package variations they have on those products).  The DCs are the final stop for finished goods inventory before they are shipped to a myriad of retailers.  Of those retailers, Wal-Mart, Staples, Home Depot, and other mass market stores constituted one third of their overall volume.  The DCs also receive some finished goods which come from other manufacturers in the form of finished goods.  The DCs are the second stage (second echelon, thus making more than one echelon, hence the name, multi-echelon) where safety stock is held.

Old Inventory Policy
Prior to Optiant's consulting work and software implementation, the manufacturer had no real method for determining their safety stock. Essentially, they used a trial and error method where they would set a level and if they were stocking out too often, they would increase inventory.  When they stopped stocking out, they would scale back inventory.  Their inventory was also high because of expansion in their product line and high service levels demanded by stores like Wal-Mart.

The manufacturer lacked the expertise regarding how to set a safety stock level that optimized each local inventory stage, and additionally, they were without the experience necessary regarding how to optimize the overall system.  As John Neale put it, this is a problem because while safety stock formulas can be useful for local optimization, one point he made was,

"Don't just optimize things in isolation."

Upon realizing that there were better ways of doing things, they contacted Optiant.

Optiant
What Optiant did for them was more than just selling them a software package. Optiant spent many weeks learning about their supply chain constraints and gathering data, and then used PowerChain®  to optimize the safety stocks for each of the 1500 SKUs and each of their 3000 raw materials.

Data Requirements
Much of this data is demand data. In order to get a feel for demand, Optiant uses historical demand projections.  In order to figure out what kind of deviation there is on these projections, they look at historical projections and compare them with historical demand realizations.  As you can imagine, a lot of companies don't keep accurate records regarding this data.  The less a company has in the way of records, the less effective software initially is.  Keep this in mind before you bring in any consultants: start collecting data before they get there, so you're ready to roll once they're on the clock.

Optiant also required supplier data, including lead times, costs, and a bill of materials (list of parts required for each SKU).

Software
Once they have the data, they can start to use their software model.  I'm not clear on the math that runs the program other than that it uses algorithms to minimize holding costs while maintaining service level requirements.  I didn't bother asking for more detail, because what I understand is this: the software they have works and is based on the kind of framework that you would expect to come from someone with a Ph.D. from MIT, which is precisely what Optiant co-founder, Sean Willems, has.  The point is, the program is complex, but it is not baseless, and it is not a hoax.  It is exactly the kind of complex software I was referring to when I wrote about the kind of advantage that professional software can offer that Excel can't even come close to providing.

Results
Before you refuse to believe the software works without understanding every detail behind it, consider that Optiant's solution allowed this adhesive manufacturer to raise their service level while lowering safety stock value by over 20%.  First of all, 20% is a very large reduction in safety stock value on its own.  In addition to this, they were able to raise their service level while lowering safety stock.  At first glance, this seems too good to be true.  Normally, the way to raise a service level is by raising safety stock, not by lowering it.  Why is this case any different?

Multi-Echelon Inventory Management
This case is different because it is a multi-echelon inventory model.  What this means in this case is that they had the opportunity to hold inventory at two stages: the raw materials stage and the finished goods stages.

Balancing Raw Materials and Finished Goods
Remember, holding costs are a function that involves the value of the inventory and at the raw materials stage the value is considerably less expensive.  This means that if the adhesive manufacturer has short production lead times from raw materials to finished goods, which they do, then they can afford to hold large amounts of raw materials, small amounts of finished goods, and still be in a position to meet demand.  Thus, by reducing finished goods inventory and increasing raw materials inventory, they can increase service level because of their ability to quickly turn raw materials into finished goods, and they can reduce inventory costs because they are holding less finished goods.

Risk Pooling
The other reason they are able to reduce safety stock value while increasing service is because they have so many SKUs that all use the same basic raw materials.  The importance here is the inherent flexibility that raw materials when they can become a variety of different finished goods.  This allows them to keep materials raw for as long as possible, which reduces their vulnerability to fluctuations in demand.  The vulnerability to these fluctuations is limited because many of their glue product SKUs are essentially pooled as one product with an overall demand that is less likely to fluctuate as long as products are kept as raw materials that can be turned into any product once demand projections are closer to demand realizations.  To further illustrate this is an example from the MITSloan Management Review about apparel manufacturer Bennetton Group SpA and how they delay final goods production by keeping raw materials in a position ready to be turned into finished goods:

An inventory of undyed sweaters gets stockpiled in one location; coloring takes place only after specific orders have been received. This pooling of demand across geographical areas, and across colors, helps Benneton greatly reduce inventory risk while more effectively meeting customer demand.1

Another example cited in the article is how the house paint industry holds only base paints which colors are added into instead of holding onto hundreds of different colors at each retail location.

The effects of this are incredible because for the adhesive manufacturer, paint companies, and Benneton, the risk of each individual product in the product line can be vastly reduced by simply keeping finished goods as raw materials for as long as possible.

Paint companies no longer have to worry about having too much blue paint and not enough red paint.  Statistically, the variations in each type of paint will even out.  So if yellow doesn't sell as much as expected and green sells twice as much as expected, paint companies are still ok as long as they have the right amount of base paint.  Unfortunately for the consumer this makes it difficult to return paint.

Luckily for the adhesive manufacturer, risk pooling works.  So does the software Optiant creates.

Final Notes on PowerChain®
Originally, the adhesive manufacturer only hired Optiant so that Optiant could use to use their software to tell provide a report detailing how to optimize each of their 1800 SKUs and 3000 raw materials.  The CFO of the adhesive firm was so impressed with the forecasting abilities of the software that he eventually invested in a license of the software.  I'm not sure whether or not they worked with Optiant to adapt the PowerChain®  software to their other computer programs for automated entry of optimal safety stock into their other systems, although this is something Optiant does.

I'm not trying to suggest that you dive right into the investment of such software, although I can't imagine Optiant would mind, but hopefully this post has given you a better understanding of what inventory management software packages can do for you and what the implementation process entails.

1 Sunil Chopra & ManMohan Sodhi, "Avoiding Supply Chain Breakdown", MITSloan Management Review, Fall 2004, Vol. 46, No. 1

EOQ Formula Derivations

In a recent article, I detailed how to find the economic order quantities for a firm.  This post will pick up where I left and will show how to find how much money you can actually save by using correct ordering costs instead of inflated costs.  The post will then cover how much money a firm can save if it can truly reduce its ordering costs.  Today's post will conclude with a formula you can use in excel.

True savings from accurate ordering costs
First, we need to determine the difference in order sizes EOQ gives us when we use the correct order costs instead of artificially high ordering costs.  The difference from the example in the previous post is 876 parts.  When looked at as average inventory for a steady production, this results in average inventory that is 867/2 which is 433.5 additional inventories per year.

It is half of 867 because average inventory for a steady production is half of the order quantity.  Intuitively, this should make sense because if you start out with 876 parts and are constantly using them until you order more, then half the time you have more than half of 876 and half the time you have less.  At a steady rate, half of 876 is the average increase in inventory held.

Effect of incorrect ordering costs on EOQ
Something important to notice is that the difference in parts ordered is not the ratio of the wrong holding cost to the right holding cost. That is to say that although the ordering costs used before were almost twice as high as the ordering costs used now, the difference in parts ordered before is not half of what it is now.  This is because of the square root, which actually makes the difference in parts the ratio of the square root of each ordering cost.

In other words, take the square root of the old ordering costs:
SQRT($82)=9.0554
And the new, correct, ordering costs:
SQRT($42)=6.4807

Find the ratio between the square root of the two ordering costs:
9.0554/6.4807=1.3972

This ratio is the ratio between the old EOQ and the new EOQ:
3053/2185=1.3972

This is useful because you can take the old ordering costs and the new ordering costs to determine the percent difference in ordering sizes.  In other words, you can see the reduction in order sizes by percentage as a result of realizing the correct ordering costs.

Percent difference:
(observed-expected)/expected
In our case that would be:
{[SQRT(New S)]-[SQRT(Old S)]}/[SQRT(Old S)]
Or:
{[SQRT($42)]-[SQRT($82)]}/SQRT($82)=-28%

This formula shows us that the new ordering costs compared to the old ordering costs represent a 28% reduction in order sizes.

Monetary impact of holding extra inventory
When ordering costs are artificially high, so are inventories.  With these inventories comes an increase in holding costs.  The additional holding costs incurred are equal to the excess inventory multiplied by the annual holding cost per part.  Remember, the excess inventory is half the excess order size.  In this example, the excess inventory is 433.5 units and the holding cost is $2.64 per unit per year (determined in previous article).

433.5*$2.64=$1146 spent on excess inventory per year.

Total Savings
The total savings, however, are actually less than that. Remember that with smaller batch sizes, orders are placed more frequently.  We were placing 49 orders per year, now we are doing 68.  This means 19 additional orders (68-49) at a rate of $42 each.  This means that the total savings in EOQ is equal to the $1146 saved from inventory control minus the additional amount paid to floor managers for processing the additional orders [(68-49)*$42].

$1146-{(68-49)*$42}=$347.65 of total money saved through correct ordering costs.

Now that we've determined the overall dollar amount in cost savings, we should determine the overall cost savings as a percent decrease of the old system.  The formula to determine this is:

[(New total cost)-(old total cost)]/(old total cost)

But first, we need to find the total cost of holding and ordering inventory.

Total cost old system=(new ordering cost*number of orders)+[(H)*(Old EOQ/2)]

The new ordering cost is used because it has always been the correct ordering cost but it was only recently realized.  It was still the true cost under the old system regardless of whether or not it was realized.

Plugging in the numbers the equation is as follows:
($42*49)+[($2.64)*(3052/2)]=$6093

Formula for the total cost of the new system is the same, but with all new number of orders and new EOQ.

Total cost of new system=($42*68)+[($2.64)*(2184/20]=$5767

Now we can take these two numbers and plug them into our percent savings formula from above:

(5767-6093)/6093=-5.34%

This means that by realizing what the true ordering costs are, Chuck Co. is able to save 5.34% on the combined values of ordering and holding inventory.

Now we'll see what were to happen if they were not only able to realize that their ordering costs were wrong, but if they were actually able to reduce ordering costs.

Reducing ordering costs through improvement
If Chuck Co. were able to actually able to reduce ordering costs, instead of merely realizing that they weren't spending as much on ordering costs than they thought they were, then Chuck Co. would be able to save some serious money.

Before, when lower ordering costs were just a discovery, they were really only saving money on holding less inventory. In fact, once they started ordering more, they spent more money on orders because it was the same ordering cost with more frequent orders.  If, however, they actually reduced inventory, then they would be able to have actual savings in both ordering and inventory holding costs.

Let's assume that ordering costs really were $82 before and they changed their methods to drop them to $42.  What would the affect be?  All of the numbers, old and new, (EOQ, ordering costs, holding costs) would be the same from our previous example.  This means we're ready to find the total cost of each system and then find the percent savings using the percent savings formula.

Total cost of old system=($82*49)+[($2.64)*(3052/2)]=$8058

Notice that the old ordering costs are used instead of the new ordering costs.  This is because the old system really did have an $82 ordering cost in this example, not like before where Chuck Co. thought it was $82 but it was really $42,  until they actually lowered it, which we'll see here:

Total cost of new system=($42*68)+[($2.64)*(2184/2)]=$5767

We then take the two costs of these systems to find the percent savings in lower ordering costs:

($5767-$8058)/$8058=-28.4%

This means that an actual reduction of ordering costs resulted in 28% savings in ordering and holding costs.

Finally, you may be aware that if ordering cost is the only term changing in the EOQ formula, then there must be some way to determine total cost savings with a formula derived from EOQ using only the variable S (ordering costs).  Well, you're right, there is a formula, and lucky for you, I spend the time to derive it.  Here it is, but first let's get familiar with the variables involved:

%TC= Percent change in total cost
Sn=New ordering cost
So=Old Ordering cost
And, as always, SQRT=Square Root

%TC=[(SQRT(Sn/2)+((1/SQRT(Sn))*Sn))-
(SQRT(So/2)+((1/SQRT(So))*So))] /
[(SQRT(So/2)+((1/SQRT(So))*So))]

If you plug in the numbers we used here:
Sn=$42
So=$82
The formula will look like such:

((SQRT($42/2)+((1/SQRT($42))*$42))-
(SQRT($$82/2)+((1/SQRT($82))*$82)))/
((SQRT($82/2)+((1/SQRT(So))*$82))) = 28.4%

This is the same reduction is total costs that we saw when we plugged in the total cost savings numbers from before.  This time, we only looked at ordering costs.  This shows that this formula can be used to determine the total cost savings EOQ can bring you when you are able to actually reduce ordering costs and when you only know your ordering costs.  In other words, regardless of holding costs and demand, you can determine how much money you can save by simply lowering ordering costs.

To use this formula for yourself, copy and paste the following into cell A1 in excel (make sure the cell has been double clicked):

=((SQRT(C5/2)+((1/SQRT(C5))*C5))-
(SQRT(B5/2)+((1/SQRT(B5))*B5)))/
((SQRT(B5/2)+((1/SQRT(B5))*B5)))

Now, make cell c5 your new ordering cost and cell b5 your old ordering cost.  Make sure cell A1 is in percent format and there you have your reduction in total costs.

McDonald's, a guide to the benefits of JIT

Just-in-Time (JIT) inventory is the big thing right now in operations.  This, along with lean operations and six-sigma are the buzz words being talked most about.  But what exactly is the deal with JIT operations?

First of all, JIT is a form of providing supplies for customers, as the name suggests, just in time.  For example, Dell, whom I wrote about, has become famous for its JIT model which involves not even being in possession of the raw materials needed to fulfill an order until that order is placed and yet they are still capable of filling orders in a short period of time.

McDonald's is another example of a JIT system wherein McDonald's doesn't begin to cook (well, I should probably say reheat and assemble what may or may not be actual food) its orders until a customer has placed a specific order.

What used to be the case was McDonald's would pre-cook a batch of hamburgers and let them sit under heat lamps.  They would keep them for as long as possible and eventually discard what couldn't be sold.  The only way to get a fresh hamburger under the old system was to make a special order.  Now, due to more sophisticated burger-making technology (including a record-breaking bun toaster), McDonald's is able to make food fast enough to wait until it's been ordered.

What both of these firms do is they provide a customer with their order as fast as possible while having the finished product sitting in inventory for as short as possible.

What are the benefits for McDonald's?
The major benefits for McDonald's are better food at a lower cost.

Let's stop here for a second to drive home a very important point: Whenever you can implement something that allows you to raise quality AND lower costs, you should definitely look into implementing that practice.  Unless illegal, immoral, socially irresponsible, or likely to drive down demand (which is unlikely considering quality is being improved), you are probably going to want to implement this practice.  Back to McDonald's.

McDonald's has found something that allows them to improve quality and lower costs.  Let's take a look at how it does both.

Improved Quality
I think benefits of a better tasting burger should be fairly apparent.  Unless of course you prefer aged burgers, the fresher burger is going to be higher quality if made fresh just for you.

The less obvious benefit is the higher quality customer service that arises from the JIT burger assembly.  When McDonald's waits for you to order the burger, they do a few things to improve customer service.  First of all, when you place a special order, it doesn't send McDonald's into a panic that causes huge delays.

Now that McDonald's is in the practice of waiting until you order a burger until they make it, they don't freak out when they have to make a special order fresh just for you.  This higher quality customer service is subject to McDonald's ability to actually produce faster.  Without this ability, McDonald's ordering costs would be sky-high because the costs associated with ordering would be the loss of customers tired of ordering fast food that really isn't fast.

Second, JIT allows McDonald's to adapt to demand a little bit better.  Seemingly, lower inventory levels would cause McDonald's bigger problems in a higher demand because they wouldn't have their safety stock.  However, because they can produce burgers in a record time, they don't have to worry about their pre-made burger inventories running out in the middle of an exceptionally busy shift.

Lower Costs
The holding costs for burger parts (beef, cheese, buns, whatever other garbage they put on their burgers) are fairly high because of their spoilage costs.  Frozen ground beef that's good today might not be so good in a few months.  Once cooked, the same ground beef's spoilage rate shoots through the roof.  Instead of having a shelf life of months or weeks, the burger needs to be sold within 15 minutes or so.  The holding costs go from roughly 20% per week to 100% per hour.

In other words, under McDonald's old system, they produced at a level that gave them high inventories so that food would be available fast, which is the main benefit of fast food.  Unfortunately, food that was unsold after a short period of time was scrapped.  Food that was sold was forced to be sold at a higher price in order to absorb the scrap costs of unsold food.  Ultimately this meant higher costs for McDonald's.

For McDonald's, the benefits of JIT are fairly clear.  For Dell, it was the same way.  So what is it that both of these firms have in common, and ultimately, when is JIT a good system to implement?

Why JIT

Economic Order Quantity Savings
A large benefit of JIT is that it reduces the total cost of ordering and holding inventory.  Let's quickly recap three firms that have achieved this and how they did so.

Dell and McDonald's
High holding costs are the nature of the computer and fast food industries.  JIT system allowed them to exploit the savings that were realized by holding less inventory.

Wal-Mart
Instead of having particularly large holding costs, Wal-Mart recognized that they were in a position to make ordering costs very small.  Because of their importance to their suppliers, along with their software made affordable through economies of scale, Wal-Mart has made ordering a very small percent of their overall costs.  By lowering ordering costs, Wal-Mart has made ordering small batches with greater frequency a profitable reality.

High holding costs and low ordering costs are the factors that drive JIT.  Generally, it's the ability to lower ordering costs that make it a feasible solution.  McDonald's and Dell were both slaves to the high holding costs.  It was just the nature of their industry.  The solution for them was that while they couldn't lower holding costs, they could lower ordering costs.  Wal-Mart didn't even have particularly high holding costs, but they realized it would be profitable to lower ordering costs which led to high holding costs as a ratio of holding costs to ordering costs.

What McDonald's, Wal-Mart, and Dell have in common is very high holding costs in comparison to their ordering costs.  Ultimately, this, coupled with the ability to lower safety stock, is when JIT is effective.  EOQ determines how much you should order and there are two factors that drive economic order quantities down: low ordering costs and high holding costs.  Depending on the product and the industry, one or both of these qualities may exist in your operations.  If they do, JIT may be right for you.  Without the ability to make ordering costs low as a percentage of holding costs then there is no need for JIT.  In fact, the increased frequency in ordering will result in cost increases.

Safety Stock Reductions
The other aspect of JIT is the drastic reduction in safety stock.  My previous article on safety stock discussed the two reasons safety stock exists:  variability in demand and variability in lead times from suppliers (in McDonald's case, the supplier is the internal production process).

It is because of this variability that safety stock exists in the first place.  What JIT does is tries to reduce the lead times and variation in lead times in order to help reduce safety stock.  Let's revisit the safety stock formula to figure out why this is:

Safety Stock:  {Z*SQRT(Avg. Lead Time*Standard Deviation of Demand^2 + Avg. Demand*Standard Deviation of Lead Time^2}

The first term is Lead Time*Standard Deviation of Demand^2.  This is the inventory needed to account for fluctuations in demand during the lead time.  If lead time is shorter, which JIT tries to accomplish, then this part of the safety stock is smaller, this lowering safety stock inventory.

Wal-Mart and Dell accomplished this by using better software and communication with their suppliers.  McDonald's accomplished this by creating a system that allowed a faster burger production (remember, McDonald's lead times are internal).

The second term is Avg. Demand*Standard Deviation of Lead Time^2.  This is the inventory needed to fill demand because of lead time variance.  If lead time has no variance or is reduced then this term can be eliminated or at least reduced.  Again, this is what JIT try to accomplish.

Wal-Mart accomplishes this by demanding it, Dell by working with suppliers, and McDonald's by standardizing production.

In order to accomplish the tasks of shortening lead times and reducing their variances, a considerable amount of work needs to be done with suppliers/internal operations.  For some firms this is worth the trouble, for others, it is not.

Conclusively, there are two major parts to JIT inventory operations: lowering the ratio between ordering costs and holding costs and shortening lead times.  What results is a firm with such high holding costs that ordering very small batches very frequently is the most profitable solution.  This eliminates average inventory above the safety stock level.  Then, if lead times and lead time variability can be decreased, safety stock can be decreased.  The result is inventory coming in as it needs to come in.  In other words, it comes in just-in-time.

Advanced Economic Order Quanitity

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.