David Edwards . Operations Professionals

Lean manufacturing theory is rife with formulas for optimizing your inventory levels by establishing statistically valid safety stock and re-order points based on given demand variability, lead times, and lot sizes. Application of these principles using simple KanBan or Re-Order Point tools can have a dramatic impact on average annual inventory levels, lowering them to the absolute minimum required to meet demand at a pre-determined service level. But once you reach that goal, where do you turn for additional savings?

Average Inventory = Safety Stock + 1/2 Order (Lot) Size. This simple calculation makes it clear that in order to reduce inventory, you have to reduce your safety stock and your lot size.

Safety Stock (for a 97.5% Service Level) = 2 Standard Deviations of Demand Variability within Replenishment Lead Time. In most cases demand variability is what it is; it is difficult, if not impossible, to greatly influence the variability of demand for a product. So in order to reduce the safety stock required to maintain desired service levels, you need to reduce the lead time for replenishing that product. In most manufacturing operations, lead time is, to a great degree, a product of lot size. When cycling a production line through a variety of products, the bigger the lot sizes you run, the longer it will be before you can run the same product again (because you need all those other products too).

This makes lot sizing critical to reducing inventory. Both as a direct part of the equation (1/2 Order Size) and because of the indirect impact on the other half of the equation (2 * StDev of Demand Variability in Replenishment Lead Time).

But reducing lot sizes is a hard sell. In most cases, as lot sizes decrease, average cost per unit increases due to the fixed cost of setting up to run the lot. Also, as lot sizes decrease, total capacity requirements increase due to the additional setup time required to run more lots. Of course, if you can cut your setup times in half, you can run twice as many lots with the same capacity, but you could also just take the cost reduction instead. And anyway, capacity requirements should be based on running the optimum lot size , not visa versa, so if running the optimum lot size exceeds current capacity, add capacity. Which means the bottom line decision on lot sizing is all about cost, right?

One of my favorite books about lean manufacturing is “The Goal” by Eli Goldratt. While the term “Lean Manufacturing” wasn’t really coined yet in 1984, the book laid out a lot of foundations prevalent in lean manufacturing theory today. For those who have read it, you should know “The Goal”. For those who haven’t, the “Goal” is simple – make more money with less money. In other words:

### Maximize Return On Investment

Return On Investment (ROI) = Return / Investment. The effect of lot sizing on ROI is direct and dramatic. Yes, if you don’t change the setup cost, the cost per unit for a product will increase as you reduce lot sizes . And if cost per unit were the only factor in ROI, you would run the largest lots possible to minimize product cost and increase Return. But there is that other factor in ROI, the “I”, the Investment, which consists of a high percentage of Inventory. So “The Goal” in lot sizing is to maximize ROI by finding the lot size that provides the most Return (Gross Margin) on the least Investment (Capital + Average Inventory Cost).

The traditional method for determining the optimum lot size for a product is the EOQ (Economic Order Quantity). This formula seeks the lowest total cost per unit by balancing the variable cost to make a unit against the variable cost of carrying inventory as order size changes. While it is widely accepted as the best method for determining optimum order (lot) sizes, it has its flaws. First of all, it requires you to determine an average cost of carrying inventory as a percent of inventory cost. This alone can tie an organization into an inescapable knot of analysis paralysis, a never ending struggle to settle on a number somewhere between the current cost of money (say 3%) and the fully loaded cost of such things as space, obsolescence, handling, and damage that can add up to more than 20%. Secondly, it assumes that the cost of an inventory unit is constant as lot sizes change, which as we have previously noted, the cost per unit changes as the lot size changes, so the carrying cost per unit of inventory changes as well. Plus it does not recongnize the fact that safety stock requirements increase as order sizes increase due to the impact on lead time. Finally, and most importantly, it doesn’t really seek to maximize Return On Investment, it seeks to lower “Cost”.

### Lot Sizing to Maximize ROI

So is there a practical way to establish a lot size that maximizes ROI? The obvious answer is yes, the real question is how. Without getting too deep into the math and developing an elegant formula, a simple spreadsheet using basic inputs and the wonderous “Solver” function will do the trick.

In the following example, a contrast of 3 different lot sizing approaches (1 Month Demand, EOQ, and Maximize ROI) will demonstrate the results of each technique. Each technique is evaluated for resulting ROI based on the simple inputs provided in figure 1. This simple spreadsheet can be loaded with base information for any product and used to determine the optimum lot size, the example product used here is representative of a typical high volume, moderately priced widget.

The first technique (figure 2) we will evaluate is a fairly typical approach where the lot size is set at 1 months average demand (18,000/12=1,500). The analysis of this technique shows that the product will be set up and run for about a week (38.5 hrs) before other products are rotated in succession. The Gross Margin of 15% is based on this 1,500 unit lot size, and as you will see, changes in the subsequent examples as the lot size changes. The total investment will be one half the lot size, plus safety stock (set to provide a 97.5% fill rate), plus capital employed. So this technique yields a 46.8% ROI based on Gross Margin / Total Investment.

Next we will evaluate the EOQ technique (figure 3). Using a reasonably high 20% inventory carrying cost and the “standard” cost of the product from figure 2 (Remember, EOQ does not recognize the standard cost change resulting from the lot size change, this would create a “circular reference”) along with the fixed setup cost and annual demand, an economic order size of 2,002 is derived. This is higher than the one month supply technique in the first example, and when plugged into the ROI calculator, yields a lower ROI of 43.7%. So much for using EOQ to maximize ROI…

Finally, the moment you have all been waiting for, the Maximum ROI calculation. Using all of the same inputs as the previous example, we structure the spreadsheet to calculate the ROI percent based on the run size entered in the upper left cell. We then invoke the wonderous “Solver” tool to maximize the ROI percent by changing the run size, and the answer we get is 744 units for a much improved 50.6% ROI. Now thats making more money with less money.

But wait a minute now, yes we increased ROI from 46.8% to 50.6%, but our gross margin went from 15% to 13.3%, we lost $1,388 in annual gross margin. But, our investment was $4,926 lower, which frees up capital to expand capacity and produce more product at a higher margin . If we were shopping for a bank, we would definitely take the one paying 50.6% over the one paying 46.8%, so why do we have such a problem with maximizing our ROI on inventory?

While the final answer in your operations may not be as simple as this, remember that the ultimate goal in lot sizing is to maximize ROI, that’s what you would do if it were your money.

Please email questions or comments to:

DavidEdwards@OperationsProfessionals.Com

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January 25, 2010 at 8:37 pm |

Good afternoon David,

You are the only other person I know that uses quantitative calculations to determine optimized lot size – I’ve used statistical lot sizing along with advanced Lean techniques very successfully for the last 10 years – that way I can get it right first time – giving the client the opportunity of maximizing cash flow or EBIT – or optimum of both.

Best regards,

Adam

720 938 0321

January 25, 2010 at 11:23 pm |

Thanks Adam, I’m a firm believer that our economic conditions would be greatly improved if companies focused more on sustainable ROI and less on chasing short term profitablity. After all, inventory is not really an investment, it’s a liability…

January 28, 2010 at 3:31 pm |

Dave,

What an excellent analysis tool! Thanks for sharing this. As you aptly point out, we often waste a portion of our investment dollars in pursuit of increased margins.

I have used statistical analysis extensively in setting inventory levels and have often wondered how to truly determine the optimum lot size for maximizing the ROI (knowing that EOQ was not the correct answer). My approach has been to implicitly work toward that point by reducing set up time so that lot sizes can be reduced (thereby reducing the average investment in inventory).

In your example, the set up time would need to be reduced (not necessarily halved, as it might appear, because of components within the safety stock calculation) to keep from eating up more overall capacity. If ROI maximization is not possible without capacity expansion and that expansion is very expensive, might the “final answer” / best option then be to optimize ROI within the current capacity?

March 7, 2011 at 2:28 pm |

This is an excellent posting. I often struggle with balancing Lean production methods against Economies of Scale.

Currently, I am struggling with understanding how this applies with a company that produces low quantities of capital intensive product. For instance, how does a manufacturer who produces 120 models of a machine per year achieve a good balance between EOQs & Lean. Inventories crawl at 3 – 4 turns per year yet setup is still 22% of costs. With some significant investments we could probably achieve 5 – 10% setup costs. As you mentioned the question then becomes “Why don’t we just take advantage of those cost savings as part of the cost of the product?”

May 2, 2011 at 9:50 am |

Dave.

Very nice article. Im not a manufacturing wiz however im on front line sales for a very large Domestic manufacturer in Georgia. My goal is to find this same kind of analysis and thinking to help my larger retailers with my product catagory.

My dilema is that they consistently miss ROI by not ordering my products after they sell. I have already implemented my version of Lean when it comes to assortment optimization thus reducing cost.

One of the key factors for not ordering is credit limit. My employer manufactures, hardwood, carpeting, tile and area rugs spread across many nationally acclaimed brands. Thus there limit is bundled together and often precludes my product and brand.

Can you suggest any book or perhaps academic university that specializes in retail management as pertains to this issue?

Many Thanks

JOhn