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Optimizing Safety Stock

By Dave Piasecki Copyright. Content on InventoryOps.com is copyright-protected and is not available for

republication.

Optimizing Safety Stock levels by calculating the magical balance of minimal inventory while

meeting variable customer demand is sometimes described as the Holy Grail of inventorymanagement (ok, forecasting is probably the true holy grail but I thought this sounded good). Manycompanies look at their own demand fluctuations and assume that there is not enough consistencyto predict future variability. They then fall back on the trial and error best guess weeks supplymethod or the over simplified 1/2 lead time usage method to manage their safety stock.Unfortunately, these methods prove to be less than effective in determining optimal inventory levelsfor many operations. If your goal is to reduce inventory levels while maintaining or increasingservice levels you will need to investigate more complex calculations.One of the most widely accepted methods of calculating safety stock uses the statistical model ofStandard Deviations of a Normal Distribution of numbers to determine probability. This statisticaltool has proven to be very effective in determining optimal safety stock levels in a variety ofenvironments. The basis for this calculation is standardized, however, its successful implementationgenerally requires customization of the formula and inputs to meet the specific characteristics of

your operation. Understanding the statistical theory behind the formula is necessary in correctlyadapting it to meet your needs. Errors in implementation are usually the result of not factoring invariables which are not part of original statistical model

Terminology and calculations

The following is a list of the variables and the terminology used in this safety stock model:

Normal distribution. Term used in statistical analysis to describe a distribution ofnumbers in which the probability of an occurrence, if graphed, would follow the form of abell shaped curve. This is the most popular distribution model for determining probabilityand has been found to work well in predicting demand variability based upon historicaldata.

Standard deviation. Used to describe the spread of the distribution of numbers.Standard deviation is calculated by the following steps:

1. determine the mean (average) of a set of numbers.2. determine the difference of each number and the mean3. square each difference4. calculate the average of the squares5. calculate the square root of the average.

You can also use Excel function STDEVPA to calculate standard deviation. In safety stockcalculations, the forecast quantity is often used instead of the mean in determining standarddeviation.

Lead time. Highly accurate lead times are essential in the safety stock/reorder pointcalculation. Lead time is the amount of time from the point at which you determine theneed to order to the point at which the inventory is on hand and available for use. Itshould include supplier or manufacturing lead time, time to initiate the purchase order orwork order including approval steps, time to notify the supplier, and the time to processthrough receiving and any inspection operations.

Lead-time demand. Forecasted demand during the lead-time period. For example, ifyour forecasted demand is 3 units per day and your lead time is 12 days your lead timedemand would be 36 units.

Forecast. Consistent forecasts are also an essential part of the safety stock calculation. Ifyou don't use a formal forecast, you can use average demand instead.

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which 84% of the occurrences will occur below, 2 standard deviations added to the mean will resultin a number in which 98% of the occurrences will occur below, and 3 standard deviations added tothe mean will result in a number in which 99.85% of the occurrences will occur below.In the safety stock calculation we will refer to the multiplier as the service factor and use thedemand history to calculate standard deviation. In its simplest form this would yield a safety stockcalculation of : safety stock = (standard deviation) * (service factor). If your lead time, order cycletime, and forecast period were all the same and if your forecast was the same for each period andequaled the mean of the actual demand for those periods, this simple formula would work great.Since this situation is highly unlikely to occur you must add factors to the formula to compensate forthese variations. This is where the trouble lies. You must add factors to adapt this theory to workwith your inventory, however, each factor you add compromises the integrity of the original theory.This isn't quite as bad as it sounds. While the factoring can get complicated you can keep tweakingit until you find an effective solution. Your final formula will look like: safety stock = (standarddeviation)*(service factor)*(lead-time factor)*(order cycle factor)*(forecast-to-mean-demand factor).There is not a general consensus on the formulas for these factors; in fact, many calculations donot even acknowledge the need for them. I will give some recommendations for these factors,however, I strongly suggest you test and tweak them with your numbers to arrive at something thatworks for you.

Lead-time factor. This is necessary to compensate for the differences between lead time andforecast period. The standard deviation was based on the forecast period, a factor is

necessary to increase or decrease the safety stock to allow for this variance. A formula youcan try is lead time factor = square root (lead time/forecast period).Order cycle factor. Since longer order cycles result in an inherent higher service level you willneed to use a factor to compensate for this. A formula you can try is Order cycle factor =square root (forecast period/order cycle). This is a simple calculation that works sometimes,but I typically use a more complex calculation (different logic completely)for this factor.Forecast-to-mean-demand factor. Remember that the original statistical model was basedupon the mean of the distribution. Substituting a forecast for the mean in the calculation ofstandard deviation creates a problem if the forecast mean and the actual demand mean arenot close and also if the forecast varies between forecast periods (seasonality, sales growth).Sorry but I don't have a canned formula for this one that I feel confident enough with to publish.The actual formula used will vary based upon the types of variances and the method forstandard deviation calculation used.

Minimum Reorder Point. For slow moving products and especially if the lead time is short,you may want to program in a minimum reorder point which is the equivalent of one averagesale.Lead-time Variances. You may have noticed that I have only discussed demand variations inthis model. While you can use this model for predicting variations in supply, I have found thatsupply variations tend to be far too random and unpredictable. Supply problems tend to berelated more to a vendor than an item and the severity of the variations do not fall into thepattern of a normal distribution. The safety stock calculated for demand variation will alsocover for some supply variations, however, the best way to deal with variable supply is to havea high level of communication with the vendor and not to count on safety stock. You may findthat certain items which are critical to your operation may require a safety stock calculationbased upon the nature of the supply chain of the specific item.

While all of these factors and their potentially detrimental effect upon the integrity of the original

formula may leave you feeling less than confident with the results of this model, you should realizethat these factors would be necessary in any method of calculating safety stock which takes ascientific approach to meeting service levels while maintaining minimal inventory levels. It is veryimportant to thoroughly test the model prior to final implementation to ensure it is working correctlyand to determine impact on inventory levels and cash flow. It's also a good idea to start with ahigher service factor initially and gradually reduce it until your actual service levels meet yourobjectives. You will never find perfection in determining probability, however this type of formula iscertainly more effective than the previously mentioned keep it simple approaches.For more detailed information onSafety Stockcheck out my bookInventory ManagementExplained. In the book I provide a much more thorough discussion of the logic as well as additional

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suggestions for adjustments. You may also want to check out my article onDependent DemandSafety Stock.Go toArticles Pagefor more articles by Dave Piasecki.

Copyright. Content on InventoryOps.com is copyright-protected and is not available for

republication.

Dave Piasecki, is owner/operator ofInventory Operations Consulting LLC, a consulting firmproviding services related to inventory management, material handling, and warehouse operations.He has over 25 years experience in operations management and can be reached through hiswebsite (http://www.inventoryops.com), where he maintains additional relevant information.

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