Optimizing Safety Stock
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 inventory management (ok, forecasting is probably the true holy grail but I thought this sounded good). Many companies look at their own demand fluctuations and assume that there is not enough consistency to predict future variability. They then fall back on the trial and error best guess weeks supply method 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 levels for many operations. If your goal is to reduce inventory levels while maintaining or increasing service levels you will need to investigate more complex calculations.
One of the most widely accepted methods of calculating safety stock uses the statistical model of Standard Deviations of a Normal Distribution of numbers to determine probability. This statistical tool has proven to be very effective in determining optimal safety stock levels in a variety of environments. The basis for this calculation is standardized, however, its successful implementation generally 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 correctly adapting it to meet your needs. Errors in implementation are usually the result of not factoring in variables 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 of numbers in which the probability of an occurrence, if graphed, would follow the form of a bell shaped curve. This is the most popular distribution model for determining probability and has been found to work well in predicting demand variability based upon historical data.
Standard deviation. Used to describe the spread of the distribution of numbers. Standard deviation is calculated by the following steps:
determine the mean (average) of a set of numbers.
determine the difference of each number and the mean
square each difference
calculate the average of the squares
calculate the square root of the average.
You can also use Excel function STDEVPA to calculate standard deviation. In safety stock calculations, the forecast quantity is often used instead of the mean in determining standard deviation.
Lead time. Highly accurate lead times are essential in the safety stock/reorder point calculation. Lead time is the amount of time from the point at which you determine the need to order to the point at which the inventory is on hand and available for use. It should include supplier or manufacturing lead time, time to initiate the purchase order or work order including approval steps, time to notify the supplier, and the time to process through receiving and any inspection operations.
Lead-time demand. Forecasted demand during the lead-time period. For example, if your forecasted demand is 3 units per day and your lead time is 12 days your lead time demand would be 36 units.
Forecast. Consistent forecasts are also an essential part of the safety stock calculation. If you don't use a formal forecast, you can use average demand instead.
Forecast period. The period of time over which a forecast is based. The forecast period used in the safety stock calculation may differ from your formal forecast periods. For example, you may have a formal forecast period of four weeks while the forecast period you use for the safety stock calculation may be one week.
Demand history. A history of demand broken down into forecast periods. The amount of history needed depends on the nature of your business. Businesses with a lot of slower moving items will need to use more demand history to get an accurate model of the demand. Generally, the more history the better, as long as sales pattern remains the same.
Order cycle. Also called replenishment cycle, order cycle refers to the time between orders of a specific item. Most easily calculated by dividing the order quantity by the annual demand and multiplying by the number of days in the year.
Reorder point. Inventory level which initiates an order. Reorder Point = Lead Time Demand + Safety Stock.
Service level. Desired service level expressed as a percentage.
Service factor. Factor used as a multiplier with the Standard Deviation to calculate a specific quantity to meet the specified service level. I have included a service factor table below or you can use Excel function NORMSINV to convert service level percentage to service factor.
By Dave Piasecki
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 inventory management (ok, forecasting is probably the true holy grail but I thought this sounded good). Many companies look at their own demand fluctuations and assume that there is not enough consistency to predict future variability. They then fall back on the trial and error best guess weeks supply method 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 levels for many operations. If your goal is to reduce inventory levels while maintaining or increasing service levels you will need to investigate more complex calculations.
One of the most widely accepted methods of calculating safety stock uses the statistical model of Standard Deviations of a Normal Distribution of numbers to determine probability. This statistical tool has proven to be very effective in determining optimal safety stock levels in a variety of environments. The basis for this calculation is standardized, however, its successful implementation generally 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 correctly adapting it to meet your needs. Errors in implementation are usually the result of not factoring in variables 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 of numbers in which the probability of an occurrence, if graphed, would follow the form of a bell shaped curve. This is the most popular distribution model for determining probability and has been found to work well in predicting demand variability based upon historical data.
Standard deviation. Used to describe the spread of the distribution of numbers. Standard deviation is calculated by the following steps:
determine the mean (average) of a set of numbers.
determine the difference of each number and the mean
square each difference
calculate the average of the squares
calculate the square root of the average.
You can also use Excel function STDEVPA to calculate standard deviation. In safety stock calculations, the forecast quantity is often used instead of the mean in determining standard deviation.
Lead time. Highly accurate lead times are essential in the safety stock/reorder point calculation. Lead time is the amount of time from the point at which you determine the need to order to the point at which the inventory is on hand and available for use. It should include supplier or manufacturing lead time, time to initiate the purchase order or work order including approval steps, time to notify the supplier, and the time to process through receiving and any inspection operations.
Lead-time demand. Forecasted demand during the lead-time period. For example, if your forecasted demand is 3 units per day and your lead time is 12 days your lead time demand would be 36 units.
Forecast. Consistent forecasts are also an essential part of the safety stock calculation. If you don't use a formal forecast, you can use average demand instead.
Forecast period. The period of time over which a forecast is based. The forecast period used in the safety stock calculation may differ from your formal forecast periods. For example, you may have a formal forecast period of four weeks while the forecast period you use for the safety stock calculation may be one week.
Demand history. A history of demand broken down into forecast periods. The amount of history needed depends on the nature of your business. Businesses with a lot of slower moving items will need to use more demand history to get an accurate model of the demand. Generally, the more history the better, as long as sales pattern remains the same.
Order cycle. Also called replenishment cycle, order cycle refers to the time between orders of a specific item. Most easily calculated by dividing the order quantity by the annual demand and multiplying by the number of days in the year.
Reorder point. Inventory level which initiates an order. Reorder Point = Lead Time Demand + Safety Stock.
Service level. Desired service level expressed as a percentage.
Service factor. Factor used as a multiplier with the Standard Deviation to calculate a specific quantity to meet the specified service level. I have included a service factor table below or you can use Excel function NORMSINV to convert service level percentage to service factor.
By Dave Piasecki
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