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# Safety Stock Calculations

Safety stock is intended to protect against uncertainty in supply and demand. Uncertainty may occur in 2 ways:** quantity uncertainty **and **timing uncertainty**. Quantity uncertainty occurs when the amount of supply and demand varies. Timing uncertainty occurs when the time of receipt of supply or demand differs from than expected.

Two common methods to determine the size of the safety stock are the availability method and the service level method. The **desired ****availability **(denoted as AV) becomes AV = probability of not running out of stock during the lead time. The **desired service level** (denoted as SL) is typically measured as SL = (demand filled) over (total demand). The safety stock is the stock carried to meet the uncertainty associated with the forecasts of the demands.

The difficulty in the above statements is that oftentimes it is confusing which method is being applied to generate the safety stock. The term service level is the most common, followed perhaps by availability and percent fill. In the above definitions, the measure of availability is a probability and the measure of service level is a ratio falling between zero and one. Although both methods of finding the safety stock yield different results -- it is noted in many references -- the term service level is often the only term used for both of the methods. That is, the definition given above for availability is often referred as the service level. Sometimes the term percent fill is used in place of the service level. For convenience in this paper, the terms availability and service level are used in the following way:

availability = probability of (not out of stock during the lead time)

service level = ratio of (demand filled / total demand)

There are 2 ways to protect against uncertainty: carry extra stock, called **safety stock**, or order earlier, called **safety lead time**. Both result in extra inventory, but the methods of calculation are different. Safety stock is the most common way of buffering. The SS required depends on the following:

- variability of demand during the lead time;

- frequency of reorder;

- service level desired;

- length of a lead time. The longer the lead time, the more safety stock has to be carried to provide a specified service level. This is one reason it is important to reduce lead time.

**Variation in demand during lead time
**Actual demand varies from forecast for 2 reasons: bias error in forecasting the average demand and random variations in demand about average. It is the latter with which we are concerned in determining safety stock. Some method of estimating the randomness of item demand is needed.

**Variation in demand about the average
**Suppose a history of weekly demand for a particular item shows an average demand. As expected, most of the demand are around it. A smaller number would be farther away from it and still fewer would be farthest away. If the weekly demands are classified into groups or ranges about the average , a picture of the distribution of demand about the average appears.

**Normal distribution
**The pattern of demand distribution about the average will differ for different products and markets. Some method is needed to described the distribution: its shape, center and spread. As long as the demand conditions remain the same, we can expect the pattern to remain very much the same. If the demand is

erratic, so is, the demand pattern, making it difficult to predict with any accuracy.

The most common predictable pattern is called a normal curve or bell curve. The normal distribution has most of the value s clustered near a central point with progressively fewer results occurring away from the center. It is symmetrical about this central point in that is spreads out evenly on both sides.

The normal curve is described by 2 characteristics. One relates to its central tendency, the average, and the other to the variation, or dispersion, of the actual values about the average.

**Average or mean
**The average or mean value is at the high point of the curve. It is the central tendency of the distribution. The symbol is x. It is calculated by adding the data Sum(x) and dividing by the total number of data (n).

**x = Sum(x) / n**

**Dispersion**

The variation, or dispersion, of actual demands about the average refers to how closely the individual values cluster around the mean. It can be measure in several ways:

- As a range of the maximum minus the minimum value;

- As the mean absolute deviation (MAD), which is a measure of the average forecast error;

- As a standard deviation.

**Standard deviation (sigma)
**The standard deviation is a statistical value that measures how closely the individual values cluster about the average. It is represented by s. It is calculated as follows:

- Calculate the deviation for each period by subtracting the actual demand from the forecast demand;

- Square each deviation;

- Add the squares of the deviations;

- Divide the value in previous step by the number of periods to determine the average of squared deviations;

- Calculate the square root of the value calculated in the previous step. This is the standard deviation.

It is important to note that the deviations in demand are for the same timeintervals as the lead time.

From statistics, we can determine that:

- The actual demand will be within ± 1s of the forecast average approximately 68% of the time,

- The actual demand will be within ± 2s of the forecast average approximately 98% of the time,

- The actual demand will be within ± 3s of the forecast average approximately 99.88% of the time.

**Determining the safety stock and order point
**One property of the normal curve is that is symmetrical about the average.

Safety stocks are needed to cover only those periods in which the demand during the lead time is greater than the average. Thus, a service level of 50% can be attained with no safety stock.

As stated earlier, we know from statistics that the error is within ± 1s of the forecast about 68% of the time. Suppose the standard deviation of demand during the lead time is 100 units and this amount is carried as safety stock. This much safety stock provides protection against stockout for 34% of the time that actual demand is greater than expected. In total, there is enough safety stock to provide protection for the 84% of the time (50% + 34%) that a stockout is possible. The service level is a statement of the percentage of time

The service level is a statement of the percentage of time there is no stockout. It means being able to supply when a stockout is possible and a stockout is possible only at the time an order is to be placed.

**Safety factor
**The service level is directly related to the number of standard deviation provided as a safety stock and is usually called the safety factor. Note that the service level is the percentage of order cycles without a stockout.

__ DETERMINING SERVICE LEVELS__Stockouts cost money for the following reasons:

- Back-order costs,

- Lost sales,

- Lost customers.

In some markets, customer service is a major competitive tool and a stockout can be very expensive. In others, it may not be a major consideration. Usually the decision about what the service level should be is a senior management decision and is part of the company’s corporate and marketing strategy.

The only time it is possible for a stockout to occur is when stock is running low and this happens every time an order is to be placed. Therefore, the chances of a stockout are directly proportional to the frequency of the reorder. The more often stock is reordered, the more often there is a chance of a stockout. When the order quantity is increased, exposure to stockout decreases. The safety stock needed decreases, but

because of the larger order quantity, the average inventory increases.

It is the responsibility of management to determine the number of stockouts per year that are tolerable. Then the service level, safety stock and order point can be calculated.