# Working Capital Optimization: Safety Stock

When it comes to inventory management, companies often underestimate the importance of safety stock and the need to maintain optimal levels.  While it may seem like the path of least resistance from a service level standpoint, holding excessive inventory stock level leads to suboptimal working capital management and, as a result, hurts profitability by curbing one of its key components: capital turnover, as Trindent Consulting has seen on medical devices inventory improvement projects.  Although determining optimal inventory level is challenging for several reasons, there are ways of optimizing it without disrupting the chosen service level.

#### Calculating Optimal Stock Levels

Depending on the business realities and the type of inventory management (Fixed Order Quantity or Q-model or Fixed Time Period or P-model), the two main questions of inventory management are when and how much to order. The answer to both questions must include two components: covering demand between the reorder periods, and safety stock to account for demand variability.  If it were not for demand variability, the decision on the size and timing of orders, and therefore inventory levels, would boil down to a simple exercise in Economic Order Quantity (EOQ), which balances ordering costs with inventory holding costs to arrive at the optimal frequency and size of ordering based on stable demand.  In this perfect scenario, we would boast 100% in-stock and fill rates and the minimum inventory determined by the EOQ calculation.

However, there is always demand variability and the desired service level to take into consideration. Service level is particularly important in the healthcare industry, where it’s not only desired but required.

To show the logic behind inventory management, let’s look at the Q-model.  Let’s assume we are dealing with a product for which the expected demand is Dp, for the period in question P.  The lead time for the delivery from the supplier (or warehouse) is L.  Let’s also assume that the demand is random and follows a normal distribution (which will not always be the case) with the mean µ and standard deviation of σ.  We can then calculate stock quantity S, which we should be attained.  As we will see below, the stock quantity will contain a sufficient amount of product to cover demand for period P+L plus the safety stock, which will depend on the service level we will choose to pursue. The formula for calculating S is as follows:

S=D_(P+L)+z*σ_(P+L)-I

where:

D_(P+L): is the demand for the period P and the lead time L, and can be calculated as D_(P+L)=µ*(P+L)

z: is the number of standard deviations in normal distribution corresponding to the service level we choose

σ_(P+L): is the standard deviation of the demand for the period P+L

I : is the inventory on hand at the time of ordering.

Notably, z*σ_(P+L) is the safety stock portion and depends on the variability of the demand, represented by the standard deviation, and the chosen service level, represented by the number of standard deviations corresponding to it.

#### Choices and Challenges

While calculating safety stock using this framework seems like an easy exercise, there are several challenging choices that need to be made, including determining the properties of expected demand when past performance may not be a good indicator of the future. This may bring the mean and the standard deviation of the normal distribution into the spotlight, and sometimes even the distribution itself may not be normal.  Another challenge is lead time variability. While the formula above assumes lead times are stable, there may need to be an additional level of analysis to arrive at a proper value for it.

The main challenge, however, is choosing the necessary service level to meet. The most calculated approach to determining service level follows the same logic as EOQ determination: by counter-balancing costs of overage (or holding costs, or h) and costs of underage (also known as backorder costs, or b), aiming to minimize both. Holding costs include the cost of capital, storage, obsolescence, and other costs related to holding inventory. Backorder costs include the lost profit from transactions that do not happen due to stock-out situations.  It is, however, very common to attribute additional meaning to backorder costs in an attempt to evaluate other negative effects of a stock-out, such as reputational cost and the effect on market share. Since we measure service level as the probability that stock-out does not occur (Pr(DP+L≤S)), the optimal service level can be reflected as follows:

Pr⁡(D_(P+L)≤S)=b/(h+b)

As we can see, depending on the value attributed to backorder costs (b), stocking out may well be decided as prohibitive.

In addition to properly calculating necessary stock levels, there are several strategies to minimizing inventory without affecting the critical service levels. For example, organizations often apply the same calculation to all the products in their roster, so products that are very important may dictate the service level for the entire list. By a simple stratification of products into A/B/C tiers and by assigning appropriate service levels to each, considerable savings may be attained.