Service Level: Which one to use for Safety Stock?

In my experience in consulting projects related to Inventory Management, it is very common for us to be asked to define inventory policies for a company and to calculate the appropriate safety stock levels for each item or group of items. However, what we often observe is a certain confusion in understanding the theory behind one of the main parameters for such analysis: the level of service.

To begin, it is worth remembering the classic safety stock formula, which considers that the distribution of demand and lead times of supply follow a normal distribution. In this formula, shown in figure 1, we have, within the root, the mean and standard deviation parameters, both for demand and for lead time of supply. Outside the root we have the parameter k, related to the level of service. In this article, I would like to explore a little about this parameter: what are the ways to calculate it and the precautions in its use and definition.

To define the service level to be used in the safety stock analysis, we can initially adopt two approaches: the first would be to calculate what the optimal service level should be, which balances the costs of shortage and excess, while the second would be based on a strategic definition, in which the company's managers define a desired service level for that item. In the first case, we will need to obtain information about the product's contribution margin (which is related to the shortage cost) and about the opportunity, storage and loss costs (which are related to the excess cost). With these parameters, it is possible to calculate the optimal service level. However, it is essential to understand what service level we are talking about, which in this case is the Cycle Service Level (CSL) or Cycle Service Level. The cycle service level represents the probability of not having a stockout during 1 cycle. This cycle represents the interval between replenishments, that is, if every week I receive a new batch of products in my inventory, the CSL would represent how many weeks within the year I had a stockout of this item (even if it was 1 item during 1 day this week). Using a numerical example (figure 2), in an interval of 50 weeks (almost 1 year), a CSL of 96% would mean that in only 2 weeks of these 50, I had a stockout. 

The second strategy would consider a definition top-down of what level of service is desired for a given item. In this case, it is quite common to use the service indicator as a reference. fill rate for the service level to be achieved. This is common because the indicator of fill rate, as discussed in post written by consultant Bruno Peixoto, is a strategic indicator, widely used by the industry and well known by executives in the areas of operations, planning and supply chain leaders. However, using the indicator fill rate as a reference for calculating the parameter k of the safety stock formula is wrong, since the fill rate considers the volume associated with the rupture, while the CSL (which is the correct reference for k) represents the frequency at which ruptures occurred. And these values ​​can be quite different, as can be seen in the example in figure 2: while the CSL reached 96% in the period analyzed, the fill rate is more than 99%, since the volume of unmet demand represents very little compared to the total demand of the 50 weeks.

It is essential to understand these concepts in order to use them appropriately when defining which safety stock will be maintained for each item, thus avoiding high costs due to a parameterization error. But the question remains: how do CSL and Fill Rate, is it possible to calculate one from the other? The answer is yes! But that is already a topic for a future post.

References

• ilos.com.br/fill-rate-importancia-e-estrategias-para-melhorar-o-indicador/
  
• web.mit.edu/2.810/www/files/readings/King_SafetyStock.pdf
  
• blog.arkieva.com/cycle-service-level-versus-fill-rate-service-level-part-one/