When I first learned inventory planning the math was rather simple. On top of the cycle stock (expected demand during lead time) I would add a percentage or a number of days (or more likely weeks). If the lead time was 2 weeks I might carry 3 or 4 weeks. I soon learned that demand for some inventory items is more volatile than for others, and some suppliers less reliable than others. I’d rather have too much then not enough, and I’d never gotten in trouble for having a little too much.
So since all items and situations are different I started using some statistics; (average demand * lead time) + (one sided Z factor * demand standard deviation) for the target inventory level; a little better approach.
Here’s another formula from Inventory Management Review;
Safety Stock:
{Z * SQRT (Avg. Lead Time * Standard Deviation of Demand ^2 + Avg. Demand ^2 * Standard Deviation of Lead Time ^2}.
Over at QuickMBA ; To calculate the safety stock, first calculate the standard loss function, designated as L(z). This function is dependent on the values of the desired fill rate f, the demand μ and its standard deviation σ , the time between orders p, and the replenishment lead time l : L(z) = ( 1 – f ) µ p / σ ( p + l )1/2. Once L(z) is known, z can be found in a look-up table and the safety stock can be calculated by:
Safety Stock = z σ ( p + l )1/2
Here’s a new one recently published by Kent Linford in the APICS Magazine Nov/Dec 2006.
SS = √ [( σFE)2 x (LTI/FI)beta + ( σLT)2 x D2] x Z x (FI/OCI)beta
Where:
SS = safety stock
FE = forecast error
LT = lead time interval
FI = forecast interval (pick a beta between 0.5 and 0.7)
D = average demand during lead time
Z = normal distribution service factor based on desired service level
OCI = order cycle interval
Dave Piasecki at InventoryOps.com uses;
safety stock = (standard deviation)*(service factor)*(lead-time factor)*(order cycle factor)*(forecast-to-mean-demand factor)
Jon Schreibfeder has another approach.
Any questions? Got any other versions? What formula do you use?
Lawrence,
could you please check the source of APICS formula, it seems that standart demand(D) should be squared.
Thank you.
Thanks Artem.
[...] Safety stock [...]
What is the difference between Saifty stock and minimum control inventory level?
Hamidur Rahman, the difference is that safety stock is generally considered a quantity, that is a number of units, while a control level is used as an action point or reorder point. The number for both can be the same. Sometimes they are not, it depends on your system and how you determine replenishment; whether you are using reorder point, time-phased reorder point, MRP, kanban, rate-based. Often I will need to hold additional inventory in flow above the safety stock quantity to handle temporary demand for promotions, or product model change, or seasonality.
What is beta?
Is it some statistical distribution?
Sean, from the article by Kent Linford … An element of this lead time adjustment is a variable called beta. This variable is used as an exponent in the adjustment. Most literature, including APICS
curriculum, recommends a beta between .5 and .7.
Sorry, but I’ve never used this approach for setting safety stock. Perhaps you could write to the author.
I am looking for a LSS focused formula for calculating specific inventory level for achieved a desired fill rate. Not sure if the above is what I need. For a given location inventory I know what items are stocked, which items moved and how much, how those items moved (ie: straight from inventory, bought out, fill rate, etc…) and based on individual item inventory stratification classification I can segregate “good” boyouts from “bad” buyouts. I also know the overall fill rate for the location. What I am looking for is a calculation incorporating these (and other?) variables in order to state “In order to achieve desired fill rate of X% – I need to carry Y Inventory ($). I am beginning to feel like I am searching for the Holy Grail. Anyone have any suggestions?
Thanks,
Susan
Susan,
A book for your consideration: Inventory Management Explained, by David J. Piasecki.
Feel free to write to me directly at lmloucka@comcast.net
What should be the formuala to calculte the safety lavaels?
what should be the formaula to calculate safety stock for flexible production systems?
Safety levels aren’t calculated, they are a management decision. The higher the level the lower the risk of ’stocking out’, but also the higher the inventory cost. You could do an optimization: cost of lost sale verses inventory cost, but can you really know the true costs of poor customer service?
what do you mean by ‘flexible production system’? For companies that make to order you may not need finished good safety stock. When well linked to suppliers with quick response and pull techniques you may not need raw material safety stock. Having no safety stock anywhere in a supply chain is rare and probably foolish.