Calculate Max Inventory
Paul Trudgian Ltd | Supply Chain & Logistics Consultancy No Comments

There’s a common thread on many industry discussion forums posing the question – ‘how can I determine a maximum level of inventory for a product?’. As with many aspects of supply chain management and optimisation, there isn’t a single answer. Due to the variables of supply and demand, along with business and product characteristics, there are many caveats to standard approaches. However, in this article we’ve gone back-to-basics to give the answer from first principles.

The First Principle of Inventory Management

The first principal of inventory management, and the basis from which you should start to consider the maximum level of inventory, is that you should only hold sufficient inventory to cover demand during the replenishment lead time. Put simply, if it takes 1 week for a supplier to replenish your inventory and you expect to sell 100 units in that 1 week, then your maximum level of inventory should be 100 units. No more, no less.

However, the real world is a little more complicated than that…

In reality, it’s unlikely that you will sell exactly 100 units. Customer orders will not always reflect your expectations and forecasts will always have a level of error. Consequently, when determining your maximum level of inventory, you must also consider demand variation and supply variation.

Demand Variation – What If You Sell More Than Expected?

By looking at historical demand, or the forecast and forecast error, you should make an assessment on the probability of demand exceeding the expected 100 units. This probability can then be translated into an additional ‘safety’ stock.

There are several methods and formulas for calculating safety stock for demand variation, but the typical way is to work with a normal (Gaussian) distribution. To do this, you take the inverse of the normal distribution, based on the service level you wish to target, and multiply it by the standard deviation of demand. You then multiply this again by the square root of the lead time. This will give you a safety stock level that should be added to the 100 units.

Supply Variation – What if Supply is Late or Not in the Expected Quantity?

As with demand variation, there is a likelihood that the supplier may not provide you with exactly 100 units, or they may deliver late. To capture this eventuality, you must follow the same logic as calculating the safety stock for demand variation. Assess the historical variation in supply and once again use the normal distribution to calculate a supply variation safety stock.

The Result – the Maximum Level of Inventory

Based on the number of units you expect to sell during the replenishment lead time, and the demand and supply variation, the maximum level of inventory you should hold is:

Expected sales + demand variation safety stock + supply variation safety stock.

Further Complicating Factors

The above result is also effectively the Reorder Point (ROP) i.e. the point at which the inventory needs to reach before a replenishment order is placed. In an ideal world the ROP and the maximum inventory level would be the same. However, there are further complicating factors to consider, two of which are supplier replenishment quantities and demand profiles that do not follow a normal distribution.

Supplier Replenishment Quantities

In the above discussion, we have assumed that the supplier replenishes exactly in accordance with usage i.e. if you sell 100 units then the supplier replenishes 100 units. Of course, that may often not be the case. The supplier may have you fixed onto a Minimum Order Quantity (MOQ) that doesn’t reflect your expected demand. If that MOQ exceeds the maximum level of stock you have calculated, then the MOQ becomes your maximum level of stock.

Even if there is no MOQ, then it may still be the case that the supplier can only supply in multiples. For example, you may want to replenish with 100 units, but the supplier may only supply in multiples of 15. This means that you need to purchase in multiples of 15 and will consequently be replenishing with 105 units. Again, as with the MOQ, 105 units will become your maximum inventory level.

Demand is Not Normally Distributed

Whilst most high velocity products will typically follow the normal distribution, slower moving products may not. Consequently, the method we have suggested for calculating demand variation, and supply variation, safety stock will not work effectively.

There are many and complex mathematical ways of dealing with other distribution types when calculating safety stock. However, the simplest way is to aggregate the time ‘buckets’ you are dealing with. So, if you are assessing the data in days, try aggregating to weeks or months to see if that provides a normal distribution.

Think of it like an Indian Takeaway – if you reviewed the sales by day for a takeaway, then the distribution of those sales is likely to be heavily skewed to Fridays and Saturdays, with very little demand on the other 5 days. However, if you aggregated to weeks, you would see a similar level of total sales for each week which is likely to be normally distributed.


Our supply chain consultants are experts in inventory management and inventory optimisation. If you would like to discuss your inventory requirements with our team please contact us on 0121 517 0008 or email [email protected]

Leave a Reply

Your email address will not be published. Required fields are marked *