Getting the right inventory model

December 6, 2013 3:27 pm
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It is “an unfortunate truth” that most inventory models learned on training courses are not applied in the real world. This is not the result of ignorance; it is because they are unfit for purpose. The three principal issues are:

  • Although the underlying concepts are valid, the formulas rely on “constants” which are in practice either not known, poorly understood or not constant.
  • There are business constraints, such a limited available storage space, available capital or product life, which the formula ignores.
  •  The formulas are impractically complex, principally because if they were simple it would not satisfy the requirement for academic rigour their authors seek.

The consequence of these issues is that businesses frequently abandon the theory and develop their own inventory rules based on pragmatic experience. These establish the common but unhappy balance of too much inventory and disappointing customer service.

A better approach

Rather than abandoning the principles, the approach should be to tailor their application to the specific business and its constraints, never losing sight of the fact that in the end there are only two reasons for holding any inventory.

  • To enable the business to manufacture or buy material in cost effective quantities.
  • To ensure that customers are satisfied despite the uncertainties of the supply chain; supplier delivery (time and quality), manufacturing attainment and variation in customer demand.

Cost effective quantities

The phrase “Economic Batch Quantities” has an appalling reputation. Nevertheless, virtually all businesses do make batches, and by inference believe these to be in some way better than larger or smaller quantities. Perhaps a better term to use is “Best batch size”.

In the classic EBQ model, the formula for the batch size attempt to minimise the total cost of setting up and storing product. The variables involved are:

  • Set up cost
  • Part unit cost
  • Typical annual % cost of inventory
  • Annual demand

No other constraints or variables are considered – and even these are open to widely differing interpretations. For example; how much does a set-up actually cost? At one end of the spectrum businesses choose this to be zero on the basis that the business costs would be the same were the set up carried out or not. This argument is popular with promoters of Lean. At the other end of the spectrum the cost is said to be the full recovery cost / hour of all the resources set up for the batch and the labour costs of the staff involved. Similarly varied arguments can be made about the annual cost of inventory.

And what if the business has other considerations, such as limited product life, limited storage space or limited capacity? How does the formula take these into account?

Where one man can articulate, another can formulate.

The difficulty is now – and always has been – articulating the business constraints clearly enough to enable the solution to be calculated. Part of the reason is that it can be surprisingly difficult to express an intuitive feeling as a logical statement and part is an irrational insistence on the textbook model. The key to getting it right is to spend time properly exploring the business constraints and using them to develop a solution suited to the business. This is usually requires several iterations as some of the stated constraints may well be contradictory, but this process in itself is of value to the business.

Rational Safety Stocks

The aim of safety stock is to ensure that the business has the required material available despite the vagaries of life. The question it attempts to answer in this case is: “How much stock do I need to keep as a buffer against the uncertainties of life to ensure I achieve my customer service targets?”

Safety stock calculations have a better name than EBQs, though perhaps they shouldn’t, as their application is usually as poor. What better place to find a formula for its calculation than Wikipedia?

Safety stock = Zx[ALT x (SDD)2 + (AD x SDLT)2]1/2

Where Z = No of Std deviations required to achieve safety level

ALT = Average Lead Time

SDD = Standard deviation of demand AD = Average Demand

SDLT = Standard deviation of Lead Time

It is worth noting three key points:

  • The particular formula above allows for varying demand and lead times but takes no account of quality (although it can be modified to do so).
  • The part of the formula dealing with the standard deviation of demand calculates the answer to the wrong question. The question it should answer is:

“What level of stock do I need to provide my target level of service?”

The actual question it answers is:

“What level of stock to I need to deliver 100% service in the target percentage of weeks?”

  • In actual fact, the standard deviation of demand is not the right measure anyway, it should be the standard deviation of the forecast error

How much difference does this make? Consider the product with the demand pattern below:

Weekly demand

Assuming a 4 week lead time, the “Wikipedia” formula suggests that 93 units are required to deliver a service level of 95%, and so, presumably, will the system programmed with it. Actually, this level of safety stock will deliver 100% service 96% of the weeks, and an overall level service level of 99.9%. In fact only 54 units are required to achieve the target service level.

So what is the solution?

Achieving the best solution does not depend on a degree in statistics but it does require the ability to convert ideas into formulas. It is worth doing; a little hard thinking can release a lot of hard cash.


Written by Paul Eastwood, Director

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