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I'm in the process of calculating inventory levels for a bunch of SKUs and I'm wondering if you all-mighty statisticians had any card up your sleeves that I could borrow.

Here's the deal: service levels are inevitably going to be affected by the amount of material I decide to put in stock. The more I stockpile, the higher the fill-rate will be (but of course inventory doesn't come cheap). The less I keep on-hand, the higher the chance of having a stock-out.

I have to strike a balance between holding costs, and service level.

Based on past sales, I was able to plot the expected fill-rate against the volume of on-hand materials. Check it out:

enter image description here

As you can all see, the service level increases very rapidly at first, but then the growth rate starts decreasing quite abruptly. Going from 90% to 100% requires 9 times the amount of material it took to go from 0% to 90%.

Now, getting to the point, is there any scientific way to tell where I should stop? How do I know when the marginal increase in fill-rate is too little for that much of an increase in stocked volume?

I know choosing the right service level is mostly a "political" decision, but I really hoped that you guys could come up with some kind of suggestion to help me in the process. I'm kinda out of my element here.

Thank you guys for your time!

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Strictly speaking this is operations research more than statistics, but the key issue is the cost of a stock-out. So you need to know (or at least estimate) the holding costs of different levels of stock, the opportunity cost in terms of potential profit forgone (and perhaps the reputational cost) of failing to meet a large order, and other costs such as those of restocking (which might include for example delivery charges). You can then model different stocking regimes - typically with a maximum and minimum level of stock held - against the pattern of orders to find the optimal approach. – Henry Apr 1 '12 at 9:04
Isn't there anything like OperationsExchange? That would be sweet :) – Bruder Apr 1 '12 at 10:08
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or-exchange.com – Emre Apr 1 '12 at 22:30
LOOOOL!!!! I mean, seriously??? That's awsome! – Bruder Apr 2 '12 at 8:03

2 Answers

up vote 1 down vote

There are many parameters to consider, but the answer is yes, by incorporating the expected value of the extra inventory. There are many costs which affect expected value:

  • Holding
  • Cost of Capital
  • Purchase
  • Obsolescence
  • Liquidation

One of the most important costs in your calculation will be the cost of a stockout. This is notoriously difficult to calculate. Sometimes the cost of a stockout is a lost sale. Sometimes it is a lost customer. Sometimes there is no cost at all (the customer is willing to wait for your stock to arrive). How you decide to calculate this cost will weigh heavily on the outcome.

Keep in mind that your expected value calculations should always be on the marginal unit.

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If you could put a price on your fill rate and inventory volume then you would be able to compare like quantities and optimize jointly. Failing that, you can pick an arbitrary fill rate (like 90%) and set your inventory volume accordingly.

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