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This problem is work related not school related. I am developing a simple inventory management system to solve a digital supply chain problem and I need help with an algorithm to control the base-stock level.

I can measure things like the units sold in a specific duration of time (minutes) over time, historical inventory levels over the same duration of time, length of time it is taking to refill inventory and so on.

I have started to read some things about Erlang distribution but frankly I don't really know if that is the right direction. Do you have any ideas about an algorithm that might work that you can share? Do you have a starting point that you can share? Can you recommend a website/tutorial on the subject?

EDIT: More detail about the system

There are 16 - 24 clients that all pull from a centralized inventory management system. There are about 1000 unique digital products that are held in the inventory management system and they are sourced from a variety of other source systems.

I can measure the number of orders that are occurring in each of the clients because they are reporting the distribution of the digital product to the centralized system. I can also track the time it takes to replenish inventory from the source systems from the time that the order was created in the inventory system.

Basic system drawing

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    In any case the business has said that they do not want excess inventory on hand if they don't have to have it. So I am left with the problem of creating a system that will dynamically set a base-stock level.2011-07-13

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Don't over think the problem. Any slight differences resulting from using the not-quite-perfect probability distribution will be over-shadowed by real world factors that you can't anticipate.

I would take the approach that you want the smallest inventory that keeps you from going out-of-stock, without concern for cost. If you know the replenishment time, and the highest number of sales in that time frame, you are already in the ball park.

At a slightly more sophisticated level, model the arrival of orders, perhaps as a Poisson distribution. Then, at any base stock (or reorder point), you can calculate the probability of going out-of-stock, and pick a suitable level (1 in 100, 1 in 1000, whatever). I'd be worried about time-of-day effects and seasonality, too.

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    A$f$ter we get the basic $f$unctionality working we will for sure look to add some of the timing considerations that a Poisson distribution brings to the table.2011-07-14