How to optimize inventory?
Let’s say that the inventory position is R, which is the sum of the physical stock and all open orders. If R is less than the safety stock (SS) and expected demand in lead-time (D), we need to replace an order.
How to find the optimum R? (Let’s say R*)
Our reorder point R has a coverage profile. It shows how much of the demand possibilities may cover. It’s shown as F(R), and a number between 0 and 1. For example, if it’s 80%, that means you may cover 80% of all demand possibilities.
If this coverage profile is equal to the customer service level, we have the optimum reorder point, and so, the safety stock. Namely, F(R*)=CSL...
For example, if CSL=95%, then F(R*)=95%. So, we need to find how much we need to cover 95% of all demand possibilities. It depends on the demand function. (i.e. if it’s a normal distribution, you may check it easily in spreadsheet programs, like excel)
Till now, everything seems OK.
- Analyze the demand and formulate the demand function F().
- Calculate CSL, and find R*.
- Figure out SS. (SS=R*-D)
However, this approach does not consider the effect of the order quantity. It assumes that the inventory will always remain on the level of R.
As usual, there are some order receipts (Q).The inventory position circles between R & R+Q. So, the coverage profile of the inventory position circles between F(R) and F(R+Q). And around CSL...
Like a planetary system, the inventory position circles around CSL.
Then, how to find R* now?
You may handle it with the Unified Supply Model. Here's the main formula;
Average[ F(R) + ... + F(R+Q) ] = CSL
If the average of the all coverage profiles between F(R) and F(R+Q) is equal to CSL, R is the optimum point.
Basically, it unifies safety & order, around service level. It provides a balance between R & Q. If we need to increase order quantity, it decreases R, to keep the balance around CSL.
You can find R*, via our Online App, easily.
More details can be seen on Unified Supply Model.
Founder at Arkhon Optima
6 年Dear Sheldon, thanks for your detailed comments. For CSL, may I propose the article below? It explains the definition of CSL. And, it's a result of business, not a decision. https://www.dhirubhai.net/pulse/how-define-customer-service-level-utkan-ekinci/ For Leadtime options, could you please check the article below? It discusses the leadtime options, and how it effects SS. https://www.dhirubhai.net/pulse/how-optimize-leadtime-utkan-ekinci/ For Leadtime variability, I didn't mention it here yet. This is a subject of another article, Supply Variance. Meanwhile, you may also check the web site, (https://unifiedsupplymodel.com/general-model45) It's explained in the section "Inputs - 4. Leadtime Demand Function". For the link between SS & R, I think that we don't need to prove it, because it is by definition. For further discussion, you may also check the section "Inputs - 6. Safety Stock and Order Quantity", on same page. Thanks again, for your valuable input. Waiting for your comments...
Simplifying Supply Chains, Elevating Value, Implementing Strategies.
6 年Okay - but this model is limited to consistent service level which you equate to SS. But SS is a function (R2 - R1 / T2 -T1) Where T is time. You assume the replenishment lead time is constant. But you never proved the correlation of change in SS with R?
Freelance Safety-/Process engineer and Safety Leader, Expert in: EHS, Quality Management, Lean Transformation, Process improvement
6 年Nice theoretical example.