1. Little's Law, which describes working capital performance (WIP = cycle time * throughput)

2. the VUT Equation, which relates capacity, variability and time buffers (CT(q) = V * U *t) and is vital to understand costing implications

3. Variance of Lead Time Demand, which drives inventory and performance (sigma

^{2}= Lead Time sigma^{2}_{D}+ Demand Sigma^{2}_{LT})
These formulas don't need derivation or mathematical explanations, but they describe some basic concepts which we can relate to as we define where we are standing and, maybe even more important, where we want to go in our efforts to optimize our SAP supply chain.

This blog deals with the first of these principles and its visualization by way of 'flow benchmarking'. Let's have a look on how to collect the information necessary to resolve Little's Law. SAP value stream mapping is a nice way to not only document the information and material flows in your supply chain, but also to determine at least two of the three variables in Little's Law. And the nice thing about that formula is the fact that it calculates the third. In an SAP values stream, which I will deal with in a future blog, one can identify lead or cycle times, inventory values and throughput. Depending on how you look at it, throughput in your supply chain may be identified as your daily sales value, WIP can be the average inventory holding (in dollars or euros) and the cycle time is the time (in days) to get raw materials through your production facilities and distribution network until the finished product arrives at the customer. Add the range of cover in days at every inventory point to that number.

Here is a slice of the value stream as I usually put it together. Note that there is information about the cycle time, and average inventory which represents WIP (in the example the values are left blank). The throughput I pull from a Sales report.

value stream example1

Now you can use Little's Law to determine the third parameter (if you don't have it already), double check on all parameters measured or calculate the minimum WIP (or average inventory holding) necessary to achieve a desired throughput (this can be the forecast-ed Sales).

With these values we can now plot a flow benchmark. In a flow benchmark you can visualize a Best Case Performance and a Marginal Performance. Then you identify your current position and hopefully you find yourself above the Marginal Case Performance and, if not, you can take measures to get into the lean zone.

flow benchmarking

It’s a busy chart but stick with me and you’ll see it’s fundamentally important for understanding your value stream and accompanying opportunities for improvement. First, the axes:

A. The left axis is throughput (or revenue) and is associated with the red lines and icons.

B. The right axis is cycle time (responsiveness)

C. The x-axis is Work in Process (a component of working capital). Note of paramount

importance: Both throughput and cycle time are related to WIP. This is a law of nature,

like the law of gravity. It is one of those fundamental Factory Physics laws, Little’s Law, and is stated as WIP = (Cycle Time) x (Throughput). You can ignore it if you want to but you will be affected by it. We have seen blind devotion to WIP and cycle time reduction (increased responsiveness) lead also to huge decreases in throughput (revenue). Huge decreases in revenue typically lead to changes in management.

To simplify the explanation, let’s stick with just the throughput (red) portion of the Flow Benchmark for now.

The red solid line (— ) shows “best case” throughput performance. This is optimal performance under perfect conditions i.e. zero variability. Your value stream cannot ever perform any better than this and typically does not perform close to this line.

The black, curved line shows “marginal case” throughput performance. This represents a practical lower limit for throughput. In the marginal case, substantial variability has been assumed (i.e. the standard deviation of process time is equal to the average process time) and most managers would agree that as a practical target they should be able to control their process times (e.g. VDF time at a furnace, tableting time at a tablet press, machining time at a mill) to have less variability than in the marginal case. The region between the Best Case and the arginal Case is called the "lean zone".

The red 'double triangle' shows what sales (throughput) you have achieved using how much average inventory (WIP) in the system.

The straight black line represents the forecast or current customer demand.

**Now what?**

Now that we know how to read the chart we can tell a few things:

- your performance at point 1 is slightly below the lean zone

- Given the current capability of the value stream, you can meet demand with reductions in variability alone - move Point 1 up vertically (increase throughput) without changing the amount of WIP or corresponding cycle time—though that is not necessarily the first approach you might want to take. Pure variability reductions are typically hard to implement. You could chose to improve performance merely by establishing WIP control, such as kanban or CONWIP, and reduce WIP from red point 1 to red point 2. Note that this also reduces cycle times, but also reduces throughput. The reduction in throughput is not that big of a problem in this case, however, imagine you would further reduce WIP from point 2. As you can see, the reduction in throughput would be unacceptable. That is because you need a certain amount of inventory to get your lines going and to achieve a certain throughput.

This relates the need for a scientifiv approach! A blind inventory reduction strategy only makes sense if you find yourself at point 1. At point 2 it would be fatal. At point two, we will have to take other measures to move up into the lean zone. That measure is a reduction in variability.

- Therefore, once you are at red point 2, you can increase throughput and go to red point 3 to meet customer demand either by decreasing pure variability effects (e.g. reduce flow variability) or by reducing variability and increasing available capacity (e.g. reducing setups).

As a manager looking at a local value stream (a production line) or an executive looking at a global value stream (a number of assembly and test operations in a supply chain feeding a distribution center), you can with one glance see how your resources are performing versus how they could be performing and in the same glance determine the type of improvement opportunities that are going to provide you with significant performance impact.

Now it is time to work with your SAP team and translate the optimization activities into the SAP system. We can now define Kanban, conWIP, a heijunka scheduling strategy or work with replenishment and planning strategies to get things moving into the right direction.

As we do this, I usually update my SAP value stream map and create a future map with all the required settings in customizing, the material master and transaction settings.

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