Behavior of a Kanban Supermarket

Setting up a kanban system is tricky, especially determining the number of kanban. The kanban formula is at best a rough estimate. It is usually advisable to adjust the number of kanban as the system is running. In general, if you have too much inventory, reduce the number of kanban. If you run out of material – and the cause is a lack of kanban – then increase the number of kanban. However, this general recommendation can be refined a bit by looking at the supermarket inventory. Let me show you how to improve your kanban system by analyzing your supermarket inventory.

This blog post is loosely based on chapter 13.2 of my new book All About Pull Production: Designing, Implementing, and Maintaining Kanban, CONWIP, and other Pull Systems in Lean Production.

Introduction: A Supermarket Inventory

Replenishment TimeA supermarket is an inventory arranged by product type in FIFO sequence at the end of a kanban loop. If an item leaves the supermarket, a signal (the kanban) is sent back to replenish the material. Depending on the fluctuations of the supply and demand, the inventory in the supermarket fluctuates (this is actually the main reason we have inventory in the supermarket). However, these fluctuations can look very different depending on the behavior of the system. Especially the replenishment time in relation to the fluctuations can make similarly performing systems look very different.

Supermarket Behavior for a Short Replenishment Time

Below is a timeline of a supermarket inventory for one part type for a system with a short replenishment time. I played around with the system to achieve delivery performances of approximately an excellent 99%, a mediocre 90%, or a bad 80%. The graphs below show a part of the entire timeline, as well as the histogram of the supermarket across the entire simulation. Due to the short replenishment time in comparison with the fluctuations, the timeline touches both the bottom (a stock-out) and the top (the inventory limit, i.e. all kanban in the supermarket) of the graph.

Especially relevant is if the curve touches the bottom and you run out of material. For a delivery performance of 99%, this happens rarely. The first timeline touches the bottom only once. With a delivery performance of 90%, a stock-out is more common. Finally, a delivery performance of only 80% touches the bottom of the graph frequently. This can also be seen in the histograms. Please note that the number of kanban differ, and hence the three histograms are on a different scale. The first graph had a 98.87% delivery performance, and the supermarket was empty for 1.03% of the time (i.e., the bottom most bar in the first histogram is 1.03% of the time). The second simulation had a delivery performance of 91.33%, and the supermarket was empty for 8.55% of the time. Finally, the last simulation had a delivery performance of 80.90%, and the supermarket was empty for 18.93% of the time.

Supermarket Behavior for a Long Replenishment Time

I also simulated a very similar system, but now with a much longer replenishment time. Hence, most of the time a majority of the kanban were under replenishment. Regardless of the delivery performance, there were never all kanban in the supermarket. In fact, there were never more than half of the kanban in the supermarket, with the other half under replenishment, or “in the pipeline,” if you will. However, similarly to the short replenishment time, the curves touch the bottom line (i.e., zero inventory) occasionally.

This can also be seen in the histograms. Please note that again the histograms have different scales. Also, since the system with a long replenishment time needs more kanban for the same output, the histograms have many more entries. In any case, the percentage the supermarket was empty also correlates closely with the delivery performance of the system.

Extreme Supermarket Behavior

Just for comparison, I also simulated systems that had way too many kanban. Below are the timelines for the system with the short and the long replenishment times, as well as the corresponding histograms. Since there were way too many kanban, the supermarket was never empty. On the contrary, the supermarket was always more than half full. The system with the short replenishment time was often completely full (as expected), while the system with the long replenishment time was never completely full (also as expected).

If your supermarket shows a behavior like that for one part type, then this is a good indication that you have too many kanban. Reducing the number of kanban would not hurt the delivery performance, but improve your inventory cost. For such an extreme case as shown here, you may be able to remove half of all kanban … although to be on the safe side, I would start with removing one-third and then continue to observe before removing more.

Lack of Capacity Is Not the Fault of Kanban

The behavior of the supermarket and hence delivery performance can be influenced by the number of kanban. The number of kanban is needed to cover fluctuations like breakdowns or swings in customer demand. However, there are also other systematic problems that can affect your supermarket fill levels. The most important one is capacity. If you have and use too much capacity, your inventory in a push system would continue to increase. This is bad. However, since we have a kanban system and hence a pull system, the pull system puts a limit to the increase in inventory. So this side of the capacity problem is covered.

However, the other capacity problem is not having enough capacity. If your system is too small and does not have enough capacity, no amount of kanban will help. Even with enormous kanban quantities, most will be waiting for production (i.e., the bottleneck), and very few will be in the supermarket. Delivery performance will suffer.

Below are the two systems with a short and a long replenishment time, but this time with a demand being much higher than capacity. The supermarkets are empty most of the time. The system with a short replenishment time is full only a few times, but completely empty most of the time. The system with a long replenishment time started out with enough capacity and with almost full supermarkets, but then demand exceeded capacity and the supermarket is getting emptier and emptier until it is almost always empty in the last third of the graph. Again, no amount of kanban will help. You can only increase capacity (or decrease customer demand) to get back to a normal running system.

Overall, the supermarket and especially the histogram of the supermarket give you a good estimate of the behavior of your kanban (or other pull) systems. You can also estimate the delivery performance based on the percentage of the time the supermarket is empty. Now, go out, take a good look at your supermarket, and organize your industry!


All About Pull Production Ebook Cover

This blog post is summarized from my latest book on pull production, where you will find many more details on all of these systems and how they can work together. You will also find a foreword by John Shook.

Roser, Christoph. All About Pull Production: Designing, Implementing, and Maintaining Kanban, CONWIP, and other Pull Systems in Lean Production. 441 pages: Publishing 2021.


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