This is the third article in a series on measuring demand variation.

## Analyzing Demand Variation for Kanban

The demand charts in part-1 of this series illustrate that a major component of demand variation is time. Thus, time is key for kanban. It is vital that demand data is segregated into the proper time periods. How do we define “proper”?

A given item may experience significant demand variation from day to day, while experiencing essentially no variation on a weekly basis. In such as situation, which time period is “right”?

With kanban, lead-time defines the appropriate time period for analyzing an item’s demand variation. As a reminder, lead-time is the time that elapses between when an order is placed and when the corresponding items are received. We cover this concept in our inventory replenishment sawtooth curve series.

Typically, this advice raises at least a few questions. After all, since kanban formulas account for daily demand, why not quantify the standard deviation of that daily demand? Better yet, why not simplify and streamline our variation analysis by defining the same analysis period (e.g. week, month, etc.) for all items?

Ultimately, we could argue that kanban purchase quantities account for target safety stock during the lead-time period. Lead-time safety stock is in the math of kanban! So, if you’re designing a kanban solution, you really have no choice, but to quantify the demand variation of lead-time.

The logic behind this approach is that lead-time demand variation is what determines our real need for safety stock. Consider an item with huge daily demand variation, but with nearly no weekly demand variation. In this circumstance, if the item’s lead-time is one week, then the high variation in daily demand is inconsequential. We have no need for safety stock to address daily variation because our lead-time gives us a week to supply parts. Analyzing the demand variation of lead-time avoids the excessive safety stock that would result from quantifying daily demand variation. Lead-time demand variation is what matters.

To illustrate this, imagine an item with exactly 100 units of demand on every 10th work-day, but with zero demand for the preceding 9 days. The item has a 10-day lead-time. By calculating the average and standard deviation of daily demand we get a daily average of 10 units with a standard deviation of 31 units per day! However, if we consider the fact that the item has a 10-day lead-time, and calculate the average demand and standard deviation accordingly, we end up with an average of 100 units per lead-time (10 units per day), but a standard deviation of zero!

## Rolling vs. Discrete Lead-Time Periods

Once we understand the necessity of quantifying the demand variation of lead-time, we must determine whether to analyze demand variation in discrete or rolling lead-time periods. Let’s assume we have demand data for a specific item. As the first 2 columns in Table 1 illustrate, the item has an average daily demand of 10 units and we have 28 weeks of data. The lead-time is four weeks. We must now decide whether to assess demand variation in rolling or discrete time periods.

**Rolling Lead-Time Periods:**As illustrated in column-3 of Table 1, rolling period demand is the demand associated with the current week and all preceding weeks, necessary to account for a complete lead-time period. With a lead-time of four weeks, the first week with four weeks of demand would be week-4. That period would consist of the sum of demand from week-1 to week-4. The week-6 rolling period would account for total demand from week-2 through week-6.Aside from being marginally quicker to setup in a spreadsheet, the benefit of using the rolling period approach, is that it maximizes the number of periods to analyze. This is especially helpful if your lead-time isn’t very long (a nice problem to have).On the other hand, with rolling periods, some weeks will be counted more or less than others meaning that their data will carry more or less weight. Consider the first and last 4 weeks in our table compared to other weeks. Week-1 is counted once, while week-4 is counted 4 times.**Discrete Lead-Time Periods:**Discrete lead-time periods consider each lead-time period as unique. 28 weeks would be segmented into 7 unique lead-time periods (28 weeks / 4-week lead-time = 7 unique lead-time periods). See Table 1 for an example. If the total number of demand observations isn’t evenly divisible by the observations per lead-time period, then you may choose to drop some of your observations so that it does.

Often, the difference in results between discrete and rolling lead-time periods is negligible. Examine the average period demand and standard deviations of each column in our table. In fact, you should pay particular attention to avoid a very common and costly mistake. As the standard deviation of the 3 columns illustrates, you should never assume that you can take the standard deviation for a series of weeks and simply multiply it by the item’s number of lead-time weeks to calculate the standard deviation for the item’s lead-time. In this case we would add a whopping 19.9 (4.9 x 4 weeks) units of safety-stock instead of the correct 5.5. That’s almost 4 times the adequate amount of safety-stock!

## Seasonal Demand Variation

For those items whose demand demonstrates seasonal effects, have to organize the weekly demand information into periods that represent those seasons. It’s important that the demand variation for a given seasonal period should be assessed exclusive of other periods. In future posts, we will cover seasonal demand variation in more detail.