Inventory Replenishment Sawtooth Curves – Part 2 of 4 – Charting Sawtooth Curves

How to Chart an Inventory Sawtooth Curve

Before we can analyze a sawtooth curve, we must understand how to chart one.

This requires analysis of 2 factors:

  1. Consumption
    Consumption rate is the speed of item usage and is a key factor in charting the sawtooth curve of any item. Consumption rate directly determines the slope of inventory draw-down and an item’s on-hand balance (OHB) at any given point in time.
    Because consumption is demand driven, it is often random to some extent. While charting every individual consumption event (or OHB change) is possible, it’s typically impractical. Rather, it often makes more sense to group consumption into broader hourly, daily, or weekly periods, within an item’s total replenishment period.
    To do that that need to know a few specifics concerning an item’s replenishment.
  2. Replenishment

    The appropriate interval period for charting your sawtooth curve will be determined by each item’s replenishment (i.e. supplier) constraints, which consists of 2 key categories:

    1. Quantity Limits: Every inventory item supplied by each unique supplier has 3 quantity limits that must be defined in order to design a reliable replenishment plan.
      • Minimum Order Quantity (MOQ): Every supplier has a minimum quantity that they can and will sell on a consistent basis. The specific limits and reasons will vary from supplier to supplier, but there is always a limit.
      • Maximum Order Quantity (MaxQ): Just as every supplier has a limit on the minimum quantity it will deliver, each supplier also has a constraint on the maximum quantity of items it can consistently deliver at once.
      • Standard Package Quantity (SPQ): An item may come packaged in a box, on a pallet, in a tote, in a pail, by truckload, or any number of other ways. Regardless, each “full” package type will contain a specific item quantity.
    2. Lead-time: Item quantity limits influence 2 major lead-time factors:
      • Supplier Lead-Time: Supplier lead-time is always required, whether the supplier is an external company or an internal work cell. Lead-time determines the minimum item quantity that you must have on-hand when you place a new order with your supplier.
      • Lead-Time Demand: Supplier lead-time and daily item usage determines the quantity of items that must be ordered per lead-time period to adequately cover total demand during the period.
        Lead-Time Demand = Supplier Lead-time Days x Daily Usage

What is the Appropriate Sawtooth Curve Time Period?
All inventory sawtooth curves chart on-hand balance (OHB) over a specific time period. The period that an item’s sawtooth curve is charted over impacts perceptual analysis. Charting over too-long of a period, can mask volatility causing inventory managers to overlook potentially dangerous instability. On the flip side, if the time period is too short, an inventory manager might misinterpret short-run inventory swings as more of a threat than they actually are.

How do we know the right interval period to chart with a sawtooth curve?

Because supplier lead-time is foundational to every inventory sawtooth curve and replenishment plan, it makes sense that lead-time would inform the time period charted by our sawtooth curve. But how many lead-time periods should we chart inventory? One lead-time period? Two lead-time periods? Why not five or ten?

A good rule of thumb is to chart about at least 2 lead-time periods (which is typically sufficient), but not more than 5, unless you have a good specific reason to do so, and are cognizant of the potential impact on perceived volatility, discussed earlier.

What is the Right Sub-Interval?
Having a good gauge of the total time period that our sawtooth curve will cover, how granular should our data-points be? The appropriate “sub-interval” period to plot an item’s on-hand balance (OHB) should be a subset of an item’s supplier lead-time. That is, if the supplier lead-time is 6 days, then OHB should be segmented into daily intervals. If supplier lead-time is 9 weeks, then charting weekly OHB would be appropriate. If your supplier lead-time is 24 hours than charting hourly OHB would make sense.

Beginning Vs. Ending On-Hand Balance
Rather than tracking every unique replenishment event, we’ve decided to plot OHB only for “sub-intervals” or smaller time periods than our full supplier lead-time. To ensure that we track OHB with consistency, with each interval we’ll need to define a common point of reference for determining the inventory level during the interval. The inventory at this point in time is what we will chart with our sawtooth curve.

To ensure the most accurate and consistent measures, it’s recommended to reference either the beginning or the end of the given sub-interval. For accuracy and consistency, it makes no difference which you use. Doing this prevents erratic inventory events during the period that could potentially undermine the integrity and value of the measurement.

Regardless of what point in time you use as your point of reference, it’s important to recognize a consequence of tracking inventory at any consistent point in time as opposed to charting every unique consumption event; you will chart different quantities depending on your point of reference.

That is, you need to recognize that a period’s starting OHB is not synonymous with the same period’s ending OHB.

In truth, when you receive an order, you have maximum inventory. This also means that before an order arrives, you have minimum inventory. Thus, when charting only at the beginning or the end of the day, the OHB data point will be slightly different.

To illustrate this, consider the example illustrated in Figure 2.


Figure 2. Beginning On-Hand Balance vs. Ending On-Hand Inventory

Figure 2 graphs OHB at the beginning and the end of each day. Daily demand is 200 units. Day 1 begins with 2,000 units on-hand and ends with 1,800 on-hand. Day 2 begins with 1,800 units and ends with 1,600. Note that Day 1’s Ending OHB and Day 2’s Beginning OHB are the same: 1,800 pieces. Like balancing a checkbook, your ending balance from the previous period is the beginning balance of the current period.

While, you could certainly chart both the Beginning OHB and Ending OHB for your inventory, as we’ve done in our example, it would be somewhat redundant and is typically confusing. Therefore, it’s best to determine which of the two ways you prefer to chart your inventory data and stick with it. With that in mind, before deciding whether to chart Beginning OHB or Ending OHB, you’ll want to consider the reporting effects of each.

Beginning OHB


Figure 3. Beginning On-Hand Balance

The challenge with charting Beginning OHB is that your chart doesn’t show how many pieces were consumed during a period. You only know the beginning balance from one period to the next. In our example, you would never see day 10’s ending balance of 0 (Figure 3).

Ending OHB


Figure 4. Ending On-Hand Balance.

The consequence of charting each period’s Ending OHB is that you never see the result of a full replenishment quantity at the beginning of the chart. This can cause confusion since most people intuitively expect to see the full replenishment quantity represented on an inventory chart. As Figure 4 illustrates, even though we received 2,000 units at the beginning of day 1, you wouldn’t know that only graphing each day’s Ending OHB.

That said, the good thing about charting Ending OHB is that you can at least see the net result of replenishment and consumption for each period. Thus, as you can see in Figure 4, we know that we ended day 10 with zero on-hand. This is far more valuable to know than what we started the day with. It is exactly for this reason, that Ending OHB is the recommended way to chart sawtooth curves, and the way we’ll use moving forward, unless stated otherwise.

In the next part of this series, we take a closer look at analyzing sawtooth curves.

2019-10-14T07:17:51-04:00October 7th, 2019|Categories: Inventory Management, Lead Time Reduction, Lean Manufacturing, Supply Chain|

About the Author:

Aaron is the Marketing Director at Falcon Fastening Solutions, Inc. He is focused on sharing Falcon's unique approach to fastening and class C production component supply chain solutions with equipment manufacturers.

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