This is the first of four posts on the topic of sawtooth curves.
All businesses that sell physical goods, must effectively manage inventory. Not carrying enough items can create lost customers and lower revenue, while overstocking items can severely inhibit cash flow. The ultimate objective of inventory managers is to achieve balance between consumption and replenishment.
Because the consumption and replenishment of items occurs at different rates, successful inventory management is all about timing.
The pace at which an on-hand inventory item is used is the consumption rate of that item. Whatever the consumption rate, inventory usage is ongoing whether it moves slowly or quickly.
This poses a replenishment challenge.
For example, let’s consider an internally manufactured part that is consumed by another work cell. The part is held in a bin that holds 5,000 units. When the part quantity drops down to 1,000 on-hand balance (OHB), you begin manufacturing more parts and continue until you reach a maximum of 5,000 units, the bin capacity.
We might ultimately need far fewer or far more than 5,000 units for a given time period, but we often have no way of knowing that with certainty until the given time period has passed. You do know that you don’t want to stock-out and risk shutting down production or missing delivery targets. Under this common scenario, it’s a challenge to estimate when to replenish inventory so you’re not wasting production time.
Unfortunately, you can’t control the consumption rate because your customers determine how much they need and when they need it. That said, you can know when inventory has been consumed. In fact, without knowing when consumption occurs, there’s no way to establish when to refill a bin or to know the optimal quantity to replenish.
Also, while you may not be able to control your inventory consumption rate, you can govern how you replenish your inventory.
Replenishment events are activities that refill or receive inventory. The frequency of replenishment events and their specific inventory quantities represent the replenishment pattern.
An ideal replenishment pattern is one that perfectly matches the replenishment quantity and timing with demand. As previously discussed, one major replenishment challenge is the inability to perfectly predict or control demand.
Since consumption needs dictate replenishment needs, replenishment needs also tend to be inconsistent. So, while we technically have control over the replenishment pattern, it tends to be challenge to efficiently manage.
Fortunately, developing efficient and reliable replenishment plans is completely possible!
In order to consistently develop reliable replenishment plans, we need a simple tool to help us quickly comprehend the challenge at hand, compare different solutions, and communicate all of this to stakeholders.
Sawtooth curves area powerful tool for illustrating consumption and replenishment events so both you and your stakeholders are better able to see on-hand inventory balance over time, anticipate the potential impact of replenishment patterns, and quickly compare alternative replenishment plans.
Anatomy of a Sawtooth Curve
To benefit from sawtooth curves, we must understand their different parts. Figure 1. is an example of a sawtooth curve for an item with steady demand. (we’ll address the much more realistic scenario of unsteady demand at a later point.)
In every inventory sawtooth curve, the y-axis represents on-hand balance and the x-axis represents lead-time units (i.e. days, weeks, months, etc.). Each data point presents an item’s on-hand balance (OHB) at a specific point in time. All inventory transactions (i.e. events) affect OHB, as indicated by the data points, that when plotted, represent the jagged edges or “teeth” of a saw. The sawtooth curve owes its distinctive “sawtooth” shape to 3 key elements, which every inventory manager should be familiar with.
- Peak: The tallest points of a sawtooth curve represent replenishment events for the related item, whether supplied by an external or internal supplier. Inventory at these points plot the planned maximum on-hand balance across the entire replenishment cycle. When charting end-of-day OHB the peak’s height is the total remaining inventory from the last delivery, plus the inventory received during the peak time period, minus the consumption for the same period. Ending OHB is what was received minus what was consumed that day.
Current Period Ending OHB = Previous Period’s Ending OHB – Current Period’s Inventory Received – Current Period’s Usage
- Decline: Just as consumption follows replenishment, following each peak on a sawtooth curve is a gradual decline, representing a series of consumption events (or gradual drawdown of inventory) between inventory replenishments. When charting daily usage, the decline would illustrate daily balance. When charting weekly usage, the decline would illustrate weekly balance. Consumption speed determines the slope of the decline. Rapid consumption results in a steeper decline. Slower consumption rates result in a shallower decline.
On-Hand Requirement = Rate of Decline x Lead-time
- Valley: The lowest point of a sawtooth curve, immediately preceding the peak, is called the valley or trough. The valley represents the planned minimum quantity of inventory. This always equals Target Safety Stock (TSS). In the example, the minimum quantity of inventory that is planned for is zero. Yes, with an appropriately tailored reliable replenishment process it is possible for the valley to equal zero.
That said, zero is by no means, the floor. In the case of a stockout, your sawtooth curve would show a negative minimum inventory (i.e. less than zero). Thus, the valley will typically be equal to some value above zero to prevent a stockout. When analyzing a sawtooth curve with a valley greater than zero, you know that safety stock is accounted for in the replenishment plan.
- Horizontal Line: While not a mandatory part of all sawtooth curves, the example also contains an additional horizontal line that complements the sawtooth. This line, located somewhere between the minimum and maximum inventory balance represents the planned average on-hand inventory.
Before we can analyze a sawtooth curve, we must understand how to chart one, which we’ll learn how to do in part 2 of this series.