In my previous article I discussed a simple change to the King Equation that can reduce working capital requirements while still maintaining service level by substituting the standard deviation of forecast error for the standard deviation of demand for companies running forecast driven MRP.

The improvement discussed in the first article addressed the assumption that demand is best described by its average, which is not true for most companies. There is likewise a hidden assumption in the second term, that lead time is fixed.

In the real world there are often split, expedited, and deferred deliveries that break this assumption. And often ERP systems are not set up well to record the data needed.

Let’s dive into the considerations and a practical, low-lift approximation for replacing the lead time variance term that can be used to improve real world results.

As a refresher, the optimized modified King Equation from the prior article is:

Safety Stock = Z * √( (PC/T_i * σ_FE^2) + (σ_LT * D_avg)^2 )

where:

  • Z = Z-score corresponding to desired service level
  • PC/T_i = Lead time normalized into the same time period that forecasting is done in (i.e. turn lead times into months if forecasting is done in monthly buckets)
  • σ_FE = Standard deviation of forecast error (Actual - Forecast)
  • σ_LT = Standard deviation of lead time (in the appropriate time buckets)
  • D_avg = Average demand

While forecast error and average demand are easily obtainable from a robust demand planning and S&OP process, the lead time data is often much harder to accurately pin down.

The two questions that need to be addressed are:

  • How is the lead time measured and how does your MRP need to be set up to support it?

  • How are expedited, split, and deferred deliveries handled in the data?

It’s clear that the ideal state for measurement of lead time variance is to use the date of purchase order requisition generation as the start of the lead time and have the ERP constrained to using the loaded lead time. It’s important to note that time for POs to be reviewed, approved, and sent to vendors, along with a standard receiving time, should be included in the loaded lead time (if they are not configurable independently in your ERP) and it should not be simply the vendor quoted lead time. This configuration gives a clean snapshot of when the ERP wanted the inventory (as best as it’s allowed to when constrained) vs when it was delivered, giving us the cleanest data on the variance of lead time. But it leaves no room for expedites when demand goes significantly over forecast and risks stock outs in exchange for clean data, which we cannot responsibly do in supply chain; we need to meet customer requirements. And not all ERPs generate requisitions, for some the purchase order creation date is the first date available, making the accurate start date murky. So this is a poor solution: the cleanest technical data produces the worst real world response.

And what happens if you request an expedited delivery due to demand significantly over forecast and the vendor ships a partial early, at your requested date, and the balance at their standard lead time? Split shipments are common practice and can often work for the supply planning team. But, it creates variance in actual lead time data when the requisition/purchase order was created on the same date and there were two (or often more) delivery dates. Or if the procurement team needs to place purchase orders beyond normal lead time to secure material when vendor allocations occur, the same situation arises. If expedited and deferred deliveries are both included the variance can become artificially inflated… for having good vendors that work with you? That doesn’t make sense. And the root cause of the expedites was demand over forecast, which is already accounted for in the first term of the King Equation, which assumes a fixed lead time. Including them in lead time variance would double count the root cause of the variance. And worse, if a business is consistently expediting then using the average actual lead time builds the expedite into their safety stocks and creates a vicious cycle of ensuring future expedites!

So, we have technical data collection issues that except in very ideal conditions can’t be operationalized in the real world. And real world procurement practices are extremely difficult to resolve to both determine an accurate actual lead time and the variance of that lead time, leaving it impossible in many cases to accurately calculate the King Equation. What do we do?

A practical approach is to replace the second term of the King Equation with a standard approximation of DOH (days on hand) coverage (also known as Cover Days).

This results in an approximated modified King Equation of:

Safety Stock = Z * √(PC/T_i * σ_FE^2) + (σ_aLT * D_avg)

where:

  • Z = Z-score corresponding to desired service level
  • PC/T_i = Lead time as loaded in the ERP normalized into the same time period that forecasting is done in (i.e. turn lead times into months if forecasting is done in monthly buckets)
  • σ_FE = Standard deviation of forecast error (Actual - Forecast)
  • σ_aLT = A standard approximation of the lead time variance you want to buffer against in PO generation, vendor variability, and receiving variability. This is often done based on ABC classification and I’ve seen ranges from 2 to 6 weeks used for A’s, 3 to 8 weeks for B’s, and 4 to 13 weeks for C’s. The appropriate range depends on the industry; a life-critical medical device should be buffered more than a low margin industrial commodity and slow internal processes should be buffered more than agile ones. This needs to be normalized into the same time bucket the average demand is measured in.
  • D_avg = Average demand

Making this simple change to approximate the second term in DOH based on risk and ABC classification enormously simplifies the data issue inherent in accurately assessing lead time variance in the real world. For many businesses accurately untangling the data is not worth the improvement in working capital from getting it exactly right, and in many cases it’s not possible at all without robust real-time data adjustment systems where the supply chain team manually logs and corrects purchase order data continuously.

Summary

The first article in this series replaced the demand variability term of the King Equation with forecast error to improve working capital while maintaining service level. This one looks at the lead time variance term, which depends on actual lead time data that is much harder to get right. A practical fix is to replace the lead time variance term with a standard days-on-hand approximation set by ABC classification and risk. For most businesses this is simpler, more defensible, and close enough that untangling the raw data is not worth the effort.