Find the optimal k factor
Use the total cost vs k curve to locate the safety factor that minimizes cost.
By the end of this tutorial you will know how to read the curve, identify the optimal point and understand why the optimum may come out high or low depending on the SKU's cost structure.
For the mathematical definition of the k factor and its relationship to service level, see Factor k and fill rate.
What you will need
- To have completed Your first inventory simulation: the simulation panel must be open for a SKU.
- Holding and shortage costs configured for that SKU.
Step 1 — Recall what the k factor controls
The k factor is a multiplier that defines how many standard deviations of demand during lead time your safety stock covers:
Safety Stock = k × σ_DLT
where σ_DLT is the standard deviation of demand during lead time.
| k | Effect |
|---|---|
| Low k (< 0.5) | Little safety stock. Low fill rate, stockout risk, high shortage cost. |
| k = 1 | Covers 1 standard deviation. Service level close to 84 % (normal demand). |
| High k (> 2) | Lots of safety stock. Very high fill rate, but elevated holding cost. |
The goal is to find the k that balances both costs at the lowest possible combined value.
Step 2 — Read the total cost vs k curve
In the simulation panel, locate the Total cost vs k chart.
The curve has three clearly distinguishable zones:
- Left zone (low k): the curve drops quickly. Small increases in k reduce shortage cost significantly without raising holding cost much.
- Minimum zone (optimal point): the curve flattens. Total cost is at its lowest. This is the optimal k.
- Right zone (high k): the curve rises slowly. Shortage cost is nearly zero, but holding keeps growing with every extra unit of stock.
TODO: screenshot of the cost vs k curve with the three zones marked and the minimum highlighted
For many SKUs the curve has a flat bottom, meaning several nearby k values have nearly equal costs. In that case you can choose any k within that zone; there is no significant penalty.
Step 3 — Identify the optimal point
- Look at the k value on the X axis where the curve reaches its lowest point.
- The system may mark that point with a vertical line or visual indicator. If it does not, locate the minimum visually.
- Read the fill rate corresponding to that k in the panel metrics. This is your optimal fill rate under the current cost structure.
Example reading:
The curve reaches its minimum at k = 1.3. At that level the fill rate is 89 % and total cost is $2,400/month. At k = 2.0 the fill rate rises to 97 % but total cost is $3,100/month. The system recommends k = 1.3.
Step 4 — Interpret extreme cases
The optimum is very high (k > 2.5)
This can occur when shortage cost is very high relative to holding cost:
- Critical products where a stockout causes large losses (contract penalties, line stoppage, etc.).
- SKUs with very variable lead time or very erratic demand.
In that case the high optimum is correct. Check with your administrator that the cost parameters reflect business reality.
The optimum is very low (k < 0.3)
This can occur when holding cost is very high relative to shortage:
- Perishable products or those with high financial cost of capital.
- Low-volume SKUs where each extra unit ties up significant capital.
Again, verify the parameters are accurate before accepting a very low k.
The curve has no clear minimum (keeps falling)
If the curve descends monotonically toward very high k with no visible minimum, shortage cost is completely dominating. Check whether the shortage cost parameter is reasonably calibrated.
Step 5 — Apply the optimal k
Once you have identified the optimal k:
- Note the recommended value.
- In the k factor field on the SKU panel, enter that value (or the one you decided on).
- The system automatically recalculates safety stock, target stock, fill rate and costs.
- Review the resulting suggested replenishment quantity (the next tutorial explains how to interpret it).
Result
You know how to read the total cost vs k curve, locate the optimal point and understand why the optimum may be high or low depending on the SKU's costs.
Next step: learn what to do with the replenishment quantity the system suggests in Interpret the suggested replenishment.