Service Level Cost Tradeoff
Turn a target service level into the safety stock, reorder point, working capital, and residual stockout risk it actually requires.
Safety stock and working capital by service-level tier
| Tier | Safety stock | Working capital |
|---|---|---|
| Entered (95.0%) | 99 units | $1,480.37 |
| 90.0% service level | 77 units | $1,153.4 |
| 95.0% service level | 99 units | $1,480.37 |
| 97.5% service level | 118 units | $1,763.97 |
| 99.0% service level | 140 units | $2,093.71 |
Continue Analysis
Based on your results, these related decisions are available.
Resources
How this works
A target service level, the chance of not running out during lead time, translates directly into a safety stock quantity once demand variability and lead time are known. Tighter targets need more safety stock; looser targets need less. This engine computes that translation directly rather than leaving the target as an abstract percentage, so it's clear in units and dollars, not just risk language.
Two products can share the exact same service-level target and still need very different amounts of safety stock, because the formula depends on how variable each product's demand actually is. A flat rule like "keep two weeks of safety stock on everything" ignores this and either overstocks steady items or understocks volatile ones.
Key terms
- Cycle service level: the probability that you don't stock out at all during one lead-time cycle, entered as a fraction (0.95 means a 5% chance of a stockout each cycle).
- Safety stock: extra inventory held above expected demand, specifically to absorb demand variability during lead time.
- Reorder point: the inventory level that triggers a new order, expected demand during lead time plus safety stock.
- Z-score: the number of standard deviations above the mean that corresponds to your target service level (looked up from the standard normal distribution, not entered directly).
- Working capital: the dollar value tied up in safety stock (units held x unit cost).
Assumptions
- Demand over lead time is normally distributed
- Inventory is reviewed continuously, not on a fixed periodic schedule
- Lead time itself is constant; only demand varies
Limitations
- Does not model lead-time variability, only demand variability
- Does not model multi-item or multi-location pooling effects
- Does not optimize order quantity (EOQ) alongside safety stock
Sources
Safety stock, reorder point, and expected shortage formulas follow Silver, Pyke, and Peterson, Inventory Management and Production Planning and Scheduling. The z-score is computed with Peter Acklam's published rational approximation for the inverse standard normal distribution, verified against standard normal tables.
Worked example
At a 95% service level, 100 units/day average demand, 20 units/day of demand variability, and a 9-day lead time, the required safety stock is about 99 units, worth $1,480 in working capital at $15/unit, with a 5% residual stockout risk (by definition, since the target service level sets the risk directly). Cut demand variability to 5 units/day, same 95% target, and safety stock drops to about 25 units, a quarter of the original, worth $370. Stockout risk stays exactly 5% either way, since risk is set by the target, not by variability. It's the working capital that variability actually drives.
Common use cases
- Setting a data-driven safety stock and reorder point instead of a flat rule of thumb
- Comparing working capital cost across a few candidate service-level targets
- Explaining to a stakeholder why two SKUs at the same service level need different stock levels
- Checking whether an existing reorder point is under- or over-protecting against variability