A uniform weeks-of-supply safety stock rule at a spare parts distributor
Meridian Medical Parts supplies service spares for imaging equipment to 900 hospitals. The inventory policy applies a uniform safety stock of four weeks of average demand to all 12,000 SKUs, and total safety stock is now $6.2M. The customer promise is 97% service; measured fill rate is 93.5% and expedite freight cost $1.1M last year. Two items illustrate the problem. Item A-118 is a high-runner board: average demand 400 units per week, weekly standard deviation 120, replenishment lead time 6 weeks with a standard deviation of 2 weeks, unit cost $85. Item B-402 is a low-volume but critical sensor: average demand 20 units per week, weekly standard deviation 15, lead time 10 weeks with a standard deviation of 3 weeks, unit cost $180. A stockout of B-402 can take a hospital scanner offline. Meridian works to a 95% cycle service level in its calculations.
1. Compute the statistically required safety stock for A-118 and B-402 and compare with the current rule. What does the comparison tell you?
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Use SS = z x sqrt(LT x sd_d^2 + d^2 x sd_LT^2), with z = 1.65 for 95%.
A-118: sqrt(6 x 120^2 + 400^2 x 2^2) = sqrt(86,400 + 640,000) = sqrt(726,400) = 852.3. SS = 1.65 x 852.3 = 1,406 units. The four-week rule gives 4 x 400 = 1,600 units, so A-118 is over-protected by about 14%.
B-402: sqrt(10 x 15^2 + 20^2 x 3^2) = sqrt(2,250 + 3,600) = sqrt(5,850) = 76.5. SS = 1.65 x 76.5 = 126 units. The rule gives 4 x 20 = 80 units, so B-402 is under-protected by about 37%.
What this tells you:
- The rule ignores lead time entirely, yet lead time is what the safety stock has to cover. B-402 has a 10-week lead time and a variable one; A-118 has 6 weeks and a steadier one.
- In both formulas the lead-time variability term is the dominant one (640,000 vs 86,400; 3,600 vs 2,250). A rule based only on average demand cannot see that at all.
- So a single weeks-of-supply rule simultaneously ties up cash on the fast movers and fails the parts that matter most. The 93.5% fill rate against a 97% promise is exactly what you would expect.
2. What policy would you put in place, and how do you handle the practical objections (12,000 SKUs, poor lead-time data)?
Read the worked answer
Replace the uniform rule with calculated safety stock plus segmentation, not with 12,000 hand-crafted decisions.
Policy structure:
- A items and critical parts (roughly 10-15% of SKUs, 70-80% of value, plus a criticality flag for anything that can take clinical equipment offline): item-level calculation using the full formula, reviewed quarterly. Move B-402 and its peers to a 99% service level or an economic service level based on the cost of a stockout, not a blanket 95%.
- B/C items: a simplified rule, but one that still scales with sqrt(lead time) and the demand coefficient of variation, so it tracks the physics rather than a fixed number of weeks.
- Obsolete and slow movers: review for write-down, not for safety stock.
Handling the objections:
- Twelve thousand SKUs: the calculation is a spreadsheet or an ERP parameter, not manual work. Automate recalculation and route only exceptions (high bias, lead-time shift, large cost impact) to a planner.
- Poor lead-time data: estimate sd_LT from 12 months of purchase-order receipt dates, not from the supplier promise. Where an item has fewer than six receipts, borrow a category-level sd_LT until enough history exists, and flag it.
- Parameter churn: recalculate quarterly with a trigger for any lead time that moves more than 25%, and do not let the system silently overwrite reviewed parameters.
Quote the prize: the current rule leaves cash on the slow movers while missing the critical parts, so this can raise service and release working capital at the same time. Confirm that with a pilot on the top 200 SKUs before the full rollout.
3. Meridian reports a 97% service target and a 93.5% fill rate. What is wrong with that comparison, and what should be measured?
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The two numbers may not be measuring the same thing, which is a common and expensive confusion.
- The safety-stock formula produces a cycle service level: the probability of not stocking out during a single replenishment cycle. For an item ordered weekly, a 95% CSL still means roughly one stockout every 20 weeks, and each stockout can last days.
- Fill rate is the fraction of demand met from stock. It is what the hospital experiences and what the 97% promise almost certainly means.
So reporting 93.5% fill against a 97% CSL-derived target is not a like-for-like gap, and chasing it by raising z across the board would over-buy. Fix the measurement first:
- Define the promise in the customer's terms: unit or order-line fill rate, and whether partial shipments count.
- Use CSL (or better, a cost-optimal service level) only as an internal parameter for sizing safety stock, and translate it into expected fill rate per SKU.
- Segment the published KPI: fill rate on critical parts should be reported separately, because an average can be 93.5% while critical parts sit at 88%.
- Track expedite freight per SKU as a service-quality signal - $1.1M of premium freight is the business buying back service the policy failed to provide.
- Check that the sd_d used in the calculation is not stale, since a policy sized on last year's variability will miss this year's.