Reliability is worth a price premium, and the premium is the annual policy cost it removes divided by the units you buy, not the stock it releases.
Price the premium as the annual inventory cost that reliability removes, divided by the units you buy in a year. For part AF-7, taking the supplier's lead-time standard deviation from 1.9 weeks to 0.5 cuts holding and shortage cost by 24,155 EUR a year on 95,680 units, so the buyer can pay up to 0.25 EUR a unit more, 0.88 per cent of the 28.6 EUR purchase price, and still come out level. The 130,171 EUR of stock released is not a second gain to add on top.
Worked in full in Supply Chain Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Procurement teams negotiate price per unit; planners talk about weeks of lead time. The two rarely meet, so a supplier offering a more regular delivery schedule for a slightly higher price is usually turned down on the price line alone. The calculation below puts reliability into the same currency as the quotation.
Part AF-7 is the single part followed through the book: a filter element bought from one supplier on a six-week lead time that is anything but regular. The board has set a 98 per cent cycle service level. A unit short costs the 18.9 EUR margin on the lost sale.
| Input | Value |
|---|---|
| Mean weekly demand / standard deviation | 1,840 / 462 units |
| Annual demand (52 weeks) | 95,680 units |
| Mean lead time | 6 weeks |
| Lead-time standard deviation: today / offered | 1.9 / 0.5 weeks |
| Purchase cost delivered | 28.6 EUR |
| Holding rate (capital, storage, obsolescence, insurance) | 13.4% |
| Holding cost per unit per year | 3.8324 EUR |
| Cost of placing an order | 385 EUR |
| Cycle service level / z | 98% / 2.0537 |
| Shortage cost per unit short (lost margin) | 18.9 EUR |
1. The spread of demand over the lead time. Demand and lead time both vary, so their variances add:
σLT = √(L × σd² + d² × σL²)
Today: √(6 × 462² + 1,840² × 1.9²) = 3,674.60 units
Offered: √(6 × 462² + 1,840² × 0.5²) = 1,458.45 units
Excel: =SQRT(6*462^2+1840^2*1.9^2)
Today 90.5 per cent of that variance comes from the supplier, which is why the spread, not the forecast, is the lever on this part.
2. Safety stock and its holding cost. Safety stock is z × σLT: 7,547 units today, 2,995 at the offered spread. At 3.8324 EUR a unit a year, holding it costs 28,922 EUR today and 11,479 EUR after.
3. Shortages. The service level is held at 98 per cent, but the units short per cycle are σLT × G(z), where G(z) = 0.00734 is the standard normal loss function at z = 2.0537. With an order quantity of 4,384.50 units, the part is replenished 21.8 times a year, so units short fall from 589 to 234 a year. At 18.9 EUR each that is 11,129 EUR against 4,417 EUR.
4. The rest of the policy. The order quantity does not depend on the lead time, so cycle stock holding and ordering are 8,402 EUR each in both cases. They cancel out of the difference, but they belong in the totals.
| Line | σL 1.9 weeks | σL 0.5 weeks | Saving |
|---|---|---|---|
| Holding safety stock | 28,922 | 11,479 | 17,443 |
| Holding cycle stock | 8,402 | 8,402 | 0 |
| Ordering | 8,402 | 8,402 | 0 |
| Shortages | 11,129 | 4,417 | 6,712 |
| Total | 56,854 | 32,699 | 24,155 |
5. Convert to a unit price.
Break-even premium = annual saving ÷ annual units = 24,154.77 ÷ 95,680 = 0.2525 EUR a unit
As a share of the 28.6 EUR purchase cost: 0.88%
A more precise version recognises that the premium also sits in every unit held and comes off the margin lost on every unit short. The break-even then falls slightly, to 0.2512 EUR. For a negotiation, 0.25 EUR a unit is the number. Over a three-year contract the reliability is worth 72,464 EUR to the buyer, undiscounted; paid as a lump sum up front it would be worth less.
| Case | Annual saving | Premium | % of cost |
|---|---|---|---|
| Spread to 0.0 weeks (perfectly regular) | 27,716 | 0.29 | 1.01% |
| Spread to 0.5 weeks (base) | 24,155 | 0.25 | 0.88% |
| Spread to 1.0 week | 16,507 | 0.17 | 0.60% |
| Spread to 1.5 weeks | 7,538 | 0.08 | 0.28% |
| 0.5 weeks, shortage cost ignored | 17,443 | 0.18 | |
| 0.5 weeks, shortage cost doubled to 37.8 | 30,867 | 0.32 | |
| 0.5 weeks, holding rate 8.0% | 15,600 | 0.16 | |
| 0.5 weeks, holding rate 20.0% | 34,234 | 0.36 |
The value comes in steady steps until demand noise takes over. Each step of improvement down to 0.5 weeks is worth roughly 0.08 to 0.09 EUR a unit: 0.08 from 1.9 to 1.5 weeks, 0.09 from 1.5 to 1.0, 0.08 from 1.0 to 0.5. The last step to perfect regularity adds only 0.04 EUR, because by then most of the remaining variance is the market's, not the supplier's. The holding rate drives the answer almost proportionally, so agree it with finance before the negotiation, not during it.
Set against the board's argument over the service level, the scale is clear: the whole dispute from 97 to 99.5 per cent was worth 6,198 EUR a year. The reliability lever is worth 3.90 times that.
Narrowing the spread releases 4,551 units of safety stock, 130,171 EUR of working capital, once. It is tempting to add that to the annual saving, for instance by spreading it over a three-year contract as 43,390 EUR a year. Do that and the acceptable premium becomes 0.71 EUR a unit, 2.80 times the true figure, and the buyer overpays by 43,390 EUR a year for as long as the contract runs.
The cash is not a separate benefit. The 13.4 per cent holding rate includes a 7.4 per cent cost of capital, and that charge on the released stock, 9,633 EUR a year, is already inside the 17,443 EUR of safety stock holding saved. The cash released belongs in the treasury forecast, not in the price comparison.
The opposite error is just as common: valuing reliability on safety stock holding alone, 0.18 EUR a unit, which misses the 6,712 EUR of shortages avoided and undervalues the offer by 27.8 per cent.
The lead-time table from 0.0 to 3.0 weeks and the premium calculation are in the free workbook for this case. The safety stock formula behind step 2 is set out in how to calculate safety stock when lead time varies, and the holding rate in how to calculate inventory carrying cost.
Recompute the full annual inventory cost, holding on safety and cycle stock, ordering and shortages, at the current and the target lead-time spread, and take the difference. For part AF-7 going from 1.9 to 0.5 weeks the cost falls from 56,854 to 32,699 EUR a year, a gain of 24,155 EUR, of which 17,443 is safety stock holding and 6,712 fewer shortages.
No. Taking the spread to 0.5 weeks releases 130,171 EUR of stock once, but the holding rate of 13.4 per cent already charges the cost of capital on that stock every year. Adding the cash, even spread over three years, raises the premium you would accept from 0.25 to 0.71 EUR a unit, 2.80 times what reliability is worth.
On a part where most of the risk comes from the supplier, the spread matters more. For AF-7, 90.5 per cent of the variance of demand over the lead time comes from the 1.9-week standard deviation of lead time, so narrowing the spread to 0.5 weeks cuts safety stock from 7,547 to 2,995 units while the six-week average is unchanged.
This calculation is worked in chapters 12 and 13 of Supply Chain Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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