Safety stock and service

A buffer is stock with a job. It protects against a stated risk while we wait for more supply. It is not a cure for every bad record or late decision. To set a buffer well, name the source of variation, the time we must cover, and the service goal. Northstar's Blue bottle gives us a small example with clear units and strong assumptions.

Mean demand is twenty bottles a day. The standard deviation of daily demand is four bottles. Think of that as a measure of spread around the mean. Lead time is fixed at three days. We assume days are independent and the demand pattern is stable. We also use a normal shape as an approximation for total demand over the wait. Those are model choices, not facts that hold for all products.

Mean demand over three days is sixty. To find spread over three independent days, add variances. Four squared is sixteen. Three times sixteen is forty eight. The square root is about six point nine three bottles. We do not multiply the daily standard deviation by three. That would treat spread in a different way. Units help us check the work: variance is in bottles squared, while standard deviation is in bottles.

For a ninety five percent cycle service goal, we use the supplied normal factor of one point six four five. Multiply it by six point nine three. The result is about eleven point four bottles of buffer. Since we stock whole bottles, round up to twelve. Add that to the mean lead time need of sixty. The reorder point is seventy two.

That result is not a promise that every order will be on time. It follows from the model and its inputs. If days move together, if demand comes in huge bursts, or if lead time changes a lot, the model may fit poorly. A high number of decimal places does not fix a weak assumption. Keep the input window and model version so another planner can tell how the rule was set.

Try two stress checks. If daily spread doubles from four to eight, the unrounded buffer doubles. If fixed lead time grows from three days to twelve, it also doubles, because the square root of the time ratio is two. Both cases round up to twenty three bottles. They have different causes even though the buffer result matches. One may call for better demand work. The other may call for a faster supply path.

Now ask what service means. Cycle service counts cycles with no shortage. Imagine ten cycles. Eight have no shortage. The cycle service result is eighty percent. Unit fill asks a different question. Across those ten cycles, demand was two hundred bottles. Only five were not supplied at the required time. We filled one hundred ninety five out of two hundred right away. That is ninety seven point five percent.

Both measures describe the same case. They do not conflict. Two failed cycles can each have a small gap or a huge gap. The cycle count stays the same, while unit fill changes. A normal factor chosen for cycle service does not directly set the same percentage of unit fill. Always name the numerator and denominator before you compare service numbers.

If the five late bottles ship the next day, backlog is cleared. Immediate fill is still ninety seven point five percent. Late recovery is useful, but it does not rewrite the original due event. Keep both views. Customers need honest promises, and the team needs to know whether it is fixing today's gap or preventing tomorrow's gap.

In the lab, test reserves of zero, one, two, and three units against the same ten cycles. Count clean cycles and missed units for each rule. Add the stated annual holding cost of the reserve. Do not claim that ten cycles prove the true long run rate. They are a small set of evidence. Use them to form a trial, track the next outcomes, and learn the cause of each miss. A useful buffer policy is measured, explained, and revised when new facts warrant a change.

One last check is about units. If your demand data are daily but your lead time is in weeks, stop before you multiply. Convert both to one time base, then check the spread assumption and the service measure again.

1. Name risk

   Three daily spread blocks lead into one window

   • Mean 20
   • SD 4
   • Lead 3
2. Add variances

   Three sixteen-unit variance blocks

   • Independent
   • Variance 48
   • SD 6.93
3. Set policy

   Mean need plus rounded buffer

   • Factor 1.645
   • Buffer 12
   • Point 72
4. Two metrics

   Cycle icons beside a unit bar

   • 8 of 10 clean
   • 195 of 200 filled
   • Different measures
5. Late recovery

   Due event and later shipment remain distinct

   • Original due
   • Backlog clears
   • Fill unchanged
6. Learn from trial

   Reserve comparison with cost cards

   • Same cycles
   • Track cost
   • Check causes