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Sem 5 Prep
← OperationsReorder point and safety stock

Formulas for this chapter

Reorder point under certainty

ROP = d x LT

Demand and lead time both constant and known. No safety stock is required.

d
Demand rate per period (day, week)
LT
Lead time in the same periods as d

Reorder point under uncertainty

ROP = expected demand during lead time + z x sigma(dLT) Safety stock = z x sigma(dLT)

Whenever demand or lead time varies. z comes from the target service level.

z
Number of standard deviations for the service level: 1.65 at 95 %, 2.33 at 99 %
sigma(dLT)
Standard deviation of demand during lead time

Sigma of lead-time demand: demand variable

sigma(dLT) = sigma(d) x sqrt(LT) ROP = d-bar x LT + z x sigma(d) x sqrt(LT)

Demand varies, lead time is constant. The square root comes from variances adding over independent days.

sigma(d)
Standard deviation of demand per period
LT
Constant lead time, in the same periods

Sigma of lead-time demand: lead time variable

sigma(dLT) = d x sigma(LT) ROP = d x LT-bar + z x d x sigma(LT)

Lead time varies, demand is constant. No square root: one late period costs a full period's demand.

d
Constant demand per period
sigma(LT)
Standard deviation of lead time, in the same periods as d

Service level

Service level = 100 % - stockout risk

To translate a management risk tolerance into a z value, per replenishment cycle rather than per year.

stockout risk
Probability demand exceeds supply during one lead time
Step 1 of 21
The ideaTheory

Leaving early for the airport

The drive takes forty minutes on a good day. You leave an hour early. That extra twenty minutes is not for the average journey; it is for the bad one.

Safety stock is those twenty minutes. It is not there for normal demand. It is there for the week demand runs hot or the delivery runs late.

And the more certain you insist on being, the more time you have to give up. The last five per cent of certainty costs more than the first fifty.

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