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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 3 of 21
The real wordsTheory

Under certainty

With demand and lead time both known and constant, the order should arrive exactly as stock hits zero.

ROP = d x LT where d = demand rate (units per day, week or period) LT = lead time, in the same time units as d

The units matter more than the formula. Daily demand with a lead time in days; weekly demand with a lead time in weeks. Never mix.

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