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