Skip to main content

SAFETY STOCK ANALYSIS: Inventory Management Models : A Tutorial


EOQ tells us HOW MUCH to order…but WHEN should we order?

p. Safety Stock
What Happens when either Demand or Lead Time Varies?
What is the Chance of a Stockout?
Finding Z

h2. Safety Stock

When both lead time & demand are constant, you know exactly what the reorder point is …

  • Under these assumptions:

Reorder point = demand during lead time

  • Where

= demand per time period
= lead time

What Happens when either Demand or Lead Time Varies?

  • Variances are caused by changes in demand rates and lead times.

  • Additional inventory beyond amount needed to meet “average” demand during lead time
  • Protect against uncertainties in demand or lead time
  • Balance the costs of stocking out against the cost of holding extra inventory
  • When holding safety stock (SS), the average inventory level is:

  • Shown graphically:

h2. What is the Chance of a Stockout?

Recalculating the reorder point to include safety stock



Calculating averages and variances of demand and lead time using historical data

Historical data for 10 weeks of demand, as well as 8 previous orders

h2. Finding Z

  • Z = number of standard deviations above average demand during lead time
  • The higher z is:
    • >> The lower the risk of stocking out
    • >> The higher the average inventory level
    • Typical choices for Z:
    • Z = 1.29 >> 90% cycle service level
    • Z = 1.65 >> 95% cycle service level
    • Z = 2.33 >> 99% cycle service level
    • Cycle service level:
  • Once the reorder is placed, the probability that stocks will be depleted before the new order arrives