Base stock model

The base stock model is a statistical model in inventory theory.

Overview

Assumptions

1.Products can be analyzed individually

2.Demands occur one at a time

3.Unfilled demand is backordered

4.Replenishment lead times are fixed and known

5.Replenishment are ordered one at a time

6.Demand can be approximated with a continuous distribution

Variables

• L=Replenishment lead time
• D=Demand during replenishment lead time
• g(x)=probability density function of demand during lead time
• G(x)=cumulative distribution function of demand during lead time
• θ=mean demand during lead time
• h=cost to carry one unit of inventory for 1 year
• b=cost to carry one unit of back-order for 1 year
• r=reorder point, which represents inventory level that triggers a replenishment order; this is the decision variable
• s=r-θ, safety stock level
• S(r)=fill rate
• B(r)=average number of outstanding back-orders
• I(r)=average on-hand inventory level