Question

Store B orders on a weekly basis. Its weekly demand is 50 units with a standard deviation of five units. The holding cost is $10 per unit per week and a 0.99 in-stock probability is desired.

C&A reports annual sales of $30 million, cost of goods sold of $15 million, inventory of $5 million, and net income of $2 million. What is C&A’s:

Answer 1

1. Average inventory consists of three primary components: the average cycle inventory determined by the demand during the lead time, the safety stock determined by the desired service level, and the pipeline inventory.

First, we find the z-value for the target service level of 0.99, which is z=NORM.S.INV.(0.99)=2.33z=NORM.S.INV.(0.99)=2.33

Now we can find the safety stock as

Safety Stock=z∗St.Dev.Demand∗√Lead Time+Review Period=2.33∗5∗√5+1≈28.54 Safety Stock=z∗St.Dev.Demand∗Lead Time+Review Period=2.33∗5∗5+1≈28.54 units.

The average cycle inventory is

Avg Cycle Inventory=Weekly Demand∗Review Period 2=50∗12=25 Avg Cycle Inventory=Weekly Demand∗Review Period 2=50∗12=25 units.

The pipeline inventory is

Pipeline Inventory=Weekly Demand∗Lead Time=50∗5=250 Pipeline Inventory=Weekly Demand∗Lead Time=50∗5=250 units.

The pipeline inventory is not usually considered to be the on-hand inventory. Hence, the on-hand inventory is

Safety Stock+Avg Cycle Inventory=28.54+25=53.54 Safety Stock+Avg Cycle Inventory=28.54+25=53.54.

2. The formula of the flow rate is:

Flow Rate = (Net Income / Annual Sales) x 100

• Flow Rate = ($2 million / $30 million) x 100
• Flow Rate =(1/15) x 100
• Flow Rate = 6.67%