Question

Two retailers are considering inventory management of one of the products they are both selling. Each of them has an average demand of 12 units per week with a standard deviation of 2 units per week. The supply lead time is constant and equal to 2 weeks.

1. How much safety stock should each retailer keep to achieve a service level of 95% (z = 1.64)? Imagine now that those two retailers are going to be combined into one integrated retailer, which will be facing the combined demand of the previous two retailers.

2. What is the average and the standard deviation of the integrated weekly demand?

3. How much safety stock should the integrated retailer keep to achieve the same service level of 95% (z = 1.64)?

4. What is the impact of integration on the total safety stock level? What if 30 stores where integrated? (Hint: Compare the safety stock of the integrated retailer with the combined safety stocks of the two previous retailers and conclude.)

Answer 1

Answer to question 1 :

Safety stock = Z value x Standard deviation of weekly demand x Square root ( Lead time ) = 1.64 x 2 x Square root ( 2 ) = 1.64x2x1.414= 4.637

Answer to question 2 :

Average demand when two retailers are combined = ( average demand of retailer 1 + average demand of retailer 2) /2 = ( 12 + 12) /2 = `12

Variance when two retailer’s demand are combined = Variance of demand of retailer 1 + Variance of demand of retailer 2 = 2^2 + 2^2 = 8

Standard deviation of demand when demand of two retailers are combined = Square root ( 8 ) = 2 x square root ( 2 )

Answer to question 3:

Safety stock should be kept = Z value x New standard deviation of demand x Square root ( lead time) = 1.414x 2x square root ( 2 ) x square root( 2) = 1.414 x 2 x 2 = 5.656

Answer to question 4 :

Impact of integration is proportionately amount of safety stock required reduces. For example safety stock for 1 retailer 4.637. Accordingly , safety stock for 2 retailers = 4.637 x 2 = 9.274. However safety stock is only 5.656

If 30 stores were combined,

Average demand = 12

Standard deviation of combined demand = 2 x Square root ( 30 ) = 2 x 5.477 = 10.954

Safety stock = Z value x standard deviation x square root ( Lead time) = 1.64 x 10.954x square root ( 2 ) = 25.405