Question

Walmart and Superstore have identical cost structure and equal average demand. Walmart has a higher standard deviation in forecast than Superstore. Will Walmart or Superstore have the higher inventory level? Explain arguments and reasoning clearly .

Answer 1

The inventory of any operation is usually given by the formula

Inventory level = Average inventory + Safety stock.

Here average inventory depends on the order quantity of a product. For example, if a product is ordered in the quantity of Q units at a time then the average inventory is Q/2.

The safety stock is a quantity that the stores keep to avoid chances of being out of stock when customer wants something. This is done by measuring the lead time and the standard deviation of demand. The formula for safety stock is z*σ*sqrt(L) where σ is the standard deviation and L is the lead time.

Now given that Walmart and Superstore have the same cost structure, equal demand and let’s assume the same lead time for the product delivery then the only differentiating factor is the standard deviation.

This will establish that the average inventory is the same for Walmart and Superstore.

The safety stock depends on the value of σ and it is directly proportional (as σ increases, the safety stock increases). This means the safety stock will be higher for Walmart. This will make the overall inventory level higher for Walmart than Superstore.

Please note that the assumption is that the order quantity, lead time, average demand and cost are all same.