Question $4$

Procter & Gamble $($P&G$)$ is an US$-$headquartered multinational consumer goods corporation. P&G maintains inventories of its wide range of products. P&G uses a fixed$-$quantity inventory system to manage one of its popular household cleaning products. Based on historical data, the demand for this product is normally distributed. The lead time is $2$ weeks. The mean of lead time demand is $400$ units and the standard deviation of lead time demand is $25$ units. Due to the competitive environment, a stockout of $2\%$ during lead time is considered acceptable.

Question $4$a

What is the amount of safety stock that needs to be kept for this particular household product? When should the order for the product be placed?

$(13$ marks$)$

Question $4$b

Suppose the company decides not to have safety stock for this product. What will be the Z value and level of stockout risk?

Analyse the advantages and disadvantages of having a low level of safety stock.

$(12$ marks$)$