g The local Target store sells a variety of Dyson vacuum cleaners. A particularly popular model is the DC22, which costs Target $275 per unit. The annual holding cost per vacuum is 10% of this cost. Demand for the DC22 is relatively constant, but experiences some fluctuations from day to day. Average daily demand for the DC22 is normally distributed with an average of 5 units and a standard deviation of 2 units (and Target is open 365 days a year). When Target places an order of DC22s from its warehouse, the order arrives 3 days later. The fixed ordering cost is $10, regardless of how many DC22s are ordered. Target is willing to tolerate a 1% chance of stockout on any one order cycle. If Target decreases its tolerance for stockouts, how will this affect the inventory policy

Something isn't right about this question, since Target's tolerance for stock-outs is already 1%, by how much can they decrease it? The question should probably say that they will increase their tolerance for stock-outs, e.g. from 1% to 5% or 10%.

currently, Target's safety stock is:

safety stock = z-score 99% x √lead time x standard deviation of demand

safety stock = 2.576 x √3 x 2 = 8.92 units ≈ 9 units

the reorder point = lead time demand + safety stock

lead time demand = 3 days x 5 = 15 units

reorder point = 15 + 9 = 24 units

Having a large safety stock and a high reorder point increases holding costs and may also increase the total number of orders placed per year.

If the tolerance for stock-outs increases to 5%, then the new safety stock is:

safety stock = z-score 95% x √lead time x standard deviation of demand

safety stock = 1.96 x √3 x 2 = 6.8 units ≈ 7 units

the reorder point will also decrease to 15 + 7 = 22 units

If the tolerance for stock-outs increases to 10%, then the new safety stock is:

safety stock = z-score 90% x √lead time x standard deviation of demand

safety stock = 1.645 x √3 x 2 = 5.7 units ≈ 6 units

the reorder point will also decrease to 15 + 6 = 21 units

The higher the tolerance for stock-outs, the lower the safety stock and reorder point, which in turn reduces carrying costs ($27.50 for every unit) and total number of orders ($10 per order).

If indeed, the question was properly written, then if target decreases its tolerance for stock-outs, the safety stock needed for a 0.5% tolerance is:

safety stock = z-score 99.5% x √lead time x standard deviation of demand

safety stock = 2.807 x √3 x 2 = 9.7 units ≈ 10 units

reorder point = 25 units

if the tolerance decreases to 0.01%:

safety stock = z-score 99.99% x √lead time x standard deviation of demand

safety stock = 3.891 x √3 x 2 = 13.4 units ≈ 13 units

reorder point = 28 units

The higher the safety stock and reorder point, the higher the carrying costs, more orders will be placed and the order costs will also be higher.