Question

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

Answer 1

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.