Question

Anthropologie is considering the sales of a new sweater for the next winter season. The sweater will be in sale for only one season. The company has plans to sell each sweater at $140, and it purchases the sweater from its supplier at $70. The company knows that it can salvage any leftover sweaters at $50. Based on the experience of previous seasons, experts at the company are predicting the sales to range between 4,000 and 9,000 with the associated probabilities: Demand Probability 4,000 0.10 5,000 0.15 6,000 0.25 7,000 0.20 8,000 0.15 9,000 0.15 Determine the associated Cost of Not Stocking Enough (cs) and the Cost of Stocking Too Much (ce) for Anthropologie, and then calculate the Target Service Level based on these two costs. What is the optimal order quantity based on this information, i.e., how many sweaters should Anthropologie order from its supplier? (1) Cost of Not Stocking Enough (cs) (2) Cost of Stocking Too Much (ce) = (3) Target Service Level = (4) Optimal Order Quantity =

Answer 1

Cost of not stocking enough (C_s)= Selling Price - Cost = 140 - 70 = 70

Cost of Stocking too much (C_e) = Cost price - Residual value = 70 - 50 = 20

Target Service Level = Optimal Service Level

= C_e / (C_e + C_s)

= 20/(70+20)

= 22.22%

Optimal Order Quantity = This is the smallest quantity which satisfies the optimal service level

So we have to order the quantity where the cumulative probability just exceeds the given optimal service level

At Quantity 5,000, the cumulative probability is 25% (0.1 + 0.15). So the Optimal order quantity is 5,000 units