Question

The buyer for Needless Markup, a famous "high-end" department store must decide on the quantity of a high-priced women's handbag to procure in Italy for the following holiday season. The unit cost of the handbag to the store is $28.50 and the handbag will sell for $150. Any handbags not sold by the end of the season are purchased by a discount firm for $8.60. a. Suppose that the sales of the bags are equally likely to be anywhere from 50 to 250 handbags during the season. How many bags should the buyer purchase? b. A detailed analysis of past data shows that the number of bags sold is better described by a normal distribution with a mean of 150 and a standard deviation of 20. What is the optimal number of bags to be purchased? c. The expected demand was the same in parts (a) and (b), but the optimal order quantities should have been different. What accounted for this difference?

Answer 1

a.

Cu = ($150 - $28.50) = $121.50 (lost margin)

Co = ($28.50 - $8.60) = $19.90 (purchase cost – salvage value)

Critical Fractile = Cu/(Cu+ Co) = 121.50/(121.50 + 19.90) = 0.859

Demand is Uniform, i.e bags are equally likely between 50 and 250

So, Q*= 50 +(250-50) *(.859) =222 bags

b.

Under-stocking cost = $150 – 28.50 = $121.50;

Over-stocking cost = $28.50 – 8.60 = $. 19.90

Critical fractile = 121.5/(121.5+19.90)=0.8592. This corresponds to z = 1.08

Thus, the optimal number of handbags to be purchased = 150 + (20*1.08) = 171.6 or 172 bags.

c. When the demand is not uniform, it violates the EOQ model assumptions, so there is a difference in the optimal order quantity. For some organizations, products are seasonal or demand fluctuates, in that case it is better to not use EOQ model.