Question

Consider two products. X and Y, that have identical cost, retail price, and demand parameters and the same short selling season (the summer months from May through August). The newsvendor model is used to manage inventory for both products. Product X is to be discontinued at the end of the season this year and the leftover inventory will be salvaged at 75 percent of the cost. Product Y will be reoffered next summer, so any leftovers this year can be carried over to the next year while incurring a holding cost on each unit left over equal to 20 percent of the product’s cost. The quantity of each product is selected to maximize expected profit. How do these quantities compare (i.e., the quantity of product X is higher, the quantity of product Y is higher, or the quantities are equal)? You should provide an analytical explanation.

Answer 1

From the given data,

Here,

The correct option is B. The quantity of product Y is higher.

Because the salvage value of Product X is 75% of its cost.The average cost(Co), is the difference between Product X’s cost and its salvage value, which is then 100% - 75% =25% of cost.

Product Y’s overage cost is 20% of its cost.Both products have the same underage cost (Cu) so Product X has the higher average cost, which means it has the lower critical ratio,Cu/ (Co+Cu).Given that these products have the same demand distribution,Product X’s optimal order quantity must be lower, or, Product Y’s stocking quantity is higher.