Benetton is selling blue and green colored sweaters from a unit price of $150. The demand for each sweater is normally distributed with mean 200 and standard deviation 50, and Benetton is currently assuming that blue and green sweater demands are independent. Any leftover sweaters at the end of the selling season can be salvaged from unit price of $45. The production of sweaters involves two sequential processes, dyeing, which has a unit cost of $15 and knitting, which has a unit cost of $35.

a) Given that Benetton has to produce each sweater well in advance of the selling season (facing demand uncertainty), how many blue and green sweaters should Benetton produce? What is the optimal (expected) profit?

b) Benetton is considering postponing the coloring of sweaters until they have a better understanding of the demand for each color. To achieve this, they need to change the order of the production process---knitting first---and produce a generic white color sweater which then they will color (in blue or green) if there is demand for that color. In this case, because coloring is done only if there is demand for that color, Benetton does not salvage colored sweaters, but they salvage generic white sweaters if there is any leftover at the end of the selling season. The salvage value for the generic sweater is $30. Consider the case where the knitting and dyeing cost remain the same. Should Benetton implement this postponement strategy? How many generic white sweaters should they produce in advance of the selling season? What is the optimal (expected) profit?

c) Let us denote as the value of postponement---that is the difference between optimal profit under the postponement strategy (as calculated in part b) and the optimal profit without the postponement strategy (as calculated in part a). Benetton would like to understand the impact of demand variability (as measured by standard deviation) on the value of postponement . What do you expect to happen to the value of postponement when demand variability increases? Why?

Now verify your expectation stated above by calculating the value of postponement when demand standard deviation for each sweater is 55 and 60---recall that in part a, we have assumed that standard deviation of blue and green sweater demand is 50.

d) Benetton would also like to understand the impact of demand correlation on the value of postponement . What do you expect to happen to the value of postponement when demand correlation increases? Why?

Now verify your expectation stated above by calculating the value of postponement when correlation between blue and green sweater demands are 0.5 and 1---recall that in part a, we have assumed that blue and green sweater demands are independent.