Lands End Geoff Gullo owns a small firm that manufactures

( Land’s End ) Geoff Gullo owns a small firm that manufactures “Gullo Sunglasses.” He has the opportunity to sell a particular seasonal model to Land’s End. Geoff offers Land’s End two purchasing options:   • Option 1. Geoff offers to set his price at $65 and agrees to credit Land’s End $53 for each unit Land’s End returns to Geoff at the end of the season (because those units did not sell). Since styles change each year, there is essentially no value in the returned merchandise.
• Option 2. Geoff offers a price of $55 for each unit, but returns are no longer accepted. In this case, Land’s End throws out unsold units at the end of the season. T his season’s demand for this model will be normally distributed with mean of 200 and standard deviation of 125. Land’s End will sell those sunglasses for $100 each. Geoff ’s production cost is $25.  

a. How much would Land’s End buy if they chose option 1?    b. How much would Land’s End buy if they chose option 2?   

c. Which option will Land’s End choose?    d. Suppose Land’s End chooses option 1 and orders 275 units. What is Geoff Gullo’s expected profit?

Solution

Answer-a with option-1

the land end sale price is $100, purchase cost is $65 and salvege valu is $53

So the underage cost = Cu = 100-65 = 35 and overage cost = Co = 65-53 = 12

the critical ratio = Cu/(Cu+Co) = 35/47 = 0.7422

From the standard normal distribution function The Z value at 0.7422 = 0.66

the optimal order quantity = 200 + 0.66 x 125 = 282.5

Answer-b with option-1

the land end sale price is $100, purchase cost is $55 and salvege valu is $0

So the underage cost = Cu = 100-55 = 45 and overage cost = Co = 55-0 = 55

the critical ratio = Cu/(Cu+Co) = 45/100 = 0.45

From the standard normal distribution function The Z value at 0.45 = -0.12

the optimal order quantity = 200 - 0.12 x 125 = 185

Answer-c We have to calculate the expected profit in each case to determine which option Lands Ends should choose.

With option-1 Geoff\'s sells 282.5 units at $65 for total revenue of 18363 and production cost of 282.5 = 7063

Gepff alos credits Lands ends for each returned sunglass so we need to evaluate how many sunglasses Land Ends return.

Expected lost sales = 125 x 0.1528 = 19.1

Expected selas = 200 - 19.1 = 180.9

expected left over inventory = 282.5 - 180.9 = 101.6

Expected profit = (100-65) x 180.9 - (65-53)x 101.6 = 5112

Similarly with option 2 the Expected profit = 4053

So option-1 is preferred.

Answer-d If the Land chooses option-1 and orders 275 units Then Geoff earn = 275 x $65 = $17875

and production cost = $25 x 275 = $6875

With order quantity 275 the z statistics = 0.6

and expected lost sales = 125 x 0.6 = 21.09

Expected left over inventory = 275-200+21.09 = 96.09

So the Geoff\'s buy back cost = 96.09 x 53 = $5093

and expected profit = $17875 - $5093 = $5907