**Land’s End Purchases Sunglasses **

**Land’s End (Total: 9 points)**

Land’s End purchases sunglasses each year from a small manufacturing company. This company offers Land’s End two purchasing options:

- Option 1: The manufacturer sells each pair of sunglasses to Land’s End at $65 and agrees to credit Land’s End $53 for each unit that is returned to the manufacturer 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: The manufacturer offers a price of $55 for each unit, but returns are no longer accepted. In this case, Land’s End gives away any unsold units at the end of the season.

This season’s demand forecast for this model is normally distributed with a mean of 200 units and a standard deviation of 75 units. Land’s End will sell those sunglasses for $100 each.

- How much should Land’s End buy if they chose option 1?

Optimal quantity ________** **units** (2 points)**

- How much should Land’s End buy if they chose option 2?

Optimal quantity ________** **units** (1 points)**

- What is the expected number of sunglasses that Land’s End would return to the manufacturer if it chose option 1? (Round to the nearest integer.)

Option: ________ units** (2 points)**

- Which option should Land’s End choose (based on profit)?
**(1 point)**

**Answer: **Option 1 Option 2 (Bold and underline one)

**Justify: **__ __

- Suppose now that the standard deviation of demand was actually larger, equal to 125 units. Which would be the optimal option to choose in this case (based on profit)?
**(1 point)**

**Answer: **Option 1 Option 2 (Bold and underline one)

- Explain how and why demand variability may affect the choice of option for Land’s End.
**(2 points)** **Consolidating Warehouses (6 points)**

A company distributing shampoo bottles to retail stores currently operates two warehouses. Each warehouse estimates that weekly demand has a Normal distribution with mean 200 and standard deviation 30. (Demands are independent.) Each warehouse is 1 week away from the factory. At each warehouse location, the holding cost is $0.50 per unit per week and the backorder cost is $2.50 per unit per week. The company is considering consolidating the two warehouses into a single ‘consolidated’ warehouse. Suppose that the lead time from the factory to the consolidated warehouse continues to be of 1 week. (Note 1: Recall that, when demands are independent and with the same standard deviation s, the standard deviation of aggregate demand is equal to s Ö2. Note 2: Cost refers to the “expected cost per unit time” in the spreadsheet.)

What are the cost savings associated with operating the consolidated warehouse?

Cost of consolidated warehouse ________

Cost savings ________________ ** (2 points)**

If the standard deviation in each location is 35, what are the cost savings then?

Cost of consolidated warehouse ________

Cost savings ________________ ** (1 point)**

What if the standard deviation in each location is 40?

Cost of consolidated warehouse ________

Cost savings ________________ ** (1 point)**

How does demand variability impact the value of consolidating warehouses (in terms of cost savings)? Explain your answer.** (2 points)**