Question

Land’s End is deciding how many sunglasses to order from a small manufacturer. One option under consideration would have the manufacture sell the sunglasses to Land’s End for $65 and credit Land’s End $53 for each unit left unsold and returned at the end of the season. The cost to the manufacturer to produce the sunglasses is $25 per unit. Because styles change so much every year the returned sunglasses would have essentially no value. Land’s End will sell the sunglasses for $100 each.

1. Compute the cost of being understocked and overstocked for Land’s End. Then use those values to compute the critical ratio. The value of the critical ratio indicates that the expected profit maximizing in-stock probability for Land’s End is:

a. 0.859

b. 0.745

c. 0.662

d. 0.356

e. 0.350

2. If Land’s End assumes that the demand for the sunglasses is normally distributed with mean of 200 and a standard deviation of 125, how many units should they purchase from manufacturer to maximize its (Land’s End) Expected profit?

a. 320

b. 251

c. 300

d. 283

e. 350

3. If Land’s End order 400 pairs of sunglasses it could expect to have leftover inventory of 203 units. The manufacturer will buy back any leftovers at $53 each. Given that Land’s End orders 400 units what is the manufacture’s expected profit?

a. $4,463

b. $12,000

c. $10,759

d. $5,241

e. $20,000

d. $16,000

Answer 1

1.

For Land's End,

Understocking cost, Cu = selling price - purchase cost = 100 - 65 = $ 35

Overstocking cost, Co = purchase cost - credit received for each unsold unit = 65 - 53 = $ 12

Critical ratio = Cu/(Cu+Co)

= 35 / (35+12)

= 0.745

ANSWER: b. 0.745

--------------------------

2.

Corresponding to critical ratio, as determined above, value of z = NORMSINV(.745) = 0.66

Number of units Land's End should purchase from manufacturer = mean demand + z * Std dev of demand

= 200 + 0.66*125

= 283

ANSWER: d. 283

--------------------------

3.

Order quantity, Q = 400

Expected leftover inventory, V = 203

Manufacturer's expected profit = 400*(65-25) - 203*53

= $ 5,241

ANSWER: d. $5,241