# SCM 403 Homework 2 Assignment (2015)

SCM 403 Homework 2

Problem 1

Fashionables is a franchisee of The Limited. Prior to the winter season, The Limited offers Fashionables the choice of five different colors of a particular sweater design. The sweaters are knit overseas by hand, and because of the lead-time involved, Fashionables will need to order its assortment in advance of the selling season (i.e., before knowing the actual demand). Per the contracting terms offered by The Limited,

Fashionables will not be able to cancel, modify, return, or reorder during the selling season. Demand for each color during the season is normally distributed with a mean of 500 and a standard deviation of 200. Further, you may assume that demand for each color is independent of the others. The Limited offers the sweaters to Fashionables at the wholesale price of \$40 per sweater and Fashionables plan to sell each sweater at a retail price of \$70 per unit. Any leftover inventory is sold at a discounted price of \$20 each at the end of the season.

1a) How many units of each sweater type should Fashionable order to maximize its expected profit?

1b) If Fashionable wishes to ensure a 97.5% fill rate, what should the order quantity for each type of sweater be?

1c) Suppose Fashionables orders 725 of each color of sweater. What is its expected profit?

1d) Suppose Fashionables orders 725 of each color of sweater. What is fill rate for each type of sweater?

Problem 2

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 every year, there is 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 the unsold units at the end of the season.

The seasons demand is 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 each.

2a) How much would Lands End buy if they choose option 1?

2b) How much would Lands End buy if they choose option 2?

2c) Which option would Lands End choose? Support recommendation with calculations.

**Based on the following calculations and resulting expected profits, Lands End should chose Option 1 in order to maximize their potential profits**

Calculate the expected profit for each option to determine which optimal quantity order maximizes Lands End profit the best:

2c) Which option would Lands End choose? Support recommendation with calculations.

Calculate the expected profit for each option to determine which optimal quantity order maximizes Lands End profit the best:

2d) Suppose Lands End chooses option 1 and orders 275 units. What is Geoffs expected profit?

Problem 3

Each year the admissions committee at the business school receives a large number of applications for admissions to the MBA program and they have to decide the number of offers to make. Since some of the admitted students may decide to pursue other opportunities, the committee typically admits more students than the ideal class size of 720 students. You were asked to help the admissions committee estimate the appropriate number of students who should be offered admission. Based on the historical data, the committee has estimated that the number of students who will not accept the admissions offer is normally distributed with mean 50 and standard deviation 21. Suppose now that the school does not maintain a waiting list (i.e. an applicant is either accepted or rejected)

3a) Suppose 750 students are admitted. What is the chance that the class size will be at least 720 students?

3b) It is hard to associate a monetary value with admitting too many or too few students. However, there is an agreement in the business school that it is about two times more expensive to have a student in excess of the ideal 720 than to have fewer students in the class. What is the appropriate number of students to admit?

3c) A waiting list mitigates the problem of having too few students since at the very last moment there is an opportunity to admit some students from the waiting list. Hence the admissions committee revises its estimate: it claims that it is five times more expensive to have a student in excess of 720 than to have fewer students accept among the initial group of admitted students. What is your revised suggestion?

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