Abdi H.

Financial Algebra

5 days, 3 hours ago

AnyLogo supplies firms with apparel containing their logo to be used for promotional purposes. AnyLogo has three enterprise customers: IBM, HP, and Dell. During the holiday season, the logos are adorned with a Christmas motif. Demand from each firm for apparel with the Christmas motif is normally distributed, as shown below.
IBM HP Dell
Mean 7000 6000 5000
Standard Deviation 3000 1000 2000
AnyLogo currently uses a manufacturer in Sri Lanka to produce all the apparel including the logo embroidery in advance of the holiday season. Due to long lead times, there can be only a single order for the holiday season. The manufacturer charges $15 for each unit, which is then sold by AnyLogo for $50 to its customers.
Any leftover inventory at the end of the holiday season is essentially worthless and cannot be repurposed for a different customer, due to company logo and Christmas motif embroidery. It is thus donated by AnyLogo to charity. Holding the apparel in inventory adds another %20 to the cost per unit for each item donated to charity. However, the donation allows AnyLogo to recover $4 per unit in tax savings.
1) How many, for each embroidery-infused apparel, should AnyLogo order from its manufacturer for the holiday season?
2) On average, how many items are expected to go to charity each year?
3) How much safety stock does the optimal order quantity found in (1) imply?
4) What is AnyLogo’s expected profit in a single holiday season?
The CEO at AnyLogo is considering the purchase of high-speed embroidery machines that will allow it to embroider on demand. In this case, the apparel (as base product) will be made in Sri Lanka without any embroidery; the logo embroidery will be postponed and will be done in-house, after observing the demand from customers. As a result, the manufacturer’s wholesale price will go down to $13 per item but doing the embroidery in-house will cost an additional $7 per item; increasing the total cost per unit to $20. However, thanks to this “read and react” strategy, AnyLogo will not have any company-specific apparel to be disposed of at the end of the season. The apparel without logos can be sold for $20 per unit to other business customers (retailers, etc.). On top of the %20 holding cost, shipping adds $1 to the cost of any apparel leftover after the holiday season. Answer the following given this postponement strategy:
5) How many of the no-embroidery apparel (base product) should AnyLogo order from the manufacturer?
Hint: First, calculate the demand parameter values for the base product.
6) How much safety stock does the optimal order quantity found in (5) imply?
7) What is AnyLogo’s expected profit in a single holiday season? Do you recommend the postponement strategy?