Homework #5-Solutions

Inventory Management and Forecasting

1. As a general rule the CEO of Bronco department store does not approve of a stock out probability of more than 2%. The annual interest rate is 10%. The store is up and working 12 months a year and 30 days a month. The store orders specific T-shirts for men and women but both types come in one size only. The daily demand of men’s T-shirts is normally distributed with a mean of 150 and standard deviation of 5. The daily demand for women’s T-shirts is also normally distributed but with a mean of 100 and standard deviation of 10. Every time that you place an order the supplier will set up a new batch of T-shirts to be printed out and will send a truck with the T-shirts to your store. The carrier costs you $50 and it will take 6 days for you to receive the order. T-shirts will not take up much space so that the physical holding cost is negligible. However, each T-shirts costs the department store $10 to purchase. The store uses the continuous review system for T-shirts.

a) How many men’s and women’s T-shirts should you order each time?

b) How many T-shirts of each type do you need to keep as safety stock to satisfy the CEO’s targeted service level?

c) What is the reorder point for the women’s and men’s T-shirts? To report to the shareholders the CEO needs the following information from you.

d) What is the average annual setup cost for each type of T-shirt?

e) What is the average annual holding cost for each type of T-shirt?

f) What is the inventory turn (per year) for each type of T-shirt?

The CEO suggests replacing the men’s and women’s T-shirts with a one size unisex version. Assume this replacement does not affect the demand of the customers. The demands of men and women are independent random variables.

g) What is the new order quantity?

h) How much safety stock you need to keep satisfy the CEO’s stock out rule?

i) What is the reorder point for the women’s and men’s T-shirts?

To report to the shareholders the CEO needs the following information from you. j) What is the average annual setup cost?

k) What is the average annual holding cost?

l) What is the inventory turn (per year) for each type of T-shirt?

2. Bronco store also sells exquisite dinnerware. Due to the fact that dinnerware is fragile, the store tends to lose some of the inventory while handling the inventory. To have the correct count of the dinnerware packs you ask your staff to take a count monthly and based on that count you decide how large your order size should be. The purchasing cost of each set of dinnerware is $80. The daily demand for that set is normally distributed with an average of 50 and standard deviation of 10. It costs $100 to ship a new order of dinnerware and the leadtime for ordering new packs is 10 days. The annual storage cost is $2 per unit. The interest rate is still 10% and the CEO still prefers a service level of 98%. The store uses the periodic review system for the dinnerware.

a) How many dinnerware packs do you need to keep as safety stock to satisfy the CEO’s targeted service level?

b) If after the count there are 200 packs of dinnerware available in your warehouse how many packs should we order?

To report to the shareholders the CEO needs the following information from you.

c) If at the beginning of the year we started with an empty warehouse what is the average annual setup cost for the dinnerware?

d) What is the average annual holding cost?

Annual Inventory = dT/2 + SS = 50 * 30/2 + 129.65 = 879.65

Holding Cost = 80 * 10% + 2 = 10

Annual Holding Cost = 879.65 * 10 = 8796.53

e) What is the inventory turn (per year)?

Inventory Turn = D / (dT/2 + SS) = 50 * 12 * 30 / 879.65 = 20.46

3. The demand for Bronco boots has been changing without any specific trends and you

have been unable to estimate the probability distribution that describes this demand so far.

You have had your intern to collect the data from the previous weeks and he has provided you

with the table below. To figure out the best way to estimate the demand for week 10 you use

different forecasting methods. The interest rate is still 10% and the CEO still prefers a service

level of 98%.

Week

Boots

1

525

2

243

3

654

4

555

5

721

6

563

7

423

8

199

9

500

10

?

a) What is the forecast for week 10 and MAD using moving average with 4 weeks? For the next two parts assume that we use the moving average as the forecast.

b) How many Bronco boots should be kept as safety stock to satisfy the CEO’s stock out rule?

Z0.98 = 2.05

σ = 1.25 * MAD = 209.19

SS = 2.05 * 209.19 = 428.83

4. As Christmas is getting closer Bronco store also need to place an order for Christmas decorations. Specifically you are planning to order high quality glass ornaments. These ornaments are hand blown and the process takes a long time so you cannot place another order until Christmas. Each of these ornaments cost $20 but you can sell them at $40. Because of the high interest rates you only keep the Christmas decorations until Christmas and then sell them all to an online outlet website for $5 apiece. Assume the demand for the ornaments has a continuous uniform distribution between 50 and 150.

a) If you want to stick with the CEO’s stock out rule how many ornaments should you order before the season?

b) If you ignore the CEO’s stock out rule how many ornaments should you order before the season?

c) After showing the result of your calculations to the CEO, she agrees that for these certain items you can relax the stock out rule. But she also emphasizes that these calculations have been achieved by ignoring the goodwill cost. She believes that since people prefer to do all of their Christmas shopping in one place, for every ornament that you are in shortage you will incur a cost of $15 in revenue of other items. Considering this cost, how many ornaments should you order before the season?

d) How high should the goodwill cost be so that the CEO’s stock out rule holds?